Epi/0000755000176200001440000000000014016527043010771 5ustar liggesusersEpi/NAMESPACE0000644000176200001440000001343314016520006012204 0ustar liggesusersuseDynLib(Epi, .registration=TRUE) export( as.Date.cal.yr, apc.frame, apc.fit, apc.plot, apc.lines, plot.apc, lines.apc, pc.points, pc.lines, pc.matpoints, pc.matlines, pc.matshade, cp.points, cp.lines, cp.matpoints, cp.matlines, cp.matshade, cal.yr, as.Date.cal.yr, ccwc, ci.pd, ci.lin, ci.exp, ci.cum, ci.surv, ci.pred, ci.ratio, ci.mat, ci.Crisk, sim2ci.Crisk, sim2ci.Srisk, sim2ci.Stime, matshade, lls, clear, contr.orth, contr.2nd, contr.cum, contr.diff, detrend, decurve, dur, erl, surv1, surv2, erl1, yll, effx, effx.match, float, print.floated, gen.exp, mat2pol, Icens, print.Icens, plotevent, fit.add, fit.mult, ftrend, fgrep, ngrep, lgrep, plotCIF, stackedCIF, show.apc.LCa, apc.LCa, LCa.fit, print.LCa, summary.LCa, predict.LCa, plot.LCa, Lexis.diagram, Lexis.lines, Life.lines, list.lex, Lexis, merge.Lexis, plot.Lexis, points.Lexis, lines.Lexis, PY.ann.Lexis, subset.Lexis, "[.Lexis", cbind.Lexis, rbind.Lexis, order.Lexis, orderLexis, sortLexis, summary.Lexis, print.summary.Lexis, splitLexis, transform.Lexis, levels.Lexis, nid.Lexis, bootLexis, Relevel.Lexis, factorize.Lexis, cutLexis, mcutLexis, rcutLexis, countLexis, stack.Lexis, tmat.Lexis, boxes.Lexis, boxes.matrix, boxes.MS, msdata.Lexis, etm.Lexis, crr.Lexis, glm.Lexis, gam.Lexis, coxph.Lexis, simLexis, addCov.Lexis, addDrug.Lexis, subset.stacked.Lexis, transform.stacked.Lexis, plot.pState, lines.pState, entry, exit, status, timeBand, timeScales, timeSince, tsNA20, breaks, absorbing, transient, preceding, before, succeeding, after, tbox, dbox, fillarr, boxarr, boxes, factorize, rm.tr, PY.ann, N2Y, tmat, nState, pState, msdata, mh, ncut, nice, NArray, ZArray, Ns, Termplot, pctab, plotEst, pointsEst, projection.ip, in.span, inSpan, id.span, idSpan, thinCol, linesEst, rateplot, Aplot, Pplot, Cplot, nid, Relevel, Relevel.factor, ROC, twoby2, Wald, stat.table, clogistic, poisreg, harm) # Import generic methods importFrom( utils, stack ) # importFrom( base, cbind, rbind ) importFrom( splines, ns, bs ) importFrom( plyr, rbind.fill ) importFrom( purrr, '%>%' ) importFrom( dplyr, summarize, group_by, arrange, left_join, select, rename, mutate, ungroup, filter) importFrom( cmprsk, crr) importFrom( etm, etm ) # importFrom( mstate, msdata ) importFrom( MASS, mvrnorm, ginv ) importFrom( survival, clogit, coxph, Surv ) importFrom( mgcv, gam ) importFrom( numDeriv, hessian ) importFrom( Matrix, nearPD ) importFrom( zoo, na.locf ) importFrom("grDevices", "gray", "rainbow", "adjustcolor", "dev.cur") importFrom("graphics", "abline", "arrows", "axis", "box", "layout", "lines", "locator", "matlines", "matplot", "matpoints", "mtext", "par", "plot", "plot.new", "plot.window", "points", "polygon", "rect", "rug", "segments", "strheight", "strwidth", "text") importFrom("stats", ".getXlevels", "addmargins", "anova", "approx", "ave", "as.formula", "binomial", "coef", "complete.cases", "contr.sum", "dpois", "fisher.test", "fitted", "formula", "gaussian", "glm", "is.empty.model", "lm", "make.link", "median", "model.extract", "model.matrix", "model.offset", "model.response", "nlm", "pchisq", "pnorm", "poisson", "predict", "predict.lm", "qnorm", "qt", "quantile", "rpois", "runif", "termplot", "update", "vcov", "weighted.mean", "xtabs") importFrom("utils", "flush.console", "str") # register S3 methods S3method( print, Icens) S3method( print, floated) S3method( plot, apc) S3method( lines, apc) S3method( plot, Lexis) S3method( plot, pState) S3method( lines, pState) S3method( points, Lexis) S3method( lines, Lexis) S3method( PY.ann, Lexis) S3method( merge, Lexis) S3method( subset, Lexis) S3method( subset, stacked.Lexis) S3method( "[", Lexis) S3method( cbind, Lexis) S3method( rbind, Lexis) S3method( summary, Lexis) S3method( print, summary.Lexis) S3method( transform, Lexis) S3method( transform, stacked.Lexis) S3method( levels, Lexis) S3method( nid, Lexis) S3method( nid, default) S3method( Relevel, Lexis) S3method( Relevel, factor) S3method( Relevel, default) S3method( factorize, Lexis) S3method( addCov, Lexis) S3method( addDrug, Lexis) S3method( stack, Lexis) S3method( tmat, Lexis) S3method( boxes, Lexis) S3method( boxes, matrix) S3method( boxes, MS) S3method( msdata, Lexis) S3method( etm, Lexis) S3method( glm, Lexis) S3method( gam, Lexis) S3method( coxph, Lexis) S3method( print, LCa) S3method( summary, LCa) S3method( predict, LCa) S3method( plot, LCa) S3method( print, stat.table) S3method( print, clogistic) S3method( coef, clogistic) S3method( vcov, clogistic) S3method( as.Date, cal.yr) Epi/data/0000755000176200001440000000000013763140361011704 5ustar liggesusersEpi/data/blcaIT.rda0000644000176200001440000000137512531361106013532 0ustar liggesusersKHTQ̔,LEQؘs㈘wYfj9430r).EDAIHHAAI}07e990UE! 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The latter is the unique values of test or linear predictor from the logistic regression in ascending order with -Inf prepended. Since the sensitivity is defined as \eqn{P(test>x)|status=TRUE}, the first row has \code{sens} equal to 1 and \code{spec} equal to 0, corresponding to drawing the ROC curve from the upper right to the lower left corner.} \item{lr}{glm object with the logistic regression result used for construction of the ROC curve} 0, 1 or 2 plots are produced according to the setting of \code{plot}. } \author{Bendix Carstensen, Steno Diabetes Center \& University of Copenhagen, \url{http://bendixcarstensen.com} } \examples{ x <- rnorm( 100 ) z <- rnorm( 100 ) w <- rnorm( 100 ) tigol <- function( x ) 1 - ( 1 + exp( x ) )^(-1) y <- rbinom( 100, 1, tigol( 0.3 + 3*x + 5*z + 7*w ) ) ROC( form = y ~ x + z, plot="ROC" ) } \keyword{manip} \keyword{htest} %\keyword{ROC-curves} %\keyword{sensitivity} %\keyword{specificity} %\keyword{predictive values} Epi/man/splitLexis.Rd0000644000176200001440000000673313751040403014177 0ustar liggesusers\name{splitLexis} \alias{splitLexis} \title{Split follow-up time in a Lexis object} \description{ The \code{splitLexis} function divides each row of a \code{Lexis} object into disjoint follow-up intervals according to the supplied break points. } \usage{ splitLexis(lex, breaks, time.scale, tol=.Machine$double.eps^0.5) } \arguments{ \item{lex}{an object of class \code{Lexis}} \item{breaks}{a vector of break points} \item{time.scale}{the name or number of the time scale to be split} \item{tol}{numeric value >= 0. Intervals shorter than this value are dropped} } \value{ An object of class \code{Lexis} with multiple rows for each row of the argument \code{lex}. Each row of the new \code{Lexis} object contains the part of the follow-up interval that falls inside one of the time bands defined by the break points. The variables representing the various time scales, are appropriately updated in the new \code{Lexis} object. The entry and exit status variables are also updated according to the rule that the entry status is retained until the end of follow-up. All other variables are considered to represent variables that are constant in time, and so are replicated across all rows having the same id value. } \note{ The \code{splitLexis()} function divides follow-up time into intervals using breakpoints that are common to all rows of the \code{Lexis} object. To split a \code{Lexis} object by break points that are unique to each row, use the \code{cut.Lexis} function. } \author{Martyn Plummer} \examples{ # A small bogus cohort xcoh <- structure( list( id = c("A", "B", "C"), birth = c("14/07/1952", "01/04/1954", "10/06/1987"), entry = c("04/08/1965", "08/09/1972", "23/12/1991"), exit = c("27/06/1997", "23/05/1995", "24/07/1998"), fail = c(1, 0, 1) ), .Names = c("id", "birth", "entry", "exit", "fail"), row.names = c("1", "2", "3"), class = "data.frame" ) # Convert the character dates into numerical variables (fractional years) xcoh$bt <- cal.yr( xcoh$birth, format="\%d/\%m/\%Y" ) xcoh$en <- cal.yr( xcoh$entry, format="\%d/\%m/\%Y" ) xcoh$ex <- cal.yr( xcoh$exit , format="\%d/\%m/\%Y" ) # See how it looks xcoh # Define as Lexis object with timescales calendar time and age Lcoh <- Lexis( entry = list( per=en ), exit = list( per=ex, age=ex-bt ), exit.status = fail, data = xcoh ) # Default plot of follow-up plot( Lcoh ) # With a grid and deaths as endpoints plot( Lcoh, grid=0:10*10, col="black" ) points( Lcoh, pch=c(NA,16)[Lcoh$lex.Xst+1] ) # With a lot of bells and whistles: plot( Lcoh, grid=0:20*5, col="black", xaxs="i", yaxs="i", xlim=c(1960,2010), ylim=c(0,50), lwd=3, las=1 ) points( Lcoh, pch=c(NA,16)[Lcoh$lex.Xst+1], col="red", cex=1.5 ) # Split time along two time-axes ( x2 <- splitLexis( Lcoh, breaks = seq(1900,2000,5), time.scale="per") ) ( x2 <- splitLexis( x2, breaks = seq(0,80,5), time.scale="age" ) ) str( x2 ) # Tabulate the cases and the person-years summary( x2 ) tapply( status(x2,"exit")==1, list( timeBand(x2,"age","left"), timeBand(x2,"per","left") ), sum ) tapply( dur(x2), list( timeBand(x2,"age","left"), timeBand(x2,"per","left") ), sum ) } \seealso{ \code{\link{timeBand}}, \code{\link{cutLexis}}, \code{\link{mcutLexis}}, \code{\link{summary.Lexis}}} \keyword{manip} Epi/man/transform.Lexis.Rd0000644000176200001440000000777114004310647015142 0ustar liggesusers\name{transform.Lexis} \alias{transform.Lexis} \alias{Relevel.Lexis} \alias{transform.stacked.Lexis} \alias{factorize} \alias{factorize.Lexis} \alias{levels.Lexis} \alias{order.Lexis} \alias{orderLexis} \alias{sortLexis} \title{Transform a Lexis (or stacked.Lexis) object} \description{ Modify a Lexis object. } \usage{ \method{factorize}{Lexis}(x, ...) \method{Relevel}{Lexis}(x, ref, \dots) \method{levels}{Lexis}(x) \method{transform}{Lexis}(`_data`, \dots) \method{transform}{stacked.Lexis}(`_data`, \dots) order.Lexis(x) orderLexis(x) sortLexis(x) } \arguments{ \item{_data}{an object of class \code{Lexis}.} \item{x}{an object of class \code{Lexis}.} \item{ref}{New names (or order) of the factor levels (states) for \code{lex.Cst} and \code{lex.Xst}. Can be a list, in which case some levels are collapsed, see the documentation for \code{\link{Relevel}}. No sanity check for the latter type of operation is undertaken.} \item{\dots}{Additional arguments to be passed to \code{\link{transform.data.frame}}, \code{\link{Relevel.factor}}.} % \code{order} or \code{sort}.} } \details{ The transform method for \code{Lexis} objects works exactly as the method for data frames, but keeps the \code{Lexis} attributes. \code{factorize} transforms the variables \code{lex.Cst} and \code{lex.Xst} to factors with identical sets of levels. \code{Relevel} does the same as \code{\link{Relevel.factor}}, but for both the factors \code{lex.Cst} and \code{lex.Xst} in \code{x}. \code{lex.Cst} and \code{lex.Xst} must be factors with the same levels. They can be made so by \code{factorize}. If \code{ref} is an integer or character vector, the levels of \code{lex.Cst} and \code{lex.Xst} are permuted to match the order of \code{ref}. If \code{ref} is \code{NULL}, as when for example the argument is not passed to the function, the returned object have levels of \code{lex.Cst}, \code{lex.Xst} (and for \code{stacked.Lexis} objects \code{lex.Tr}) shaved down to the actually occurring values; that is, empty levels are discarded. \code{order.Lexis} returns the order of the rows in a Lexis object to sort it by ()\code{lex.id},\code{ts}), where \code{ts} is a timescale in the Lexis object with no \code{NA}s. \code{orderLexis} is just a synonym. \code{sortLexis} returns the Lexis object sorted by (\code{lex.id}, \code{ts}) where \code{ts} is one of the \code{\link{timeScales}} with no \code{NA}s. } \value{ A transformed \code{Lexis} object. The function \code{levels} returns the names of the states (levels of the factors \code{lex.Cst} and \code{lex.Xst}. } \author{Martyn Plummer, Bendix Carstensen} \seealso{\code{\link{Lexis}}, \code{\link{merge.Lexis}}, \code{\link{subset.Lexis}}, \code{\link{subset.stacked.Lexis}}, \code{\link{Relevel}}, \code{\link{transient}}, \code{\link{absorbing}}} \examples{ data( nickel ) nic <- Lexis( data = nickel, id = id, entry = list(age = agein), exit = list(age = ageout, cal = ageout+dob, tfh = ageout-age1st), # Lung cancer deaths end as 2 and other deaths as 1 exit.status = factor((icd > 0) + (icd \%in\% c(162,163)), labels = c("Alive","Dead","Lung") ) ) str( nic ) levels( nic ) nit <- transform( nic, cumex = exposure * (agein - age1st) ) str( nit ) # It is still a Lexis object! summary(nic) # change order of levels nix <- Relevel(nic, c("Alive", "Lung", "Dead")) summary(nix) # change names of levels niw <- Relevel(nix, list("Alive" = 1, "Pulm" = "Lung", "Mort" = "Dead")) summary(niw) boxes(niw, boxpos = TRUE) # combine levels niz <- Relevel(niw, list("Alive", c("Pulm", "Mort")), coll=" \n& ") summary(niz) par( new = TRUE ) boxes(niz, boxpos = TRUE) #stack Lexis object siw <- stack(niw) str(siw) } \keyword{manip} Epi/man/lungDK.Rd0000644000176200001440000000361413751040403013216 0ustar liggesusers\name{lungDK} \alias{lungDK} \docType{data} \title{Male lung cancer incidence in Denmark} \description{ Male lung cancer cases and population riks time in Denmark, for the period 1943--1992 in ages 40--89. } \usage{data(lungDK)} \format{ A data frame with 220 observations on the following 9 variables. \tabular{rl}{ \code{A5}: \tab Left end point of the age interval, a numeric vector. \cr \code{P5}: \tab Left enpoint of the period interval, a numeric vector. \cr \code{C5}: \tab Left enpoint of the birth cohort interval, a numeric vector. \cr \code{up}: \tab Indicator of upper trianges of each age by period rectangle in the Lexis diagram. (\code{up=(P5-A5-C5)/5}). \cr \code{Ax}: \tab The mean age of diagnois (at risk) in the triangle. \cr \code{Px}: \tab The mean date of diagnosis (at risk) in the triangle. \cr \code{Cx}: \tab The mean date of birth in the triangle, a numeric vector. \cr \code{D}: \tab Number of diagnosed cases of male lung cancer. \cr \code{Y}: \tab Risk time in the male population, person-years. \cr } } \details{ Cases and person-years are tabulated by age and date of diagnosis (period) as well as date of birth (cohort) in 5-year classes. Each observation in the dataframe correponds to a triangle in a Lexis diagram. Triangles are classified by age and date of diagnosis, period of diagnosis and date of birth, all in 5-year groupings. } \source{The Danish Cancer Registry and Statistics Denmark. } \references{ For a more thorough exposition of statistical inference in the Lexis diagram, see: B. Carstensen: Age-Period-Cohort models for the Lexis diagram. Statistics in Medicine, 26: 3018-3045, 2007. } \examples{ data( lungDK ) # Draw a Lexis diagram and show the number of cases in it. attach( lungDK ) Lexis.diagram( age=c(40,90), date=c(1943,1993), coh.grid=TRUE ) text( Px, Ax, paste( D ), cex=0.7 ) } \keyword{datasets} Epi/man/lgrep.Rd0000644000176200001440000000221013751040403013132 0ustar liggesusers\name{lgrep} \alias{fgrep} \alias{ngrep} \alias{lgrep} \title{ Convenience versions of grep } \description{ Often you want the elements of a vector (or its names or levels) that meet a certain pattern. But \code{grep} only gives you the position, so these functions are designed to give you that. } \usage{ fgrep( pattern, x, ... ) ngrep( pattern, x, ... ) lgrep( pattern, x, ... ) } \arguments{ \item{pattern}{Pattern searched for.} \item{x}{Object where \code{pattern} is searched. Or in whose \code{names} or \code{levels} attributes \code{pattern} is sought.} \item{...}{Arguments passed on to \code{\link[base]{grep}}.} } \value{Elements of the input \code{x} (\code{fgrep}) or its names attribute (\code{ngrep}) or levels attribute (\code{lgrep}). } \author{Bendix Carstensen, \email{b@bxc.dk}, \url{http://bendixcarstensen.com} } \seealso{\code{\link{grep}}} \examples{ ff <- factor( ll <- paste( sample( letters[1:3], 20, replace=TRUE ), sample( letters[1:3], 20, replace=TRUE ), sep="" ) ) ff fgrep( "a", ff ) fgrep( "a", ll ) ngrep( "a", ff ) lgrep( "a", ff ) lgrep( "a", ff, invert=TRUE ) } \keyword{ manip } Epi/man/Ns.Rd0000644000176200001440000001453613751040403012417 0ustar liggesusers\name{Ns} \alias{Ns} \title{ Natural splines - (cubic splines linear beyond outermost knots) with convenient specification of knots and possibility of centering, detrending and clamping. } \description{ This function is partly for convenient specification of natural splines in practical modeling. The convention used is to take the smallest and the largest of the supplied knots as boundary knots. It also has the option of centering the effects provided at a chosen reference point as well as projecting the columns on the orthogonal space to that spanned by the intercept and the linear effect of the variable, and finally fixing slopes beyond boundary knots (clamping). } \usage{ Ns( x, ref = NULL, df = NULL, knots = NULL, intercept = FALSE, Boundary.knots = NULL, fixsl = c(FALSE,FALSE), detrend = FALSE ) } \arguments{ \item{x}{A variable.} \item{ref}{Scalar. Reference point on the \code{x}-scale, where the resulting effect will be 0.} \item{df}{degrees of freedom.} \item{knots}{knots to be used both as boundary and internal knots. If \code{Boundary.knots} are given, this will be taken as the set of internal knots.} \item{intercept}{Should the intercept be included in the resulting basis? Ignored if any of \code{ref} or \code{detrend} is given.} \item{Boundary.knots}{The boundary knots beyond which the spline is linear. Defaults to the minimum and maximum of \code{knots}.} \item{fixsl}{Specification of whether slopes beyond outer knots should be fixed to 0. \code{FALSE} correponds to no restriction; a curve with 0 slope beyond the upper knot is obtained using \code{c(FALSE,TRUE)}. Ignored if \code{!(detrend==FALSE)}.} \item{detrend}{If \code{TRUE}, the columns of the spline basis will be projected to the orthogonal of \code{cbind(1,x)}. Optionally \code{detrend} can be given as a vector of non-negative numbers og length \code{length(x)}, used to define an inner product as \code{diag(detrend)} for projection on the orthogonal to \code{cbind(1,x)}. The default is projection w.r.t. the inner product defined by the identity matrix.} } \value{ A matrix of dimension c(length(x),df) where either \code{df} was supplied or if \code{knots} were supplied, \code{df = length(knots) - 1 + intercept}. \code{Ns} returns a spline basis which is centered at \code{ref}. \code{Ns} with the argument \code{detrend=TRUE} returns a spline basis which is orthogonal to \code{cbind(1,x)} with respect to the inner product defined by the positive definite matrix \code{diag(detrend)} (an assumption which is checked). Note the latter is data dependent and therefore making predictions with a \code{newdata} argument will be senseless. } \author{ Bendix Carstensen \email{b@bxc.dk}, Lars Jorge D\'iaz, Steno Diabetes Center Copenhagen. } \note{ The need for this function is primarily from analysis of rates in epidemiology and demography, where the dataset are time-split records of follow-up, and the range of data therefore rarely is of any interest (let alone meaningful). In Poisson modeling of rates based on time-split records one should aim at having the same number of \emph{events} between knots, rather than the same number of observations. } \examples{ require(splines) require(stats) require(graphics) ns( women$height, df = 3) Ns( women$height, knots=c(63,59,71,67) ) # Gives the same results as ns: summary( lm(weight ~ ns(height, df = 3), data = women) ) summary( lm(weight ~ Ns(height, df = 3), data = women) ) # Get the diabetes data and set up as Lexis object data(DMlate) DMlate <- DMlate[sample(1:nrow(DMlate),500),] dml <- Lexis( entry = list(Per=dodm, Age=dodm-dobth, DMdur=0 ), exit = list(Per=dox), exit.status = factor(!is.na(dodth),labels=c("DM","Dead")), data = DMlate ) # Split follow-up in 1-year age intervals dms <- splitLexis( dml, time.scale="Age", breaks=0:100 ) summary( dms ) # Model age-specific rates using Ns with 6 knots # and period-specific RRs around 2000 with 4 knots # with the same number of deaths between each pair of knots n.kn <- 6 ( a.kn <- with( subset(dms,lex.Xst=="Dead"), quantile( Age+lex.dur, probs=(1:n.kn-0.5)/n.kn ) ) ) n.kn <- 4 ( p.kn <- with( subset( dms, lex.Xst=="Dead" ), quantile( Per+lex.dur, probs=(1:n.kn-0.5)/n.kn ) ) ) m1 <- glm( lex.Xst=="Dead" ~ Ns( Age, kn=a.kn ) + Ns( Per, kn=p.kn, ref=2000 ), offset = log( lex.dur ), family = poisson, data = dms ) # Plot estimated age-mortality curve for the year 2005 and knots chosen: nd <- data.frame( Age=seq(40,100,0.1), Per=2005, lex.dur=1000 ) par( mfrow=c(1,2) ) matplot( nd$Age, ci.pred( m1, newdata=nd ), type="l", lwd=c(3,1,1), lty=1, col="black", log="y", ylab="Mortality rates per 1000 PY", xlab="Age (years)", las=1, ylim=c(1,1000) ) rug( a.kn, lwd=2 ) # Clamped Age effect to the right of rightmost knot. m1.c <- glm( lex.Xst=="Dead" ~ Ns( Age, kn=a.kn, fixsl=c(FALSE,TRUE) ) + Ns( Per, kn=p.kn, ref=2000 ), offset = log( lex.dur ), family = poisson, data = dms ) # Plot estimated age-mortality curve for the year 2005 and knots chosen. matplot( nd$Age, ci.pred( m1.c, newdata=nd ), type="l", lwd=c(3,1,1), lty=1, col="black", log="y", ylab="Mortality rates per 1000 PY", xlab="Age (years)", las=1, ylim=c(1,1000) ) rug( a.kn, lwd=2 ) par( mfrow=c(1,1) ) # Including a linear Age effect of 0.05 to the right of rightmost knot. m1.l <- glm( lex.Xst=="Dead" ~ Ns( Age, kn=a.kn, fixsl=c(FALSE,TRUE) ) + Ns( Per, kn=p.kn, ref=2000 ), offset = log( lex.dur ) + pmax( Age, max( a.kn ) ) * 0.05, family = poisson, data = dms ) # Plot estimated age-mortality curve for the year 2005 and knots chosen. nd <- data.frame(Age=40:100,Per=2005,lex.dur=1000) matplot( nd$Age, ci.pred( m1.l, newdata=nd ), type="l", lwd=c(3,1,1), lty=1, col="black", log="y", ylab="Mortality rates per 1000 PY", xlab="Age (years)", las=1, ylim=c(1,1000) ) rug( a.kn, lwd=2 ) } \keyword{regression} Epi/man/Lexis.Rd0000644000176200001440000001703613751040403013121 0ustar liggesusers\name{Lexis} \alias{Lexis} \title{Create a Lexis object} \description{ Create an object of class \code{Lexis} to represent follow-up in multiple states on multiple time scales. } \usage{ Lexis( entry, exit, duration, entry.status = 0, exit.status = 0, id, data, merge=TRUE, states, notes=TRUE, tol=.Machine$double.eps^0.5, keep.dropped=FALSE ) } \arguments{ \item{entry}{a named list of entry times. Each element of the list is a numeric variable representing the entry time on the named time scale. All time scales must have the same units (e.g. years). The names of the timescales must be different from any column name in \code{data}.} \item{exit}{a named list of exit times.} \item{duration}{a numeric vector giving the duration of follow-up.} \item{entry.status}{a vector or a factor giving the status at entry} \item{exit.status}{a vector or factor giving status at exit. Any change in status during follow-up is assumed to take place exactly at the exit time.} \item{id}{a vector giving a unique identity value for each person represented in the Lexis object. Defaults to \code{1:nrow(data)}} \item{data}{an optional data frame, list, or environment containing the variables. If not found in \code{data}, the variables are taken from the environment from which \code{Lexis} was called.} \item{merge}{a logical flag. If \code{TRUE} then the \code{data} argument will be coerced to a data frame and then merged with the resulting \code{Lexis} object.} \item{states}{A vector of labels for the states. If given, the state variables \code{lex.Cst} and \code{lex.Xst} are returned as factors with identical levels attributes equal to \code{states}.} \item{notes}{Logical. Should notes on entry states and time be given.} \item{tol}{Numerical tolerance for follow-up time. Rows with duration less than this value are automatically dropped.} \item{keep.dropped}{Logical. Should dropped rows from \code{data} be saved as an attribute with the object for inspection?} } \details{ The analysis of long-term population-based follow-up studies typically requires multiple time scales to be taken into account, such as age, calender time, or time since an event. A \code{Lexis} object is a data frame with additional attributes that allows these multiple time dimensions of follow-up to be managed. Separate variables for current end exit state allows representation of multistate data. Lexis objects are named after the German demographer Wilhelm Lexis (1837-1914), who is credited with the invention of the "Lexis diagram" for representing population dynamics simultaneously by several timescales. The \code{Lexis} function can create a minimal \code{Lexis} object with only those variables required to define the follow-up history in each row. Additional variables can be merged into the \code{Lexis} object using the \code{merge} method for \code{Lexis} objects. The latter is the default. There are also \code{merge}, \code{subset} and \code{transform} methods for \code{Lexis} objects. They work as the corresponding methods for data-frames but ensures that the result is a \code{Lexis} object. } \note{ Only two of the three arguments \code{entry}, \code{exit} and \code{duration} need to be given. If the third parameter is missing, it is imputed. \code{entry}, \code{exit} must be numeric, using \code{\link{Date}} variables will cause some of the utilities to crash. Transformation by \code{\link{cal.yr}} is recommended. If only either \code{exit} or \code{duration} are supplied it is assumed that \code{entry} is 0. This is only meaningful (and therefore checked) if there is only one timescale. If any of \code{entry.status} or \code{exit.status} are of mode character, they will both be converted to factors. If \code{entry.status} is not given, then its class is automatically set to that of \code{exit.status}. If \code{exit.status} is a character or factor, the value of \code{entry.status} is set to the first level. This may be highly undesirable, and therefore noted. For example, if \code{exit.status} is character the first level will be the first in the alphabetical ordering; slightly unfortunate if values are \code{c("Well","Diseased")}. If \code{exit.status} is logical, the value of \code{entry.status} set to \code{FALSE}. If \code{exit.status} is numeric, the value of \code{entry.status} set to 0. If \code{entry.status} or \code{exit.status} are factors or character, the corresponding state variables in the returned \code{Lexis} object, \code{lex.Cst} and \code{lex.Xst} will be (unordered) factors with identical set of levels, namely the union of the levels of \code{entry.status} and \code{exit.status}. } \value{ An object of class \code{Lexis}. This is represented as a data frame with a column for each time scale (with names equal to the union of the names of \code{entry} and \code{exit}), and additional columns with the following names: \item{lex.id}{Identification of the persons.} \item{lex.dur}{Duration of follow-up.} \item{lex.Cst}{Entry status (\code{C}urrent \code{st}ate), i.e. the state in which the follow up takes place.} \item{lex.Xst}{Exit status (e\code{X}it \code{st}ate), i.e. that state taken up after \code{dur} in \code{lex.Cst}.} If \code{merge=TRUE} (the default) then the \code{Lexis} object will also contain all variables from the \code{data} argument. } \author{Martyn Plummer with contributions from Bendix Carstensen} \examples{ # A small bogus cohort xcoh <- structure( list( id = c("A", "B", "C"), birth = c("14/07/1952", "01/04/1954", "10/06/1987"), entry = c("04/08/1965", "08/09/1972", "23/12/1991"), exit = c("27/06/1997", "23/05/1995", "24/07/1998"), fail = c(1, 0, 1) ), .Names = c("id", "birth", "entry", "exit", "fail"), row.names = c("1", "2", "3"), class = "data.frame" ) # Convert the character dates into numerical variables (fractional years) xcoh <- cal.yr( xcoh, format="\%d/\%m/\%Y", wh=2:4 ) # See how it looks xcoh str( xcoh ) # Define a Lexis object with timescales calendar time and age Lcoh <- Lexis( entry = list( per=entry ), exit = list( per=exit, age=exit-birth ), exit.status = fail, data = xcoh ) Lcoh # Using character states may have undesired effects: xcoh$Fail <- c("Dead","Well","Dead") Lexis( entry = list( per=entry ), exit = list( per=exit, age=exit-birth ), exit.status = Fail, data = xcoh ) # ...unless you order the levels correctly ( xcoh$Fail <- factor( xcoh$Fail, levels=c("Well","Dead") ) ) Lexis( entry = list( per=entry ), exit = list( per=exit, age=exit-birth ), exit.status = Fail, data = xcoh ) } \seealso{ \code{\link{plot.Lexis}}, \code{\link{splitLexis}}, \code{\link{cutLexis}}, \code{\link{mcutLexis}}, \code{\link{rcutLexis}}, \code{\link{addCov.Lexis}}, % \code{\link{glm.Lexis}}, % \code{\link{gam.Lexis}}, % \code{\link{coxph.Lexis}}, \code{\link{merge.Lexis}}, \code{\link{subset.Lexis}}, \code{\link{cbind.Lexis}}, \code{\link{rbind.Lexis}}, \code{\link{transform.Lexis}}, \code{\link{summary.Lexis}}, \code{\link{timeScales}}, \code{\link{timeBand}}, \code{\link{entry}}, \code{\link{exit}}, \code{\link{transient}}, \code{\link{absorbing}}, \code{\link{dur}} } \keyword{survival} \keyword{manip} Epi/man/Y.dk.Rd0000644000176200001440000000267113751040403012641 0ustar liggesusers\name{Y.dk} \alias{Y.dk} \docType{data} \title{Population risk time in Denmark} \description{ Risk time (person-years) in the Danish population, classified by sex, age, period and date of birth in 1-year classes. This corresponds to triangles in a Lexis diagram. } \usage{data(Y.dk)} \format{ A data frame with 13860 observations on the following 6 variables. \describe{ \item{\code{sex}}{Sex. 1:males, 2:females} \item{\code{A}}{One-year age class} \item{\code{P}}{Period} \item{\code{C}}{Birth cohort} \item{\code{Y}}{Person-years} \item{\code{upper}}{Indicator of upper triangle in the Lexis diagram} } } \details{ The risk time is computed from the population size figures in \code{\link{N.dk}}, using the formulae devised in: B. Carstensen: Age-period-cohort models for the Lexis diagram. Statistics in Medicine, 10; 26(15):3018-45, 2007. } \source{ \url{http://www.statistikbanken.dk/statbank5a/SelectTable/omrade0.asp?SubjectCode=02&PLanguage=1&ShowNews=OFF} } \examples{ data(Y.dk) str(Y.dk) # Compute mean age, period for the triangles attach( Y.dk ) age <- A + (1+upper)/3 per <- P + (2-upper)/3 # Plot a Lexis diagram library( Epi ) Lexis.diagram( age=c(0,10), date=c(1990,2000), coh.grid=TRUE, int=1 ) box() # Print the person-years for males there text( per[sex==1], age[sex==1], formatC( Y[sex==1]/1000, format="f", digits=1 ) ) } \keyword{datasets} Epi/man/Icens.Rd0000644000176200001440000000673513751040403013102 0ustar liggesusers\name{Icens} \alias{Icens} \alias{print.Icens} \title{ Fits a regression model to interval censored data. } \description{ The models fitted assumes a piecewise constant baseline rate in intervals specified by the argument \code{breaks}, and for the covariates either a multiplicative relative risk function (default) or an additive excess risk function. } \usage{ Icens( first.well, last.well, first.ill, formula, model.type=c("MRR","AER"), breaks, boot=FALSE, alpha=0.05, keep.sample=FALSE, data ) } \arguments{ \item{first.well}{Time of entry to the study, i.e. the time first seen without event. Numerical vector.} \item{last.well}{Time last seen without event. Numerical vector.} \item{first.ill}{Time first seen with event. Numerical vector.} \item{formula}{Model formula for the log relative risk.} \item{model.type}{Which model should be fitted.} \item{breaks}{Breakpoints between intervals in which the underlying timescale is assumed constant. Any observation outside the range of \code{breaks} is discarded.} \item{boot}{Should bootstrap be performed to produce confidence intervals for parameters. If a number is given this will be the number of bootsrap samples. The default is 1000.} \item{alpha}{1 minus the confidence level.} \item{keep.sample}{Should the bootstrap sample of the parameter values be returned?} \item{data}{Data frame in which the times and formula are interpreted.} } \details{ The model is fitted by calling either \code{\link{fit.mult}} or \code{\link{fit.add}}. } \value{ An object of class \code{"Icens"}: a list with three components: \item{rates}{A glm object from a binomial model with log-link, estimating the baseline rates, and the excess risk if \code{"AER"} is specfied.} \item{cov}{A glm object from a binomial model with complementary log-log link, estimating the log-rate-ratios. Only if \code{"MRR"} is specfied.} \item{niter}{Nuber of iterations, a scalar} \item{boot.ci}{If \code{boot=TRUE}, a 3-column matrix with estimates and 1-\code{alpha} confidence intervals for the parameters in the model.} \item{sample}{A matrix of the parameterestimates from the bootstrapping. Rows refer to parameters, columns to bootstrap samples.} } \references{ B Carstensen: Regression models for interval censored survival data: application to HIV infection in Danish homosexual men. Statistics in Medicine, 15(20):2177-2189, 1996. CP Farrington: Interval censored survival data: a generalized linear modelling approach. Statistics in Medicine, 15(3):283-292, 1996. } \author{ Martyn Plummer, \email{martyn.plummer@r-project.org}, Bendix Carstensen, \email{b@bxc.dk} } \seealso{ \code{\link{fit.add}} \code{\link{fit.mult}} } \examples{ data( hivDK ) # Convert the dates to fractional years so that rates are # expressed in cases per year for( i in 2:4 ) hivDK[,i] <- cal.yr( hivDK[,i] ) m.RR <- Icens( entry, well, ill, model="MRR", formula=~pyr+us, breaks=seq(1980,1990,5), data=hivDK) # Currently the MRR model returns a list with 2 glm objects. round( ci.lin( m.RR$rates ), 4 ) round( ci.lin( m.RR$cov, Exp=TRUE ), 4 ) # There is actually a print method: print( m.RR ) m.ER <- Icens( entry, well, ill, model="AER", formula=~pyr+us, breaks=seq(1980,1990,5), data=hivDK) # There is actually a print method: print( m.ER ) } \keyword{ models } \keyword{ regression } \keyword{ survival } Epi/man/detrend.Rd0000644000176200001440000000265613751040403013464 0ustar liggesusers\name{detrend} \alias{detrend} \alias{decurve} \title{ Projection of a model matrix on the orthogonal complement of a trend or curvature.} \description{ The columns of a model matrix \code{M} is projected on the orthogonal complement to the matrix \code{(1,t)}, resp. \code{(1,t,t^2)}. Orthogonality is w.r.t. an inner product defined by the positive definite matrix matrix \code{diag(weight)}. Non-diagonal matrices defining the inner product is not supported. } \usage{ detrend( M, t, weight = rep(1, nrow(M)) ) decurve( M, t, weight = rep(1, nrow(M)) ) } \arguments{ \item{M}{A model matrix.} \item{t}{The trend defining a subspace. A numerical vector of length \code{nrow(M)}.} \item{weight}{ Weights defining the inner product of vectors \code{x} and \code{y} as \code{sum(x*w*y)}. A numerical vector of length \code{nrow(M)}, defaults to a vector of \code{1}s. Must be all non-negative.} } \details{ The functions are intended to be used in construction of particular parametrizations of age-period-cohort models. } \value{ \code{detrend} returns full-rank matrix with columns orthogonal to \code{(1,t)}; \code{decurve} returns full-rank matrix with columns orthogonal to \code{(1,t,t^2)}. } \author{ Bendix Carstensen, Steno Diabetes Center Copenhagen, \url{http://bendixcarstensen.com}, with essential help from Peter Dalgaard. } \seealso{ \code{\link{projection.ip}} } \keyword{array} Epi/man/births.Rd0000644000176200001440000000165513751040403013330 0ustar liggesusers\name{births} \alias{births} \docType{data} \title{Births in a London Hospital} \description{ Data from 500 singleton births in a London Hospital } \usage{data(births)} \format{ A data frame with 500 observations on the following 8 variables. \tabular{rl}{ \code{id}: \tab Identity number for mother and baby. \cr \code{bweight}: \tab Birth weight of baby. \cr \code{lowbw}: \tab Indicator for birth weight less than 2500 g. \cr \code{gestwks}: \tab Gestation period. \cr \code{preterm}: \tab Indicator for gestation period less than 37 weeks. \cr \code{matage}: \tab Maternal age. \cr \code{hyp}: \tab Indicator for maternal hypertension. \cr \code{sex}: \tab Sex of baby: 1:Male, 2:Female. \cr } } \source{ Anonymous } \references{ Michael Hills and Bianca De Stavola (2002). A Short Introduction to Stata 8 for Biostatistics, Timberlake Consultants Ltd } \examples{ data(births) } \keyword{datasets} Epi/man/nickel.Rd0000644000176200001440000000233113751040403013272 0ustar liggesusers\name{nickel} \alias{nickel} \docType{data} \title{A Cohort of Nickel Smelters in South Wales} \description{ The \code{nickel} data frame has 679 rows and 7 columns. The data concern a cohort of nickel smelting workers in South Wales and are taken from Breslow and Day, Volume 2. For comparison purposes, England and Wales mortality rates (per 1,000,000 per annum) from lung cancer (ICDs 162 and 163), nasal cancer (ICD 160), and all causes, by age group and calendar period, are supplied in the dataset \code{\link{ewrates}}. } \format{ This data frame contains the following columns: \tabular{rl}{ \code{id}: \tab Subject identifier (numeric) \cr \code{icd}: \tab ICD cause of death if dead, 0 otherwise (numeric) \cr \code{exposure}: \tab Exposure index for workplace (numeric) \cr \code{dob}: \tab Date of birth (numeric) \cr \code{age1st}: \tab Age at first exposure (numeric) \cr \code{agein}: \tab Age at start of follow-up (numeric) \cr \code{ageout}: \tab Age at end of follow-up (numeric) \cr } } \source{ Breslow NE, and Day N, Statistical Methods in Cancer Research. Volume II: The Design and Analysis of Cohort Studies. IARC Scientific Publications, IARC:Lyon, 1987. } \examples{ data(nickel) str(nickel) } \keyword{datasets} Epi/man/ci.cum.Rd0000644000176200001440000001220713751040403013206 0ustar liggesusers\name{ci.cum} \alias{ci.cum} \alias{ci.surv} \title{ Compute cumulative sum of estimates. } \description{ Computes the cumulative sum of parameter functions and the standard error of it. Used for computing the cumulative rate, or the survival function based on a \code{glm} with parametric baseline. } \usage{ ci.cum( obj, ctr.mat = NULL, subset = NULL, intl = 1, alpha = 0.05, Exp = TRUE, ci.Exp = FALSE, sample = FALSE ) ci.surv( obj, ctr.mat = NULL, subset = NULL, intl = 1, alpha = 0.05, Exp = TRUE, sample = FALSE ) } \arguments{ \item{obj}{A model object (of class \code{lm}, \code{glm}. } \item{ctr.mat}{Matrix or data frame. If \code{ctr.mat} is a matrix, it should be a contrast matrix to be multiplied to the parameter vector, i.e. the desired linear function of the parameters. If it is a data frame it should have columns corresponding to a prediction data frame for \code{obj}, see details for \code{\link{ci.lin}}.} \item{subset}{ Subset of the parameters of the model to which a matrix \code{ctr.mat} should be applied. } \item{intl}{ Interval length for the cumulation. Either a constant or a numerical vector of length \code{nrow(ctr.mat)}. } \item{alpha}{ Significance level used when computing confidence limits. } \item{Exp}{ Should the parameter function be exponentiated before it is cumulated?} \item{ci.Exp}{ Should the confidence limits for the cumulative rate be computed on the log-scale, thus ensuring that exp(-cum.rate) is always in [0,1]?} \item{sample}{Should a sample of the original parameters be used to compute a cumulative rate?} } \details{ The purpose of this function is to the compute cumulative rate (integrated intensity) at a set of points based on a model for the rates. \code{ctr.mat} is a matrix which, when premultiplied to the parameters of the model returns the (log)rates at a set of increasing time points. If log-rates are returned from the model, the they should be exponentiated before cumulated, and the variances computed accordingly. Since the primary use is for log-linear Poisson models the \code{Exp} parameter defaults to TRUE. Each row in the object supplied via \code{ctr.mat} is assumed to represent a midpoint in an interval. \code{ci.cum} will then return the cumulative rates at the \emph{end} of these intervals. \code{ci.surv} will return the survival probability at the \emph{start} of each of these intervals, assuming the the first interval starts at 0 - the first row of the result is \code{c(1,1,1)}. The \code{ci.Exp} argument ensures that the confidence intervals for the cumulative rates are always positive, so that exp(-cum.rate) is always in [0,1]. } \value{ A matrix with 3 columns: Estimate, lower and upper c.i. and standard error, unless \code{se=TRUE}, in which case the standard error is returned too. If \code{sample} is TRUE, a sampled vector is returned, if \code{sample} is numeric a matrix with \code{sample} columns is returned, each column a cumulative rate based on a random sample from the distribution of the parameter estimates. \code{ci.surv} returns a 3 column matrix with estimate, lower and upper confidence interval. } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com} } \seealso{ See also \code{\link{ci.lin}}, \code{\link{ci.pred}} } \examples{ # Packages required for this example library( splines ) library( survival ) data( lung ) par( mfrow=c(1,2) ) # Plot the Kaplan-meier-estimator plot( survfit( Surv( time, status==2 ) ~ 1, data=lung ) ) # Declare data as Lexis lungL <- Lexis( exit=list(tfd=time), exit.status=(status==2)*1, data=lung ) summary( lungL ) # Split the follow-up every 10 days sL <- splitLexis( lungL, "tfd", breaks=seq(0,1100,10) ) summary( sL ) # Fit a Poisson model with a natural spline for the effect of time (left # end points of intervals are used as covariate) mp <- glm( cbind(lex.Xst==1,lex.dur) ~ Ns(tfd,knots=c(0,50,100,200,400,700)), family=poisreg, data=sL ) # mp is now a model for the rates along the time scale tfd # prediction data frame for select time points on this time scale nd <- data.frame( tfd = seq(5,995,10) ) # *midpoints* of intervals Lambda <- ci.cum ( mp, nd, intl=10 ) surv <- ci.surv( mp, nd, intl=10 ) # Put the estimated survival function on top of the KM-estimator # recall the ci.surv return the survival at *start* of intervals matshade( nd$tfd-5, surv, col="Red", alpha=0.15 ) # Extract and plot the fitted intensity function lambda <- ci.pred( mp, nd )*365.25 # mortality matshade( nd$tfd, lambda, log="y", ylim=c(0.2,5), plot=TRUE, xlab="Time since diagnosis", ylab="Mortality per year" ) # same thing works with gam from mgcv library( mgcv ) mg <- gam( cbind(lex.Xst==1,lex.dur) ~ s(tfd), family=poisreg, data=sL ) matshade( nd$tfd-5, ci.surv( mg, nd, intl=10 ), plot=TRUE, xlab="Days since diagnosis", ylab="P(survival)" ) matshade( nd$tfd , ci.pred( mg, nd )*365.25 , plot=TRUE, log="y", xlab="Days since diagnosis", ylab="Mortality per 1 py" ) } \keyword{models} \keyword{regression} Epi/man/occup.Rd0000644000176200001440000000333313751040403013141 0ustar liggesusers\name{occup} \alias{occup} \docType{data} \title{ A small occupational cohort } \description{This is the data that is behind the illustrative Lexis diagram in Breslow & Day's book on case-control studies.} \usage{data(occup)} \format{ A data frame with 13 observations on the following 4 variables. \describe{ \item{\code{AoE}}{a numeric vector, Age at Entry} \item{\code{DoE}}{a numeric vector, Date of entry} \item{\code{DoX}}{a numeric vector, Date of eXit} \item{\code{Xst}}{eXit status \code{D}-event, \code{W}-withdrawal, \code{X}-censoring} } } \references{ Breslow & Day: Statistical Methods in Cancer Research, vol 1: The analysis of case-control studies, figure 2.2, p. 48.} \examples{ data(occup) lx <- Lexis( entry = list( per=DoE, age=AoE ), exit = list( per=DoX ), entry.status = "W", exit.status = Xst, data = occup ) plot( lx ) # Split follow-up in 5-year classes sx <- splitLexis( lx, seq(1940,1960,5), "per" ) sx <- splitLexis( sx, seq( 40, 60,5), "age" ) plot( sx ) # Plot with a bit more paraphernalia and a device to get # the years on the same physical scale on both axes ypi <- 2.5 # Years per inch dev.new( height=15/ypi+1, width=20/ypi+1 ) # add an inch in each direction for par( mai=c(3,3,1,1)/4, mgp=c(3,1,0)/1.6 ) # the margins set in inches by mai= plot(sx,las=1,col="black",lty.grid=1,lwd=2,type="l", xlim=c(1940,1960),ylim=c(40,55),xaxs="i",yaxs="i",yaxt="n", xlab="Calendar year", ylab="Age (years)") axis( side=2, at=seq(40,55,5), las=1 ) points(sx,pch=c(NA,16)[(sx$lex.Xst=="D")+1] ) box() # Annotation with the person-years PY.ann.Lexis( sx, cex=0.8 ) } \keyword{datasets} Epi/man/ccwc.Rd0000644000176200001440000000413413751040403012747 0ustar liggesusers\name{ccwc} \alias{ccwc} \title{Generate a nested case-control study} \usage{ ccwc( entry=0, exit, fail, origin=0, controls=1, match=list(), include=list(), data=NULL, silent=FALSE ) } \arguments{ \item{entry}{ Time of entry to follow-up } \item{exit}{ Time of exit from follow-up } \item{fail}{ Status on exit (1=Fail, 0=Censored) } \item{origin}{ Origin of analysis time scale } \item{controls}{ The number of controls to be selected for each case } \item{match}{ List of categorical variables on which to match cases and controls } \item{include}{ List of other variables to be carried across into the case-control study } \item{data}{ Data frame in which to look for input variables } \item{silent}{ If FALSE, echos a . to the screen for each case-control set created; otherwise produces no output. } } \description{ Given the basic outcome variables for a cohort study: the time of entry to the cohort, the time of exit and the reason for exit ("failure" or "censoring"), this function computes risk sets and generates a matched case-control study in which each case is compared with a set of controls randomly sampled from the appropriate risk set. Other variables may be matched when selecting controls. } \value{ The case-control study, as a dataframe containing: \item{Set}{ case-control set number } \item{Map}{ row number of record in input dataframe } \item{Time}{ failure time of the case in this set } \item{Fail}{ failure status (1=case, 0=control) } These are followed by the matching variables, and finally by the variables in the \code{include} list } \references{ Clayton and Hills, Statistical Models in Epidemiology, Oxford University Press, Oxford:1993. } \author{ David Clayton } \seealso{ \code{\link{Lexis}} } \examples{ # # For the diet and heart dataset, create a nested case-control study # using the age scale and matching on job # data(diet) dietcc <- ccwc( doe, dox, chd, origin=dob, controls=2, data=diet, include=energy, match=job) } \keyword{datagen} Epi/man/crr.Lexis.Rd0000644000176200001440000000737613763470050013724 0ustar liggesusers\name{crr.Lexis} \alias{crr.Lexis} \title{Fit a competing risks regression model (Fine-Gray model) using a Lexis object) } \description{ Fits a competing risks regression model using a \code{\link{Lexis}} object assuming that every person enters at time 0 and exits at time \code{lex.dur}. Thus is only meaningful for Lexis objects with one record per person, (so far). } \usage{ crr.Lexis( obj, mod, quiet=FALSE, ...) } \arguments{ \item{obj}{A Lexis object; variables in \code{mod} are taken from this.} \item{mod}{Formula, with the l.h.s. a character constant equal to a level of \code{obj$lex.Xst}, and the r.h.s. a model formula interpreted in \code{obj}.} \item{quiet}{Logical indicating whether a brief summary should be printed.} \item{\dots}{Further arguments passed on to \code{\link[cmprsk:crr]{crr}}.} } \details{ This function is a simple wrapper for \code{crr}, allowing a formula-specification of the model (which allows specifications of covariates on the fly), and utilizing the structure of Lexis objects to simplify specification of the outcome. Prints a summary of the levels used as event, competing events and censoring. By the structure of the \code{\link{Lexis}} object it is not necessary to indicate what the censoring code or competing events are, that is automatically derived from the \code{Lexis} object. Currently only one state is allowed as l.h.s. (response) in \code{mod}. } \value{ A \code{\link[cmprsk:crr]{crr}} object (which is a list), with two extra elements in the list, \code{model.Lexis} - the model formula supplied, and \code{transitions} - a table of transitions and censorings showing which transition was analysed and which were taken as competing events. } \author{Bendix Carstensen, \url{http://bendixcarstensen.com} } \seealso{ \code{\link[cmprsk:crr]{crr}}, \code{\link{Lexis}} } \examples{ # Thorotrats patients, different histological types of liver cancer # Load thorotrast data, and restrict to exposed data(thoro) tht <- thoro[thoro$contrast==1,] # Define exitdate as the date of livercancer tht$dox <- pmin( tht$liverdat, tht$exitdat, na.rm=TRUE ) tht <- subset( tht, dox > injecdat ) # Convert to calendar years in dates tht <- cal.yr( tht ) # Set up a Lexis object with three subtypes of liver cancer and death tht.L <- Lexis( entry = list( per = injecdat, tfi = 0 ), exit = list( per = dox ), exit.status = factor( 1*hepcc+2*chola+3*hmang+ 4*(hepcc+chola+hmang==0 & exitstat==1), labels=c("No cancer","hepcc","chola","hmang","Dead") ), data = tht ) summary( tht.L ) # Show the transitions boxes( tht.L, boxpos=list(x=c(20,rep(80,3),30), y=c(60,90,60,30,10) ), show.BE="nz", scale.R=1000 ) # Fit a model for the Hepatocellular Carcinoma as outcome # - note that you can create a variable on the fly: library( cmprsk ) hepcc <- crr.Lexis( tht.L, "hepcc" ~ volume + I(injecdat-1940) ) hepcc$model.Lexis hepcc$transitions # Models for the three other outcomes: chola <- crr.Lexis( tht.L, "chola" ~ volume + I(injecdat-1940) ) hmang <- crr.Lexis( tht.L, "hmang" ~ volume + I(injecdat-1940) ) dead <- crr.Lexis( tht.L, "Dead" ~ volume + I(injecdat-1940) ) # Compare the effects # NOTE: This is not necessarily a joint model for all transitions. zz <- rbind( ci.exp(hepcc), ci.exp(chola), ci.exp(hmang), ci.exp(dead) ) zz <- cbind( zz[c(1,3,5,7) ,], zz[c(1,3,5,7)+1,] ) rownames( zz ) <- c("hepcc","chola","hmang","dead") colnames( zz )[c(1,4)] <- rownames( ci.exp(chola) ) round( zz, 3 ) } \keyword{survival} Epi/man/bdendo.Rd0000644000176200001440000000423513751040403013265 0ustar liggesusers\name{bdendo} \alias{bdendo} \alias{bdendo11} \docType{data} \title{A case-control study of endometrial cancer} \description{ The \code{bdendo} data frame has 315 rows and 13 columns, \code{bdendo11} 126 rows. These data concern a study in which each case of endometrial cancer was matched with 4 controls. \code{bdendo11} is a 1:1 mathed subset of \code{bdendo}. Matching was by date of birth (within one year), marital status, and residence. } \format{ These data frames have the following columns: \tabular{rl}{ \code{set}: \tab Case-control set: a numeric vector \cr \code{d}: \tab Case or control: a numeric vector (1=case, 0=control) \cr \code{gall}: \tab Gall bladder disease: a factor with levels \code{No} \code{Yes}. \cr \code{hyp}: \tab Hypertension: a factor with levels \code{No} \code{Yes}. \cr \code{ob}: \tab Obesity: a factor with levels \code{No} \code{Yes}. \cr \code{est}: \tab A factor with levels \code{No} \code{Yes}. \cr \code{dur}: \tab Duration of conjugated oestrogen therapy: a factor with levels \code{0}, \code{1}, \code{2}, \code{3}, \code{4}. \cr \code{non}: \tab Use of non oestrogen drugs: a factor with levels \code{No} \code{Yes}. \cr \code{duration}: \tab Months of oestrogen therapy: a numeric vector. \cr \code{age}: \tab A numeric vector. \cr \code{cest}: \tab Conjugated oestrogen dose: a factor with levels \code{0}, \code{1}, \code{2}, \code{3}. \cr \code{agegrp}: \tab A factor with levels \code{55-59} \code{60-64} \code{65-69} \code{70-74} \code{75-79} \code{80-84} \cr \code{age3}: \tab a factor with levels \code{<64} \code{65-74} \code{75+} \cr } } \source{ Breslow NE, and Day N, Statistical Methods in Cancer Research. Volume I: The Analysis of Case-Control Studies. IARC Scientific Publications, IARC:Lyon, 1980. } \examples{ data(bdendo) str(bdendo) } \keyword{datasets} Epi/man/mcutLexis.Rd0000644000176200001440000001040613763206636014023 0ustar liggesusers\name{mcutLexis} \alias{mcutLexis} \title{ Cut follow-up at multiple event dates and keep track of order of events } \description{ A generalization of \code{\link{cutLexis}} to the case where different events may occur in any order (but at most once for each). } \usage{ mcutLexis( L0, timescale = 1, wh, new.states = NULL, precursor.states = transient(L0), seq.states = TRUE, new.scales = NULL, ties.resolve = FALSE ) } \arguments{ \item{L0}{A Lexis object.} \item{timescale}{Which time scale do the variables in \code{L0[,wh]} refer to. Can be character or integer.} \item{wh}{Which variables contain the event dates. Character or integer vector} \item{new.states}{Names of the events forming new states. If \code{NULL} equal to the variable names from \code{wh}.} \item{precursor.states}{Which states are precursor states. See \code{\link{cutLexis}} for definition of precursor states.} \item{seq.states}{Should the sequence of events be kept track of? That is, should A-B be considered different from B-A. If \code{FALSE}, the state with combined preceding events A and B will be called A+B (alphabetically sorted). May also be supplied as character: \code{s} - sequence, keep track of sequence of states occupied (same as \code{TRUE}), \code{u} - unordered, keep track only of states visited (same as \code{FALSE}) or \code{l}, \code{c} - last or current state, only record the latest state visited. If given as character, only the first letter converted to lower case is used.} \item{new.scales}{Should we construct new time scales indicating the time since each of the event occurrences.} \item{ties.resolve}{Should tied event times be resolved by adding random noise to tied event dates. If \code{FALSE} the function will not accept that two events occur at the same time for a person (ties). If \code{TRUE} a random quantity in the range \code{c(-1,1)/100} will be added to all event times in all records with at least one tie. If \code{ties.resolve} is numeric a random quantity in the range \code{c(-1,1)*ties.resolve} will be added to all event times in all records with at least one tie.} } \value{A \code{\link{Lexis}} object with extra states created by occurrence of a number of intermediate events. } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com} } \seealso{ \code{\link{cutLexis}}, \code{\link{rcutLexis}}, \code{\link{addCov.Lexis}}, \code{\link{Lexis}}, \code{\link{splitLexis}} } \examples{ # A dataframe of times set.seed(563248) dd <- data.frame( id = 1:30, doN = round(runif(30,-30, 0),1), doE = round(runif(30, 0,20),1), doX = round(runif(30, 50,60),1), doD = round(runif(30, 50,60),1), # these are the event times doA = c(NA,21,NA,27,35,NA,52, 5,43,80, NA,22,56,28,53,NA,51, 5,43,80, NA,23,NA,33,51,NA,55, 5,43,80), doB = c(NA,20,NA,53,27,NA, 5,52,34,83, NA,20,23,37,35,NA,52, 8,33,NA, 25,NA,37,40,NA,NA,15,23,36,61) ) # set up a Lexis object with time from entry to death/exit Lx <- Lexis( entry = list(time=doE, age=doE-doN), exit = list(time=pmin(doX,doD)), exit.status = factor(doD}".} \author{ Bendix Carstensen, \email{b@bxc.dk}, \url{http://bendixcarstensen.com} } \examples{ data(DMlate) str(DMlate) dml <- Lexis( entry=list(Per=dodm, Age=dodm-dobth, DMdur=0 ), exit=list(Per=dox), exit.status=factor(!is.na(dodth),labels=c("DM","Dead")), data=DMlate ) dmi <- cutLexis( dml, cut=dml$doins, new.state="Ins", pre="DM" ) summary( dmi ) ls.dmi <- stack( dmi ) str( ls.dmi ) # Check that all the transitions and person-years got across. with( ls.dmi, rbind( table(lex.Fail,lex.Tr), tapply(lex.dur,lex.Tr,sum) ) ) } \seealso{ \code{\link{splitLexis}} \code{\link{cutLexis}} \code{\link{Lexis}} } \keyword{survival} Epi/man/diet.Rd0000644000176200001440000000474413751040403012764 0ustar liggesusers\name{diet} \alias{diet} \docType{data} \title{Diet and heart data} \description{ The \code{diet} data frame has 337 rows and 14 columns. The data concern a subsample of subjects drawn from larger cohort studies of the incidence of coronary heart disease (CHD). These subjects had all completed a 7-day weighed dietary survey while taking part in validation studies of dietary questionnaire methods. Upon the closure of the MRC Social Medicine Unit, from where these studies were directed, it was found that 46 CHD events had occurred in this group, thus allowing a serendipitous study of the relationship between diet and the incidence of CHD. } \format{ This data frame contains the following columns: \tabular{rl}{ \code{id}: \tab subject identifier, a numeric vector. \cr \code{doe}: \tab date of entry into follow-up study, a \code{\link{Date}} variable. \cr \code{dox}: \tab date of exit from the follow-up study, a \code{\link{Date}} variable. \cr \code{dob}: \tab date of birth, a \code{\link{Date}} variable. \cr \code{y}: \tab number of years at risk, a numeric vector. \cr \code{fail}: \tab status on exit, a numeric vector (codes 1, 3 and 13 represent CHD events) \cr \code{job}: \tab occupation, a factor with levels \code{Driver} \code{Conductor} \code{Bank worker} \cr \code{month}: \tab month of dietary survey, a numeric vector \cr \code{energy}: \tab total energy intake (kCal per day/100), a numeric vector \cr \code{height}: \tab (cm), a numeric vector \cr \code{weight}: \tab (kg), a numeric vector \cr \code{fat}: \tab fat intake (10 g/day), a numeric vector \cr \code{fibre}: \tab dietary fibre intake (10 g/day), a numeric vector \cr \code{energy.grp}: \tab high daily energy intake, a factor with levels \code{<=2750 KCal} \code{>2750 KCal} \cr \code{chd}: \tab CHD event, a numeric vector (1=CHD event, 0=no event) \cr } } \source{ The data are described and used extensively by Clayton and Hills, Statistical Models in Epidemiology, Oxford University Press, Oxford:1993. They were rescued from destruction by David Clayton and reentered from paper printouts. } \examples{ data(diet) # Illustrate the follow-up in a Lexis diagram Lexis.diagram( age=c(30,75), date=c(1965,1990), entry.date=cal.yr(doe), exit.date=cal.yr(dox), birth.date=cal.yr(dob), fail=(fail>0), pch.fail=c(NA,16), col.fail=c(NA,"red"), cex.fail=1.0, data=diet ) } \keyword{datasets} Epi/man/Epi.Rd0000644000176200001440000000130713751040403012544 0ustar liggesusers\docType{package} \name{Epi} \alias{Epi} \alias{Epi-package} \title{Epi: Functions for manipulation and statistical analysis of epidemiological data} \description{ \pkg{Epi} has grown out of the course 'Statistical Practise in Epidemiology with R' \url{http://bendixcarstensen.com/SPE/}. The major contributions from this course have been the \code{\link{stat.table}} function for advanced tabulation and summary, and the functions for representation and the \code{\link{Lexis}} function(s) for manipulation of multistate data with multiple time scales. } \details{Click on the \code{Index} link below the line to access vignettes (tutorial documents) and an alphabetic list of the functions in \code{Epi}.}Epi/man/Life.lines.Rd0000644000176200001440000000404013751040403014014 0ustar liggesusers\name{Life.lines} \alias{Life.lines} \title{ Compute dates/ages for life lines in a Lexis diagram } \description{ Fills out the missing information for follow up of persons in a Lexis diagram if sufficient information is given. } \usage{ Life.lines( entry.date = NA, exit.date = NA, birth.date = NA, entry.age = NA, exit.age = NA, risk.time = NA ) } \arguments{ \item{entry.date, exit.date,birth.date, entry.age, exit.age, risk.time}{Vectors defining lifelines to be plotted in the diagram. At least three must be given to produce a result. Not all subsets of three will suffice, the given subset has to define life lines. If insufficient data is given, nothing is returned and a warning is given.} } \value{ Data frame with variables \code{entry.date}, \code{entry.age}, \code{exit.date}, \code{exit.age}, \code{risk.time}, \code{birth.date}, with all entries computed for each person. If any of \code{entry.date}, \code{exit.date} or \code{birth.date} are of class \code{Date} or if any of \code{entry.age}, \code{exit.age} or \code{risk.time} are of class \code{difftime} the date variables will be of class \code{Date} and the other three of class \code{difftime}. } \examples{ ( Life.lines( entry.age = c(3,30,45), risk.time = c(25,5,14), birth.date = c(1970,1931,1925.7) ) ) # Draw a Lexis diagram Lexis.diagram() # Compute entry and exit age and date. ( LL <- Life.lines( entry.age = c(3,30,45), risk.time = c(25,5,14), birth.date = c(1970,1931,1925.7) ) ) segments( LL[,1], LL[,2], LL[,3], LL[,4] ) # Plot the life lines. # Compute entry and exit age and date, supplying a date variable bd <- ( c(1970,1931,1925.7) - 1970 ) * 365.25 class( bd ) <- "Date" ( Life.lines( entry.age = c(3,30,45), risk.time = c(25,5,14), birth.date = bd ) ) } \seealso{ \code{\link{Lexis.diagram}}, \code{\link{Lexis.lines}} } \keyword{ manip } \keyword{ dplot } Epi/man/Termplot.Rd0000644000176200001440000000643613751040403013645 0ustar liggesusers\name{Termplot} \alias{Termplot} \title{ A wrapper for \code{termplot} that optionally (but by default) exponentiates terms, and plot them on a common log-scale. Also scales x-axes to the same physical scale. } \description{ The function uses \code{\link{termplot}} to extract terms from a model with, say, spline, terms, including the standard errors, computes confidence intervals and transform these to the rate / rate-ratio scale. Thus the default use is for models on the log-scale such as Poisson-regression models. The function produces a plot with panels side-by-side, one panel per term, and returns the } \usage{ Termplot( obj, plot = TRUE, xlab = NULL, ylab = NULL, xeq = TRUE, yshr = 1, alpha = 0.05, terms = NULL, max.pt = NULL ) } \arguments{ \item{obj}{An object with a \code{terms}-method --- for details the the documentation for \code{\link{termplot}}. } \item{plot}{Should a plot be produced?} \item{xlab}{Labels for the \code{x}-axes. Defaults to the names of the terms.} \item{ylab}{Labels for the \code{x}-axes. Defaults to blank.} \item{xeq}{Should the units all all plots have the same physical scale for the \code{x}-axes).} \item{yshr}{Shrinking of \code{y}-axis. By default, the \code{y}-axes have an extent that accommodates the entire range of confidence intervals. This is a shrinking parameter for the \code{y}-axes, setting it to less than 1 will lose a bit of the confidence limits on some of the panels.} \item{alpha}{1 minus the confidence level for computing confidence intervals} \item{terms}{Which terms should be reported. Passed on to \code{\link{termplot}} and eventually \code{\link{predict}}.} \item{max.pt}{The maximal number of points in which to report the terms. If \code{NULL} all unique points from the analysis dataset are reported for each term (this is a feature of \code{\link{termplot}}).} } \value{ A list with one component per term in the model object \code{obj}, each component is a 4-column matrix with $x$ as the first column, and 3 columns with estimae and lower and upper confidence limit. } \author{ Bendix Cartensen } \seealso{ \code{\link{Ns}}, \code{termplot} } \examples{ # Get the diabetes data and set up as Lexis object data(DMlate) DMlate <- DMlate[sample(1:nrow(DMlate),500),] dml <- Lexis( entry = list(Per=dodm, Age=dodm-dobth, DMdur=0 ), exit = list(Per=dox), exit.status = factor(!is.na(dodth),labels=c("DM","Dead")), data = DMlate ) # Split in 1-year age intervals dms <- splitLexis( dml, time.scale="Age", breaks=0:100 ) # Model with 6 knots for both age and period n.kn <- 6 # Model age-specific rates with period referenced to 2004 ( a.kn <- with( subset(dms,lex.Xst=="Dead"), quantile( Age+lex.dur, probs=(1:n.kn-0.5)/n.kn ) ) ) ( p.kn <- with( subset(dms,lex.Xst=="Dead"), quantile( Per+lex.dur, probs=(1:n.kn-0.5)/n.kn ) ) ) m2 <- glm( lex.Xst=="Dead" ~ -1 + Ns( Age, kn=a.kn, intercept=TRUE ) + Ns( Per, kn=p.kn, ref=2004 ), offset = log( lex.dur ), family=poisson, data=dms ) # Finally we can plot the two effects: Termplot( m2, yshr=0.9 ) } \keyword{hplot} Epi/man/addDrug.Lexis.Rd0000644000176200001440000001441414016517671014502 0ustar liggesusers\name{addDrug.Lexis} \alias{addDrug.Lexis} \title{ Expand a Lexis object with information of drug exposure based on purchase dates and -amounts } \description{ A \code{\link{Lexis}} object will contain information on follow-up for a cohort of persons through time, each record containing information of one time interval, including the time at the beginning of each interval. If information on drug purchase is known for the persons via \code{lex.id} in a list of data frames, \code{addDrug.Lexis} will expand the \code{Lexis} object by cutting at all drug purchase dates, and compute the exposure status for any number of drugs, and add these as variables. } \usage{ addDrug.Lexis(Lx, # Lexis object pdat, # list of data frames with drug purchase information amt = "amt", # name of the variable with purchased amount apt = "apt", # name of the variable with amount consumed per time method = "ext", # method use to compute exposure maxt = NULL, # max duration for a purchase when using \code{method="fix"} grace = 0, # grace period to be added tnam = setdiff(names(pdat[[1]]), c("lex.id", amt))[1], # name of the prefix = NULL, # character vector of length \code{length(pdat)} suffix = NULL, # character vector of length \code{length(pdat)} sepfix = ".") # what should the separator be when forming prefix/suffix } \arguments{ \item{Lx}{A \code{Lexis} object. } \item{pdat}{Named list of data frames with drug \code{p}urchase \code{dat}a. } \item{amt}{Name of the variable in the data frames in \code{pdat} with the purchased \code{am}oun\code{t}. } \item{apt}{Name of the variable in the data frames in \code{pdat} with the consumed \code{a}mount \code{p}er \code{t}ime. Must be given in units of units of \code{amt} per units of \code{lex.dur} in \code{Lx}. } \item{method}{Character. One of \code{"ext"} (default), \code{"amt"} or \code{"fix"}, for a description, see details. } \item{maxt}{Numerical. Maximal duration for a purchase when using \code{method="fix"}, same units as \code{lex.dur}. } \item{grace}{Numeric. Grace period to be added after last time of computed drug coverage to define end of exposure, same units as \code{lex.dur}. } \item{tnam}{Character. Name of the timescale used in the data frames in \code{pdat}. } \item{prefix}{Character vector of length \code{length(pdat)}. Used to prefix the 4 generated exposure variables. } \item{suffix}{Character vector of length \code{length(pdat)}. Used to suffix the 4 generated exposure variables. } \item{sepfix}{Character, used to separate the \code{prefix} and the name of the generated type of variable. } } \details{ This function internally uses \code{\link{addCov.Lexis}} to attach exposure status for several drugs (dispensed medicine) to follow-up in a \code{Lexis} object. Once that is done, the exposure measures are calculated at each time. There is one input data frame per type of drug, each with variables \code{lex.id}, \code{amt}, a timescale variable and possibly \code{apt}. Three different methods for computing drug exposures from dates and amounts of purchases are supported via the argument \code{method}. \itemize{ \item \code{"ext"}: Extrapolation: the first drug purchase is assumed consumed over the interval to the second purchase. Exposure for next purchases are assumed to last as long as it would have if consumed at a speed corresponding to the previous purchase being consumed over the time span between the previous and current purchase, plus a period of length \code{grace}. \item \code{"dos"}: Dosage: assumes that each purchase lasts \code{amt}/\code{apt} plus \code{grace}. \item \code{"fix"}: Fixed time: assumes that each purchase lasts \code{maxt}. } So for each purchase we have defined an end of coverage (expiry date). If next purchase is before this, we assume that the amount purchased is consumed over the period between the two purchases, otherwise over the perido to the end of coverage. So the only difference between the methods is the determination of the coverage for each purchase. Based on this, for each date in the resulting \code{\link{Lexis}} four exposure variables are computed, see next section. } \value{ A \code{\link{Lexis}} object with the same risk time, states and events as \code{Lx}. The follow-up for each person has been cut at the purchase times of each of the drugs, as well as at the expiry times for drug coverage. Further for each drug (i.e. data frame in the \code{pdat} list) 4 variables have been added: \itemize{ \item \code{pre.ex}: logical; is the person exposed in this interval \item \code{pre.tf}: numeric: time since first purchase, same units as \code{lex.dur} \item \code{pre.ct}: numeric: cumulative time on the drug, same units as \code{lex.dur} \item \code{pre.cd}: numeric: cumulative dose of the drug, same units as \code{amt} } } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com} } \seealso{ \code{\link{addCov.Lexis}}, \code{\link{gen.exp}}, \code{\link{cutLexis}}, \code{\link{rcutLexis}}, \code{\link{mcutLexis}} } \examples{ # Follow-up of 2 persons fu <- data.frame(doe = c(2006, 2008), dox = c(2015, 2018), dob = c(1950, 1951), xst = factor(c("A","D"))) Lx <- Lexis(entry = list(per = doe, age = doe- dob), exit = list(per = dox), exit.status = xst, data = fu) Lx <- subset(Lx, select = -c(doe, dob, dox, xst)) # split FU in 1 year intervals Sx <- splitLexis(Lx, "per", breaks = seq(1990, 2020, 1.0)) rc <- data.frame(per = c(2007 + runif(12,0,10)), amt = sample(2:4, 12, r = TRUE), lex.id = sample(1:2, 12, r = TRUE)) rc <- rc[order(rc$lex.id, rc$per),] rd <- data.frame(per = c(2009 + runif(10, 0, 10)), amt = sample(round(2:4/3,1), 10, r = TRUE), lex.id = sample(1:2, 10, r = TRUE)) rd <- rd[order(rd$lex.id, rd$per),] pdat <- list(Joe = rc, Pat = rd) pdat addDrug.Lexis(Sx, pdat, method = "ext") # default addDrug.Lexis(Sx, pdat, method = "ext", grace = 0.2) addDrug.Lexis(Sx, pdat, method = "dos", apt = 6) addDrug.Lexis(Sx, pdat, method = "fix", maxt = 1) } \keyword{survival} \keyword{manip} Epi/man/rm.tr.Rd0000644000176200001440000000354513751040403013077 0ustar liggesusers\name{rm.tr} \alias{rm.tr} \title{ Remove transitions from a Lexis object. } \description{ Sometimes certain transitions are not of interest. This function removes these and assigns the risk time in the target state of the transitions to the originating state. } \usage{ rm.tr(obj, from, to) } \arguments{ \item{obj}{ A \code{Lexis} object. } \item{from}{ Character; name of the state from which the transition to be purged originates. Must be a valid state name for \code{obj}. } \item{to}{ Character; name of the state to which the transition to be purged targets. Must be a valid state name for \code{obj}. } } \details{ The function removes all transitions from \code{from} to \code{to}, and assigns all risk time in the \code{to} state after the transition (\code{lex.dur}) to the \code{from} state. This is only done for risk time in \code{to} occurring directly after \code{from}. Risk time in \code{to} occurring after a transition from states different from \code{from} is not affected. Transitions from \code{to} to another state, \code{other}, say, will be changed to transitions from \code{from} to \code{other}. } \value{ A \code{\link{Lexis}} object with the indicated transition removed. } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com}. } \seealso{ \code{\link{Relevel}} } \examples{ data(DMlate) dml <- Lexis( entry = list(Per=dodm, Age=dodm-dobth, DMdur=0 ), exit = list(Per=dox), exit.status = factor(!is.na(dodth),labels=c("DM","Dead")), data = DMlate ) # A small subset for illustration dml <- subset( dml, lex.id \%in\% c(13,15,20,28,40) ) # Cut the follow-up at start of insulin therapy dmi <- cutLexis( dml, cut = dml$doins, pre = "DM", new.state = "Ins" )[,1:10] # How does it look? dmi # Remove all transitions DM -> Ins rm.tr( dmi, "DM", "Ins" ) } \keyword{manip} Epi/man/projection.ip.Rd0000644000176200001440000000171613751040403014616 0ustar liggesusers\name{projection.ip} \alias{projection.ip} \title{ Projection of columns of a matrix. } \description{ Projects the columns of the matrix \code{M} on the space spanned by the columns of the matrix \code{X}, with respect to the inner product defined by \code{weight}: \code{=sum(x*w*y)}. } \usage{ projection.ip(X, M, orth = FALSE, weight = rep(1, nrow(X))) } \arguments{ \item{X}{ Matrix defining the space to project onto. } \item{M}{ Matrix of columns to be projected. Must have the same number of rows as \code{X}. } \item{orth}{ Should the projection be on the orthogonal complement to \code{span(X)}? } \item{weight}{ Weights defining the inner product. Numerical vector of length \code{nrow(X)}. } } \value{ A matrix of full rank with columns in \code{span(X)} } \author{ Bendix Carstensen, Steno Diabetes Center, \url{http://bendixcarstensen.com}, with help from Peter Dalgaard. } \seealso{ \code{\link{detrend}} } \keyword{array} Epi/man/harm.Rd0000644000176200001440000000223213751040403012754 0ustar liggesusers\name{harm} \alias{harm} \title{Create a basis of harmonic functions. } \description{Returns a matrix of harmonic functions usable for modeling periodic effects } \usage{ harm(x, ord=1, per=1, verbose=FALSE ) } \arguments{ \item{x}{A numeric variable. } \item{ord}{Integer, the order of the harmonic. } \item{per}{Numeric, the length of the period on the \code{x} scale. } \item{verbose}{Logical: shall I tell what I do with dates? } } \details{ Columns are constructed under the assumption that the periodic function has period \code{per} on the \code{x} scale. Thus, the first columns is defined as \code{sin(2*pi*x/per)}, \code{cos(2*pi*x/per)}, \code{sin(4*pi*x/per)} etc. Since \code{sin} and \code{cos} are periodic functions there is no requirement that \code{x} be in any particular range. } \value{A matrix with \code{nrow(x)} rows and 2*\code{deg} columns and columnnames \code{sin1}, \code{cos1}, \code{sin2}, \code{cos2} etc. } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com} } \examples{ x <- seq(-1,1,0.01) head( harm(x,ord=2) ) matplot( x, harm(x,ord=2), type="l", lty=1, lwd=3 ) } \keyword{models} \keyword{regression} Epi/man/ci.Crisk.Rd0000644000176200001440000001467514003725771013521 0ustar liggesusers\name{ci.Crisk} \alias{ci.Crisk} \alias{sim2ci.Crisk} \alias{sim2ci.Srisk} \alias{sim2ci.Stime} \title{ Compute cumulative risk and/or expected sojourn time from competing risks models. } \description{ Consider a list of parametric models for rates of competing events, such as different causes of death, A, B, C, say. From estimates of the cause-specific rates we can then by simple numerical integration compute the cumulative risk of being in each state ('Surv' (=no event) and A, B and C) at different times, as well as the stacked cumulative rates such as A, A+C, A+C+Surv. Finally, we can compute the expected (truncated) sojourn times in each state up to each time point. This function does this for simulated samples from the parameter vectors of supplied model objects, and computes the mentioend quantities with simulation-based confidence intervals. Some call this a prametric bootstrap. The times and other covariates determining the cause-specific rates must be supplied in a data frame which will be used for predicting rates for all transitions. } \usage{ ci.Crisk(mods, nd, int = mean(diff(nd[, 1])), nB = 1000, perm = length(mods):0 + 1, alpha = 0.05, sim.res = 'none') sim2ci.Crisk(probs, alpha = 0.05) sim2ci.Srisk(probs, perm = 1:dim(probs)[2], alpha = 0.05) sim2ci.Stime(probs, int = attr(probs, "int"), alpha = 0.05) } \arguments{ \item{mods}{A named list of \code{glm}/\code{gam} model objects representing the cause-specific rates. If the list is not named the function will crash. The names will be used as names for the states (competing risks), while the state without any event will be called "\code{Surv}". } \item{nd}{A data frame of prediction points and covariates. Must represent midpoints of equidistant intervals. } \item{int}{Numeric, the length of the intervals. Defaults to the differences in the first column of \code{nd}. } \item{nB}{Scalar. The number of simulations, that is samples from the (posterior) distribution of the model parameters. } \item{perm}{Numerical vector of length \code{lengh(mods)+1} indicating the order in which states are to be stacked. The \code{'Surv'} state is taken to be the first, the remaining in the reverse order supplied in the \code{mods} argument. The default is therefore to stack with the survival as the first, which may not be what you normally want. } \item{alpha}{numeric. 1 minus the confidence level used in calculating the c.i.s } \item{sim.res}{Character. What simulation samples should be returned. If \code{'none'} (the default) the function returns a list of 3 arrays (see under 'value'). If \code{'rates'} it returns an array of dimension \code{nrow(nd)} x \code{length(mod)} x \code{nB} of bootstrap samples of the rates. If \code{'crisk'} it returns an array of dimension \code{(nrow(nd)+1)} x \code{length(mod)} x \code{nB} of bootstrap samples of the culmulative rates. Only the first letter matters, regardless of whether it is in upper lower case. } \item{probs}{Three-way array of simulated cumulative risks classified by 1) time points, 2) causes (incl. surv) and 3) Samples. A structure as returned by \code{ci.Crisk} with \code{sim.res='crisk'}. } } \value{A named list of three-way arrays with results from simulation (parametric bootstrap) from the distribution of the parameters in the models in \code{mods}: \itemize{ \item \code{Crisk} Cumulative risks for the \code{length(mods)} events \emph{and} the survival \item \code{Srisk} Stacked versions of the cumulative risks \item \code{Stime} Sojourn times in each states } All three arrays have (almost) the same dimensions: \itemize{ \item \code{time}: end points of intervals starting with "\code{0}". Length \code{nrow(nd)+1}, except for \code{Stime} where it is only \code{nrow(nd)}, "\code{0}" not included. \item State. \code{Crisk} and \code{Stime} has values \code{Surv} plus the names of the list \code{mods} (first argument). \code{Srisk} has length \code{length(mod)}, with each level representing a cumultive sum of cumulatieve risks, in order indicated by the \code{perm} argument. \item \code{ci.50\%}, \code{ci.2.5\%}, \code{ci.97.5\%} representing quantiles of the quantities derived from the bootstrap samples. If \code{alpha} is different from 0.05, names are of course different. } } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com} } \seealso{ \code{\link{mat2pol}} \code{\link{simLexis}} \code{\link{plotCIF}} \code{\link{ci.surv}} } \examples{ library(Epi) data(DMlate) # A Lexis object for survival Ldm <- Lexis(entry = list( per = dodm, age = dodm-dobth, tfd = 0 ), exit = list( per = dox ), exit.status = factor( !is.na(dodth), labels = c("DM","Dead") ), data = DMlate[sample(1:nrow(DMlate),1000),] ) summary(Ldm, timeScales = TRUE) # Cut at OAD and Ins times Mdm <- mcutLexis( Ldm, wh = c('dooad','doins'), new.states = c('OAD','Ins'), precursor = 'Alive', seq.states = FALSE, ties = TRUE ) summary( Mdm$lex.dur ) # restrict to DM state Sdm <- splitLexis(factorize(subset(Mdm, lex.Cst == "DM")), time.scale = "tfd", breaks = seq(0,20,1/12)) summary(Sdm) summary(Relevel(Sdm, c(1, 4, 2, 3))) boxes(Relevel(Sdm, c(1, 4, 2, 3)), boxpos = list(x = c(15, 85, 80, 15), y = c(85, 85, 20, 15)), scale.R = 100) # glm models for the cause-specific rates system.time( mD <- glm.Lexis(Sdm, ~ Ns(tfd, knots=0:6*2), to = 'Dead') ) system.time( mO <- glm.Lexis(Sdm, ~ Ns(tfd, knots=0:6*2), to = 'OAD' ) ) system.time( mI <- glm.Lexis(Sdm, ~ Ns(tfd, knots=0:6*2), to = 'Ins' ) ) # intervals for calculation of predicted rates int <- 1/100 nd <- data.frame( tfd = seq(int,10,int)-int/2 ) # not the same as the split, # and totally unrelated to it # cumulaive risks with confidence intervals # (too few timepoints, too few simluations) system.time( res <- ci.Crisk(list(OAD = mO, Ins = mI, Dead = mD), nd = data.frame(tfd = (1:100-0.5)/10), nB = 100, perm = 4:1)) str(res) } \keyword{regression} Epi/man/B.dk.Rd0000644000176200001440000000421113751040403012602 0ustar liggesusers\name{B.dk} \alias{B.dk} \docType{data} \title{Births in Denmark by year and month of birth and sex} \description{ The number of live births as entered from printed publications from Statistics Denmark. } \usage{data(B.dk)} \format{ A data frame with 1248 observations on the following 4 variables. \describe{ \item{\code{year}}{Year of birth} \item{\code{month}}{Month of birth} \item{\code{m}}{Number of male births} \item{\code{f}}{Number of female births} } } \details{ Division of births by month and sex is only avaialble for the years 1957--69 and 2002ff. For the remaining period, the total no. births in each month is divided between the sexes so that the fraction of boys is equal to the overall fraction for the years where the sex information is available. There is a break in the series at 1920, when Sonderjylland was joined to Denmark. } \source{ Statistiske Undersogelser nr. 19: Befolkningsudvikling og sundhedsforhold 1901-60, Copenhagen 1966. Befolkningens bevaegelser 1957. Befolkningens bevaegelser 1958. ... Befolkningens bevaegelser 2003. Befolkningens bevaegelser 2004. Vital Statistics 2005. Vital Statistics 2006. } \examples{ data( B.dk ) str( B.dk ) attach( B.dk ) # Plot the no of births and the M/F-ratio par( las=1, mar=c(4,4,2,4) ) matplot( year+(month-0.5)/12, cbind( m, f ), bty="n", col=c("blue","red"), lty=1, lwd=1, type="l", ylim=c(0,5000), xlab="Date of birth", ylab="" ) usr <- par()$usr mtext( "Monthly no. births in Denmark", side=3, adj=0, at=usr[1], line=1/1.6 ) text( usr[1:2] \%*\% cbind(c(19,1),c(19,1))/20, usr[3:4] \%*\% cbind(c(1,19),c(2,18))/20, c("Boys","Girls"), col=c("blue","red"), adj=0 ) lines( year+(month-0.5)/12, (m/(m+f)-0.5)*30000, lwd=1 ) axis( side=4, at=(seq(0.505,0.525,0.005)-0.5)*30000, labels=c("","","","",""), tcl=-0.3 ) axis( side=4, at=(50:53/100-0.5)*30000, labels=50:53, tcl=-0.5 ) axis( side=4, at=(0.54-0.5)*30000, labels="\% boys", tick=FALSE, mgp=c(3,0.1,0) ) abline( v=1920, col=gray(0.8) ) } \keyword{datasets} Epi/man/ewrates.Rd0000644000176200001440000000172213751040403013502 0ustar liggesusers\name{ewrates} \alias{ewrates} \docType{data} \title{Rates of lung and nasal cancer mortality, and total mortality.} \description{ England and Wales mortality rates from lung cancer, nasal cancer, and all causes 1936 - 1980. The 1936 rates are repeated as 1931 rates in order to accomodate follow up for the \code{\link{nickel}} study. } \usage{data(ewrates)} \format{ A data frame with 150 observations on the following 5 variables: \tabular{rl}{ \code{id}: \tab Subject identifier (numeric) \cr \code{year} \tab Calendar period, 1931: 1931--35, 1936: 1936--40, \ldots \cr \code{age} \tab Age class: 10: 10--14, 15:15--19, \ldots \cr \code{lung} \tab Lung cancer mortality rate per 1,000,000 py. \cr \code{nasal} \tab Nasal cancer mortality rate per 1,000,000 py. \cr \code{other} \tab All cause mortality rate per 1,000,000 py. } } \source{ From Breslow and Day, Vol II, Appendix IX. } \examples{ data(ewrates) str(ewrates) } \keyword{datasets} Epi/man/plotevent.Rd0000644000176200001440000000216413751040403014051 0ustar liggesusers\name{plotevent} \alias{plotevent} \title{ Plot Equivalence Classes } \description{ For interval censored data, segments of times between last.well and first.ill are plotted for each conversion in the data. It also plots the equivalence classes. } \usage{ plotevent(last.well, first.ill, data) } \arguments{ \item{last.well}{ Time at which the individuals are last seen negative for the event } \item{first.ill}{ Time at which the individuals are first seen positive for the event } \item{data}{ Data with a transversal shape } } \details{ last.well and first.ill should be written as character in the function. } \value{ Graph } \references{ Carstensen B. Regression models for interval censored survival data: application to HIV infection in Danish homosexual men.Stat Med. 1996 Oct 30;15(20):2177-89. Lindsey JC, Ryan LM. Tutorial in biostatistics methods for interval-censored data.Stat Med. 1998 Jan 30;17(2):219-38. } \author{ Delphine Maucort-Boulch, Bendix Carstensen, Martyn Plummer } \seealso{ \code{\link{Icens}} } % \examples{ % } \keyword{ models } \keyword{ regression } \keyword{ survival } Epi/man/addCov.Lexis.Rd0000644000176200001440000001142214004041532014305 0ustar liggesusers\name{addCov.Lexis} \alias{addCov.Lexis} \title{ Add covariates (typically clinical measurements) taken at known times to a Lexis object. } \description{ When follow-up in a multistate model is represented in a \code{\link{Lexis}} object we may want to add information on covariates, for example clinical measurements, obtained at different times. This function cuts the follow-up time (see \code{\link{cutLexis}}) at the times of measurement and carries the measurements forward in time to the next measurement occasion. } \usage{ \method{addCov}{Lexis}(Lx, clin, timescale = 1, exnam, tfc = "tfc") } \arguments{ \item{Lx}{ A Lexis object with follow-up of a cohort. } \item{clin}{ A data frame with covariates to add (typically clinical measurements). Must contain a variable \code{lex.id} identifying the persons represented in \code{Lx}, as well as a variable with the same name as one of the \code{\link{timeScales}} in \code{Lx}, identifying the time at which covariates are measured. The times must be unique within each person; if not records with duplicate times are discarded, and a warning issued. This is done using \code{duplicated}, so not very well-defined, it is advisable that you do this by yourself. } \item{timescale}{ Numerical or character. Number or name of a timescale in \code{Lx}. The \code{clin} data frame must have a variable of this name indicating the time at which the covariate measurements were taken. } \item{exnam}{ Character. Name of the variable in \code{clin} with the examination names (such as \code{wave1}, \code{wave2} etc.). Values may not be repeated within person and cannot be equal to any of \code{levels(Lx)}. Will be carried over to the resulting \code{Lexis} object. If there is no such variable in \code{clin} it will be constructed; if the argument is omitted, a variable called \code{exnam} with values \code{ex1}, \code{ex2} etc. will be constructed. } \item{tfc}{ Character (\code{t}ime \code{f}rom \code{c}linical visit). Name of the variable in the result which will contain the time since the most recent covariate date. If the argument is omitted a variable called \code{tfc} will be constructed. If \code{addScales} is \code{TRUE} this is included among the time scales, even it is not formally a time scale. } } \value{ A \code{Lexis} object representing the same follow-up as \code{Lx}, with cuts added at the times of examination, and covariate measurements added for all records representing follow-up after the most recent time of measurement. } \author{ Bendix Carstensen, \email{b@bxc.dk}, \url{http://bendixcarstensen.com} } \seealso{ \code{\link{cutLexis}}, \code{\link{mcutLexis}}, \code{\link{splitLexis}}, \code{\link{Lexis}} } \examples{ # A small bogus cohort xcoh <- structure( list( id = c("A", "B", "C"), birth = c("1952-07-14", "1954-04-01", "1987-06-10"), entry = c("1965-08-04", "1972-09-08", "1991-12-23"), exit = c("1997-06-27", "1995-05-23", "1998-07-24"), fail = c(1, 0, 1) ), .Names = c("id", "birth", "entry", "exit", "fail"), row.names = c("1", "2", "3"), class = "data.frame" ) # Convert the character dates into numerical variables (fractional years) xcoh$bt <- cal.yr( xcoh$birth ) xcoh$en <- cal.yr( xcoh$entry ) xcoh$ex <- cal.yr( xcoh$exit ) # Define as Lexis object with timescales calendar time and age Lcoh <- Lexis( entry = list( per=en ), exit = list( per=ex, age=ex-bt ), exit.status = factor( fail, 0:1, c("Alive","Dead") ), data = xcoh ) str( Lcoh ) Lx <- Lcoh[,1:7] # Data frame with clinical examination data, date of examination in per clin <- data.frame( lex.id = c(1,1,3,2), per = c(1977.3,1971.7,1996.2,1990.6), bp = c(120,140,160,157), chol = c(5,7,8,9), xnam = c("X2","X1","X1","X2") ) Lx clin # Different behavours using exnam and addScales addCov.Lexis( Lx, clin ) addCov.Lexis( Lx, clin, exnam="xnam" ) # Works with time split BEFORE Lb <- addCov.Lexis(splitLexis(Lx, time.scale="age", breaks=seq(0,80,5) ), clin, exnam="clX" ) Lb # and also AFTER La <- splitLexis(addCov.Lexis( Lx, clin, exnam = "xnam" ), breaks=seq(0,80,5), time.scale="age" ) La La$tfc == Lb$tfc La$age == Lb$age str(La) str(Lb) } \keyword{ survival } Epi/man/erl.Rd0000644000176200001440000001751513751040403012621 0ustar liggesusers\name{erl} \alias{surv1} \alias{surv2} \alias{erl1} \alias{erl} \alias{yll} \title{Compute survival functions from rates and expected residual lifetime in an illness-death model as well as years of life lost to disease. } \description{ These functions compute survival functions from a set of mortality and disease incidence rates in an illness-death model. Expected residual life time can be computed under various scenarios by the \code{erl} function, and areas between survival functions can be computed under various scenarios by the \code{yll} function. Rates are assumed supplied for equidistant intervals of length \code{int}. } \usage{ surv1( int, mu , age.in = 0, A = NULL ) erl1( int, mu , age.in = 0 ) surv2( int, muW, muD, lam, age.in = 0, A = NULL ) erl( int, muW, muD, lam=NULL, age.in = 0, A = NULL, immune = is.null(lam), yll=TRUE, note=TRUE ) yll( int, muW, muD, lam=NULL, age.in = 0, A = NULL, immune = is.null(lam), note=TRUE ) } \arguments{ \item{int}{ Scalar. Length of intervals that rates refer to. } \item{mu}{ Numeric vector of mortality rates at midpoints of intervals of length \code{int} } \item{muW}{ Numeric vector of mortality rates among persons in the "Well" state at midpoints of intervals of length \code{int}. Left endpoint of first interval is \code{age.in}. } \item{muD}{ Numeric vector of mortality rates among persons in the "Diseased" state at midpoints of intervals of length \code{int}. Left endpoint of first interval is \code{age.in}. } \item{lam}{ Numeric vector of disease incidence rates among persons in the "Well" state at midpoints of intervals of length \code{int}. Left endpoint of first interval is \code{age.in}. } \item{age.in}{ Scalar indicating the age at the left endpoint of the first interval. } \item{A}{ Numeric vector of conditioning ages for calculation of survival functions. } \item{immune}{ Logical. Should the years of life lost to the disease be computed using assumptions that non-diseased individuals are immune to the disease (\code{lam}=0) and that their mortality is yet still \code{muW}. } \item{note}{ Logical. Should a warning of silly assumptions be printed? } \item{yll}{ Logical. Should years of life lost be included in the result? } } \details{ The mortality rates given are supposed to refer to the ages \code{age.in+(i-1/2)*int}, \code{i=1,2,3,...}. The units in which \code{int} is given must correspond to the units in which the rates \code{mu}, \code{muW}, \code{muD} and \code{lam} are given. Thus if \code{int} is given in years, the rates must be given in the unit of events per year. The ages in which the survival curves are computed are from \code{age.in} and then at the end of \code{length(muW)} (\code{length(mu)}) intervals each of length \code{int}. The \code{age.in} argument is merely a device to account for rates only available from a given age. It has two effects, one is that labeling of the interval endpoint is offset by this quantity, thus starting at \code{age.in}, and the other that the conditioning ages given in the argument \code{A} will refer to the ages defined by this. The \code{immune} argument is \code{FALSE} whenever the disease incidence rates are supplied. If set to \code{TRUE}, the years of life lost is computed under the assumption that individuals without the disease at a given age are immune to the disease in the sense that the disease incidence rate is 0, so transitions to the diseased state (with presumably higher mortality rates) are assumed not to occur. This is a slightly peculiar assumption (but presumably the most used in the epidemiological literature) and the resulting object is therefore given an attribute, \code{NOTE}, that point this out. If however \code{muW} is the total mortality in the population (including the diseased) the result is a good approximation to the correct YLL. The default of the \code{surv2} function is to take the possibility of disease into account.} \value{\code{surv1} and \code{surv2} return a matrix whose first column is the ages at the ends of the intervals, thus with \code{length(mu)+1} rows. The following columns are the survival functions (since \code{age.in}), and conditional on survival till ages as indicated in \code{A}, thus a matrix with \code{length(A)+2} columns. Columns are labeled with the actual conditioning ages; if \code{A} contains values that are not among the endpoints of the intervals used, the nearest smaller interval border is used as conditioning age, and columns are named accordingly. \code{surv1} returns the survival function for a simple model with one type of death, occurring at intensity \code{mu}. \code{surv2} returns the survival function for a person in the "Well" state of an illness-death model, taking into account that the person may move to the "Diseased" state, thus requiring all three transition rates to be specified. The conditional survival functions are conditional on being in the "Well" state at ages given in \code{A}. \code{erl1} returns a three column matrix with columns \code{age}, \code{surv} (survival function) and \code{erl} (expected residual life time) with \code{length(mu)+1} rows. \code{erl} returns a two column matrix, columns labeled "Well" and "Dis", and with row-labels \code{A}. The entries are the expected residual life times given survival to \code{A}. If \code{yll=TRUE} the difference between the columns is added as a third column, labeled "YLL". } \author{Bendix Carstensen, \email{b@bxc.dk} } \seealso{ \code{\link{ci.cum}} } \examples{ library( Epi ) data( DMlate ) # Naive Lexis object Lx <- Lexis( entry = list( age = dodm-dobth ), exit = list( age = dox -dobth ), exit.status = factor( !is.na(dodth), labels=c("DM","Dead") ), data = DMlate ) # Cut follow-up at insulin inception Lc <- cutLexis( Lx, cut = Lx$doins-Lx$dob, new.state = "DM/ins", precursor.states = "DM" ) summary( Lc ) # Split in small age intervals Sc <- splitLexis( Lc, breaks=seq(0,120,2) ) summary( Sc ) # Overview of object boxes( Sc, boxpos=TRUE, show.BE=TRUE, scale.R=100 ) # Knots for splines a.kn <- 2:9*10 # Mortality among DM mW <- glm( lex.Xst=="Dead" ~ Ns( age, knots=a.kn ), offset = log(lex.dur), family = poisson, data = subset(Sc,lex.Cst=="DM") ) # Mortality among insulin treated mI <- update( mW, data = subset(Sc,lex.Cst=="DM/ins") ) # Total motality mT <- update( mW, data = Sc ) # Incidence of insulin inception lI <- update( mW, lex.Xst=="DM/ins" ~ . ) # From these we can now derive the fitted rates in intervals of 1 year's # length. In real applications you would use much smaller interval like # 1 month: # int <- 1/12 int <- 1 # Prediction frame to return rates in units of cases per 1 year # - we start at age 40 since rates of insulin inception are largely # indeterminate before age 40 nd <- data.frame( age = seq( 40+int, 110, int ) - int/2, lex.dur = 1 ) muW <- predict( mW, newdata = nd, type = "response" ) muD <- predict( mI, newdata = nd, type = "response" ) lam <- predict( lI, newdata = nd, type = "response" ) # Compute the survival function, and the conditional from ages 50 resp. 70 s1 <- surv1( int, muD, age.in=40, A=c(50,70) ) round( s1, 3 ) s2 <- surv2( int, muW, muD, lam, age.in=40, A=c(50,70) ) round( s2, 3 ) # How much is YLL overrated by ignoring insulin incidence? round( YLL <- cbind( yll( int, muW, muD, lam, A = 41:90, age.in = 40 ), yll( int, muW, muD, lam, A = 41:90, age.in = 40, immune=TRUE ) ), 2 )[seq(1,51,10),] par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, bty="n", las=1 ) matplot( 40:90, YLL, type="l", lty=1, lwd=3, ylim=c(0,10), yaxs="i", xlab="Age" ) } \keyword{survival} Epi/man/plotEst.Rd0000644000176200001440000001057113751040403013464 0ustar liggesusers\name{plotEst} \alias{plotEst} \alias{pointsEst} \alias{linesEst} \title{ Plot estimates with confidence limits (forest plot) } \description{ Plots parameter estimates with confidence intervals, annotated with parameter names. A dot is plotted at the estimate and a horizontal line extending from the lower to the upper limit is superimposed. } \usage{ plotEst( ests, y = dim(ests)[1]:1, txt = rownames(ests), txtpos = y, ylim = range(y)-c(0.5,0), xlab = "", xtic = nice(ests[!is.na(ests)], log = xlog), xlim = range( xtic ), xlog = FALSE, pch = 16, cex = 1, lwd = 2, col = "black", col.txt = "black", font.txt = 1, col.lines = col, col.points = col, vref = NULL, grid = FALSE, col.grid = gray(0.9), restore.par = TRUE, ... ) linesEst( ests, y = dim(ests)[1]:1, pch = 16, cex = 1, lwd = 2, col="black", col.lines=col, col.points=col, ... ) pointsEst( ests, y = dim(ests)[1]:1, pch = 16, cex = 1, lwd = 2, col="black", col.lines=col, col.points=col, ... ) } \arguments{ \item{ests}{Matrix with three columns: Estimate, lower limit, upper limit. If a model object is supplied, \code{\link{ci.lin}} is invoked for this object first.} \item{y}{Vertical position of the lines.} \item{txt}{Annotation of the estimates. Either a character vector or an expression vector.} \item{txtpos}{Vertical position of the text. Defaults to \code{y}.} \item{ylim}{Extent of the vertical axis.} \item{xlab}{Annotation of the horizontal axis.} \item{xtic}{Location of tickmarks on the x-axis.} \item{xlim}{Extent of the x-axis.} \item{xlog}{Should the x-axis be logarithmic?} \item{pch}{What symbol should be used?} \item{cex}{Expansion of the symbol.} \item{col}{Colour of the points and lines.} \item{col.txt}{Colour of the text annotating the estimates.} \item{font.txt}{Font for the text annotating the estimates.} \item{col.lines}{Colour of the lines.} \item{col.points}{Colour of the symbol.} \item{lwd}{Thickness of the lines.} \item{vref}{Where should vertical reference line(s) be drawn?} \item{grid}{If TRUE, vertical gridlines are drawn at the tickmarks. If a numerical vector is given vertical lines are drawn at \code{grid}.} \item{col.grid}{Colour of the vertical gridlines} \item{restore.par}{Should the graphics parameters be restored? If set to \code{FALSE} the coordinate system will still be available for additional plotting, and \code{par("mai")} will still have the very large value set in order to make room for the labelling of the estimates.} \item{...}{Arguments passed on to \code{ci.lin} when a model object is supplied as \code{ests}.} } \details{ \code{plotEst} makes a news plot, whereas \code{linesEst} and \code{pointsEst} (identical functions) adds to an existing plot. If a model object of class \code{"glm"}, \code{"coxph"}, \code{"clogistic"} or \code{"gnlm"} is supplied the argument \code{xlog} defaults to \code{TRUE}, and exponentiated estimates are extracted by default. } \value{ NULL } \author{ Bendix Carstensen, \email{b@bxc.dk}, \url{http://bendixcarstensen.com}} \seealso{ ci.lin } \examples{ # Bogus data and a linear model f <- factor( sample( letters[1:5], 100, replace=TRUE ) ) x <- rnorm( 100 ) y <- 5 + 2 * as.integer( f ) + 0.8 * x + rnorm(100) * 2 m1 <- lm( y ~ f ) # Produce some confidence intervals for contrast to first level ( cf <- ci.lin( m1, subset=-1 )[,-(2:4)] ) # Plots with increasing amounts of bells and whistles par( mfcol=c(3,2), mar=c(3,3,2,1) ) plotEst( cf ) plotEst( cf, grid=TRUE, cex=2, lwd=3 ) plotEst( cf, grid=TRUE, cex=2, col.points="red", col.lines="green" ) plotEst( cf, grid=TRUE, cex=2, col.points="red", col.lines="green", xlog=TRUE, xtic=c(1:8), xlim=c(0.8,6) ) rownames( cf )[1] <- "Contrast to fa:\n fb" plotEst( cf, grid=TRUE, cex=2, col.points=rainbow(4), col.lines=rainbow(4), vref=1 ) # etxt <- expression("Plain text, qouted", "combined with maths:"*sqrt(a)*phi[c], f^d*" Hb"*A[1][c], eff^e*" kg/"*m^2) plotEst( cf, txt=etxt, grid=TRUE, cex=2, col.points=rainbow(4), col.lines =rainbow(4), vref=1 ) } \keyword{hplot} \keyword{models} Epi/man/fit.add.Rd0000644000176200001440000000265713751040403013351 0ustar liggesusers\name{fit.add} \alias{fit.add} \title{ Fit an addive excess risk model to interval censored data. } \description{ Utility function. The model fitted assumes a piecewise constant intensity for the baseline, and that the covariates act additively on the rate scale. } \usage{ fit.add( y, rates.frame, cov.frame, start ) } \arguments{ \item{y}{Binary vector of outcomes} \item{rates.frame}{Dataframe expanded from the original data by \code{\link{expand.data}}, cooresponding to covariates for the rate parameters.} \item{cov.frame}{ do., but covariates corresponding to the \code{formula} argument of \code{\link{Icens}}} \item{start}{Starting values for the rate parameters. If not supplied, then starting values are generated.} } \value{ A list with one component: \item{rates}{A glm object from a binomial model with log-link function.} } \references{ B Carstensen: Regression models for interval censored survival data: application to HIV infection in Danish homosexual men. Statistics in Medicine, 15(20):2177-2189, 1996. CP Farrington: Interval censored survival data: a generalized linear modelling approach. Statistics in Medicine, 15(3):283-292, 1996. } \author{ Martyn Plummer, \email{martyn.plummer@r-project.org} } \seealso{ \code{\link{Icens}} \code{\link{fit.mult}} } \examples{ data( HIV.dk ) } \keyword{ models } \keyword{ regression } \keyword{ survival } Epi/man/ci.pd.Rd0000644000176200001440000000476313751040403013035 0ustar liggesusers\name{ci.pd} \alias{ci.pd} \title{ Compute confidence limits for a difference of two independent proportions. } \description{ The usual formula for the c.i. of at difference of proportions is inaccurate. Newcombe has compared 11 methods and method 10 in his paper looks like a winner. It is implemented here. } \usage{ ci.pd(aa, bb=NULL, cc=NULL, dd=NULL, method = "Nc", alpha = 0.05, conf.level=0.95, digits = 3, print = TRUE, detail.labs = FALSE ) } \arguments{ \item{aa}{Numeric vector of successes in sample 1. Can also be a matrix or array (see details).} \item{bb}{Successes in sample 2.} \item{cc}{Failures in sample 1.} \item{dd}{Failures in sample 2.} \item{method}{Method to use for calculation of confidence interval, see "Details".} \item{alpha}{Significance level} \item{conf.level}{Confidence level} \item{print}{Should an account of the two by two table be printed.} \item{digits}{How many digits should the result be rounded to if printed.} \item{detail.labs}{Should the computing of probability differences be reported in the labels.} } \details{ Implements method 10 from Newcombe(1998) (method="Nc") or from Agresti & Caffo(2000) (method="AC"). \code{aa}, \code{bb}, \code{cc} and \code{dd} can be vectors. If \code{aa} is a matrix, the elements \code{[1:2,1:2]} are used, with successes \code{aa[,1:2]}. If \code{aa} is a three-way table or array, the elements \code{aa[1:2,1:2,]} are used. } \value{ A matrix with three columns: probability difference, lower and upper limit. The number of rows equals the length of the vectors \code{aa}, \code{bb}, \code{cc} and \code{dd} or, if \code{aa} is a 3-way matrix, \code{dim(aa)[3]}. } \references{ RG Newcombe: Interval estimation for the difference between independent proportions. Comparison of eleven methods. Statistics in Medicine, 17, pp. 873-890, 1998. A Agresti & B Caffo: Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures. The American Statistician, 54(4), pp. 280-288, 2000. } \author{ Bendix Carstensen, Esa Laara. \url{http://bendixcarstensen.com} } \seealso{ \code{\link{twoby2}}, \code{\link{binom.test}} } \examples{ ( a <- matrix( sample( 10:40, 4 ), 2, 2 ) ) ci.pd( a ) twoby2( t(a) ) prop.test( t(a) ) ( A <- array( sample( 10:40, 20 ), dim=c(2,2,5) ) ) ci.pd( A ) ci.pd( A, detail.labs=TRUE, digits=3 ) } \keyword{distribution} \keyword{htest} Epi/man/steno2.Rd0000644000176200001440000001047614007532512013252 0ustar liggesusers\name{steno2} \alias{steno2} \alias{st2clin} \alias{st2alb} \docType{data} \title{ Clinical trial: Steno2 baseline and follow-up. } \description{ Steno-2 was a clinical trial conducted at Steno Diabetes Center 1993-2001. The intervention was intensified treatment versus conventional treatment of diabetes patients with micro-albuminuria. The datsets here concern the extended follow-up of the trial population till 2015. Three files are provided: \code{steno2} with one record per person, \code{st2clin} with one record per clinical visit and \code{st2alb} with one record per transition between states of albuminuria. These dataset are entirely simulated, but designed to give approximately the same results as the original. } \usage{data("steno2") data("st2clin") data("st2alb") } \format{ \code{steno2} is a data frame with 160 observations on the following 14 variables: \describe{ \item{\code{id}}{person id, numeric} \item{\code{allo}}{Original trial allocation, a factor with levels \code{Int} \code{Conv}} \item{\code{sex}}{Sex, a factor with levels \code{F} \code{M}} \item{\code{baseCVD}}{0/1 indicator of preexisting CVD at baseline} \item{\code{deathCVD}}{0/1 indicator whether cause of death was CVD} \item{\code{doBth}}{Date of birth, a Date} \item{\code{doDM}}{Date of diabetes diagnosis, a Date} \item{\code{doBase}}{Date of entry to study, a Date} \item{\code{doCVD1}}{Date of 1st CVD event, a Date} \item{\code{doCVD2}}{Date of 2nd CVD event, a Date} \item{\code{doCVD3}}{Date of 3rd CVD event, a Date} \item{\code{doESRD}}{Date of end stage renal disease, a Date} \item{\code{doEnd}}{Date of exit from follow-up, a Date} \item{\code{doDth}}{Date of death, a Date} } \code{st2clin} is data frame with 750 observations on clinical measurements at different clinical visits: \describe{ \item{\code{id}}{person id, numeric} \item{\code{doV}}{Date of clinical visit, a Date} \item{\code{a1c}}{Glycosylated hemoglobin, mmol/mol} \item{\code{chol}}{Total cholesterol, mg/mol} \item{\code{crea}}{Creatinine, mg/mol} } \code{st2alb} is data frame with 307 observations of changes in complication (albuminuria) state \describe{ \item{\code{id}}{person id, numeric} \item{\code{doTr}}{Date of transition, a Date} \item{\code{state}}{State of albuminuria, factor with levels \code{Norm}, \code{Mic}, \code{Mac}. All persons begin in the state \code{Mic}ro-albuminuria.} } } \details{ The data are not the original; all values of measurements and dates have been randomly perturbed, to prevent identifiability of individuals. Analysis of these data will give only (very) approximately the same results as in the published article, and only some of the aspects of data are included. } \references{ P. Gaede, J. Oellgaard, B. Carstensen, P. Rossing, H. Lund-Andersen, H. H. Parving & O. Pedersen: Years of life gained by multifactorial intervention in patients with type 2 diabetes mellitus and microalbuminuria: 21 years follow-up on the Steno-2 randomised trial. Diabetologia (2016), 59, pp 2298-2307 } \examples{ data(steno2) data(st2alb) L2 <- Lexis( entry = list(per = doBase, age = doBase - doBth), exit = list(per = doEnd), exit.status = factor(deathCVD + !is.na(doDth), labels=c("Mic","D(oth)","D(CVD)")), id = id, data = cal.yr(steno2) ) summary(L2) # # Cut at intermediate transitions cut2 <- data.frame(lex.id = st2alb$id, cut = cal.yr(st2alb$do), new.state = st2alb$state) L3 <- rcutLexis(L2, cut2) summary(L3) # # no direct transitions Mic <-> Mac allowed, so put a cut in between: dd <- subset(L3, (lex.Cst == "Mac" & lex.Xst =="Norm") | (lex.Cst =="Norm" & lex.Xst == "Mac")) # artificial visits to the middle state Mic: cut3 <- data.frame( lex.id = dd$lex.id, cut = dd$per + dd$lex.dur/2, new.state = "Mic") L4 <- rcutLexis(L3, cut3) summary(L4) # # Show all transitions boxes(L4, boxpos = list(x = c(15,15,15,85,85), y = c(50,15,85,25,75)), show.BE = TRUE, scale.R = 1000, cex=0.8, pos.arr=0.7, font=1, font.arr=1) } \keyword{datasets} Epi/man/boxes.MS.Rd0000644000176200001440000003676113763206455013517 0ustar liggesusers\name{boxes.MS} \Rdversion{1.1} \alias{tbox} \alias{dbox} \alias{fillarr} \alias{boxarr} \alias{boxes} \alias{boxes.Lexis} \alias{boxes.matrix} \alias{boxes.MS} \title{ Draw boxes and arrows for illustration of multistate models. } \description{ Boxes can be drawn with text (\code{tbox}) or a cross (\code{dbox}), and arrows pointing between the boxes (\code{boxarr}) can be drawn automatically not overlapping the boxes. The \code{boxes} method for \code{\link{Lexis}} objects generates displays of states with person-years and transitions with events or rates. } \usage{ tbox( txt, x, y, wd, ht, font=2, lwd=2, col.txt=par("fg"), col.border=par("fg"), col.bg="transparent" ) dbox( x, y, wd, ht=wd, font=2, lwd=2, cwd=5, col.cross=par("fg"), col.border=par("fg"), col.bg="transparent" ) boxarr( b1, b2, offset=FALSE, pos=0.45, ... ) \method{boxes}{Lexis}( obj, boxpos = FALSE, wmult = 1.20, hmult = 1.20 + 0.85*(!show.Y), cex = 1.40, show = inherits( obj, "Lexis" ), show.Y = show, scale.Y = 1, digits.Y = 1, show.BE = FALSE, BE.sep = c("",""," ",""), show.D = show, scale.D = FALSE, digits.D = as.numeric(as.logical(scale.D)), show.R = show & is.numeric(scale.R), scale.R = 1, digits.R = as.numeric(as.logical(scale.R)), DR.sep = if( show.D ) c("\n(",")") else c("",""), eq.wd = TRUE, eq.ht = TRUE, wd, ht, subset = NULL, exclude = NULL, font = 1, lwd = 2, col.txt = par("fg"), col.border = col.txt, col.bg = "transparent", col.arr = par("fg"), lwd.arr = lwd, font.arr = font, pos.arr = 0.45, txt.arr = NULL, col.txt.arr = col.arr, offset.arr = 2, ... ) \method{boxes}{matrix}( obj, ... ) \method{boxes}{MS}( obj, sub.st, sub.tr, cex=1.5, ... ) fillarr( x1, y1, x2, y2, gap=2, fr=0.8, angle=17, lwd=2, length=par("pin")[1]/30, ... ) } \arguments{ \item{txt}{Text to be placed inside the box.} \item{x}{x-coordinate of center of box.} \item{y}{y-coordinate of center of box.} \item{wd}{width of boxes in percentage of the plot width.} \item{ht}{height of boxes in percentage of the plot height.} \item{font}{Font for the text. Defaults to 2 (=bold).} \item{lwd}{Line width of the box borders.} \item{col.txt}{Color for the text in boxes.} \item{col.border}{Color of the box border.} \item{col.bg}{Background color for the interior of the box.} \item{\dots}{Arguments to be passed on to the call of other functions.} \item{cwd}{Width of the lines in the cross.} \item{col.cross}{Color of the cross.} \item{b1}{Coordinates of the "from" box. A vector with 4 components, \code{x}, \code{y}, \code{w}, \code{h}.} \item{b2}{Coordinates of the "to" box; like \code{b1}.} \item{offset}{Logical. Should the arrow be offset a bit to the left.} \item{pos}{Numerical between 0 and 1, determines the position of the point on the arrow which is returned.} \item{obj}{A \code{\link{Lexis}} object or a transition matrix; that is a square matrix indexed by state in both dimensions, and the \eqn{(i,j)}th entry different from \code{NA} if a transition \eqn{i} to \eqn{j} can occur. If \code{show.D=TRUE}, the arrows between states are annotated by these numbers. If \code{show.Y=TRUE}, the boxes representing states are annotated by the numbers in the diagonal of \code{obj}. For \code{boxes.matrix} \code{obj} is a matrix and for \code{boxes.MS}, \code{obj} is an \code{MS.boxes} object (see below).} \item{boxpos}{If \code{TRUE} the boxes are positioned equidistantly on a circle, if \code{FALSE} (the default) you are queried to click on the screen for the positions. This argument can also be a named list with elements \code{x} and \code{y}, both numerical vectors, giving the centers of the boxes. These must be numbers between 0 and 100 indicating percentages of the display in the two directions.} \item{wmult}{Multiplier for the width of the box relative to the width of the text in the box.} \item{hmult}{Multiplier for the height of the box relative to the height of the text in the box.} \item{cex}{Character expansion for text in the box.} \item{show}{Should person-years and transitions be put in the plot. Ignored if \code{obj} is not a \code{Lexis} object.} \item{show.Y}{If logical: Should person-years be put in the boxes. If numeric: Numbers to put in boxes.} \item{scale.Y}{What scale should be used for annotation of person-years.} \item{digits.Y}{How many digits after the decimal point should be used for the person-years.} \item{show.BE}{Logical. Should number of persons beginning resp. ending follow up in each state be shown? If given as character "nz" or "noz" the numbers will be shown, but zeros omitted.} \item{BE.sep}{Character vector of length 4, used for annotation of the number of persons beginning and ending in each state: 1st element precedes no. beginning, 2nd trails it, 3rd precedes the no. ending (defaults to 8 spaces), and the 4th trails the no. ending.} \item{show.D}{Should no. transitions be put alongside the arrows. Ignored if \code{obj} is not a \code{Lexis} object.} \item{scale.D}{Synonymous with \code{scale.R}, retained for compatibility.} \item{digits.D}{Synonymous with \code{digits.R}, retained for compatibility.} \item{show.R}{Should the transition rates be shown on the arrows?} \item{scale.R}{If this a scalar, rates instead of no. transitions are printed at the arrows, scaled by \code{scale.R}.} \item{digits.R}{How many digits after the decimal point should be used for the rates.} \item{DR.sep}{Character vector of length 2. If rates are shown, the first element is inserted before and the second after the rate.} \item{eq.wd}{Should boxes all have the same width?} \item{eq.ht}{Should boxes all have the same height?} \item{subset}{Draw only boxes and arrows for a subset of the states. Can be given either as a numerical vector or character vector state names.} \item{exclude}{Exclude states from the plot. The complementary of \code{subset}. Ignored if \code{subset} is given.} \item{col.arr}{Color of the arrows between boxes. A vector of character strings, the arrows are referred to as the row-wise sequence of non-NA elements of the transition matrix. Thus the first ones refer to the transitions out of state 1, in order of states.} \item{lwd.arr}{Line widths of the arrows.} \item{font.arr}{Font of the text annotation the arrows.} \item{pos.arr}{Numerical between 0 and 1, determines the position on the arrows where the text is written.} \item{txt.arr}{Text put on the arrows.} \item{col.txt.arr}{Colors for text on the arrows.} \item{offset.arr}{The amount offset between arrows representing two-way transitions, that is where there are arrows both ways between two boxes.} \item{sub.st}{Subset of the states to be drawn.} \item{sub.tr}{Subset of the transitions to be drawn.} \item{x1}{x-coordinate of the starting point.} \item{y1}{y-coordinate of the starting point.} \item{x2}{x-coordinate of the end point.} \item{y2}{y-coordinate of the end point.} \item{gap}{Length of the gap between the box and the ends of the arrows.} \item{fr}{Length of the arrow as the fraction of the distance between the boxes. Ignored unless given explicitly, in which case any value given for \code{gap} is ignored.} \item{angle}{What angle should the arrow-head have?} \item{length}{Length of the arrow head in inches. Defaults to 1/30 of the physical width of the plot.} } \details{ These functions are designed to facilitate the drawing of multistate models, mainly by automatic calculation of the arrows between boxes. \code{tbox} draws a box with centered text, and returns a vector of location, height and width of the box. This is used when drawing arrows between boxes. \code{dbox} draws a box with a cross, symbolizing a death state. \code{boxarr} draws an arrow between two boxes, making sure it does not intersect the boxes. Only straight lines are drawn. \code{boxes.Lexis} takes as input a Lexis object sets up an empty plot area (with axes 0 to 100 in both directions) and if \code{boxpos=FALSE} (the default) prompts you to click on the locations for the state boxes, and then draws arrows implied by the actual transitions in the \code{Lexis} object. The default is to annotate the transitions with the number of transitions. A transition matrix can also be supplied, in which case the row/column names are used as state names, diagonal elements taken as person-years, and off-diagonal elements as number of transitions. This also works for \code{boxes.matrix}. Optionally returns the R-code reproducing the plot in a file, which can be useful if you want to produce exactly the same plot with differing arrow colors etc. \code{boxarr} draws an arrow between two boxes, on the line connecting the two box centers. The \code{offset} argument is used to offset the arrow a bit to the left (as seen in the direction of the arrow) on order to accommodate arrows both ways between boxes. \code{boxarr} returns a named list with elements \code{x}, \code{y} and \code{d}, where the two former give the location of a point on the arrow used for printing (see argument \code{pos}) and the latter is a unit vector in the direction of the arrow, which is used by \code{boxes.Lexis} to position the annotation of arrows with the number of transitions. \code{boxes.MS} re-draws what \code{boxes.Lexis} has done based on the object of class \code{MS} produced by \code{boxes.Lexis}. The point being that the \code{MS} object is easily modifiable, and thus it is a machinery to make variations of the plot with different color annotations etc. \code{fill.arr} is just a utility drawing nicer arrows than the default \code{\link{arrows}} command, basically by using filled arrow-heads; called by \code{boxarr}. } \value{The functions \code{tbox} and \code{dbox} return the location and dimension of the boxes, \code{c(x,y,w,h)}, which are designed to be used as input to the \code{boxarr} function. The \code{boxarr} function returns the coordinates (as a named list with names \code{x} and \code{y}) of a point on the arrow, designated to be used for annotation of the arrow. The function \code{boxes.Lexis} returns an \code{MS} object, a list with five elements: 1) \code{Boxes} - a data frame with one row per box and columns \code{xx}, \code{yy}, \code{wd}, \code{ht}, \code{font}, \code{lwd}, \code{col.txt}, \code{col.border} and \code{col.bg}, 2) an object \code{State.names} with names of states (possibly an expression, hence not possible to include as a column in \code{Boxes}), 3) a matrix \code{Tmat}, the transition matrix, 4) a data frame, \code{Arrows} with one row per transition and columns: \code{lwd.arr}, \code{col.arr}, \code{pos.arr}, \code{col.txt.arr}, \code{font.arr} and \code{offset.arr} and 5) an object \code{Arrowtext} with names of states (possibly an expression, hence not possible to include as a column in \code{Arrows}) An \code{MS} object is used as input to \code{boxes.MS}, the primary use is to modify selected entries in the \code{MS} object first, e.g. colors, or supply sub-setting arguments in order to produce displays that have the same structure, but with different colors etc. } \author{Bendix Carstensen} \examples{ par( mar=c(0,0,0,0), cex=1.5 ) plot( NA, bty="n", xlim=0:1*100, ylim=0:1*100, xaxt="n", yaxt="n", xlab="", ylab="" ) bw <- tbox( "Well" , 10, 60, 22, 10, col.txt="blue" ) bo <- tbox( "other Ca", 45, 80, 22, 10, col.txt="gray" ) bc <- tbox( "Ca" , 45, 60, 22, 10, col.txt="red" ) bd <- tbox( "DM" , 45, 40, 22, 10, col.txt="blue" ) bcd <- tbox( "Ca + DM" , 80, 60, 22, 10, col.txt="gray" ) bdc <- tbox( "DM + Ca" , 80, 40, 22, 10, col.txt="red" ) boxarr( bw, bo , col=gray(0.7), lwd=3 ) # Note the argument adj= can takes values outside (0,1) text( boxarr( bw, bc , col="blue", lwd=3 ), expression( lambda[Well] ), col="blue", adj=c(1,-0.2), cex=0.8 ) boxarr( bw, bd , col=gray(0.7) , lwd=3 ) boxarr( bc, bcd, col=gray(0.7) , lwd=3 ) text( boxarr( bd, bdc, col="blue", lwd=3 ), expression( lambda[DM] ), col="blue", adj=c(1.1,-0.2), cex=0.8 ) # Set up a transition matrix allowing recovery tm <- rbind( c(NA,1,1), c(1,NA,1), c(NA,NA,NA) ) rownames(tm) <- colnames(tm) <- c("Cancer","Recurrence","Dead") tm boxes.matrix( tm, boxpos=TRUE ) # Illustrate texting of arrows boxes.Lexis( tm, boxpos=TRUE, txt.arr=c("en","to","tre","fire") ) zz <- boxes( tm, boxpos=TRUE, txt.arr=c(expression(lambda[C]), expression(mu[C]), "recovery", expression(mu[R]) ) ) # Change color of a box zz$Boxes[3,c("col.bg","col.border")] <- "green" boxes( zz ) # Set up a Lexis object data(DMlate) str(DMlate) dml <- Lexis( entry=list(Per=dodm, Age=dodm-dobth, DMdur=0 ), exit=list(Per=dox), exit.status=factor(!is.na(dodth),labels=c("DM","Dead")), data=DMlate[1:1000,] ) # Cut follow-up at Insulin dmi <- cutLexis( dml, cut=dml$doins, new.state="Ins", pre="DM" ) summary( dmi ) boxes( dmi, boxpos=TRUE ) boxes( dmi, boxpos=TRUE, show.BE=TRUE ) boxes( dmi, boxpos=TRUE, show.BE="nz" ) boxes( dmi, boxpos=TRUE, show.BE="nz", BE.sep=c("In:"," Out:","") ) # Set up a bogus recovery date just to illustrate two-way transitions dmi$dorec <- dmi$doins + runif(nrow(dmi),0.5,10) dmi$dorec[dmi$dorec>dmi$dox] <- NA dmR <- cutLexis( dmi, cut=dmi$dorec, new.state="DM", pre="Ins" ) summary( dmR ) boxes( dmR, boxpos=TRUE ) boxes( dmR, boxpos=TRUE, show.D=FALSE ) boxes( dmR, boxpos=TRUE, show.D=FALSE, show.Y=FALSE ) boxes( dmR, boxpos=TRUE, scale.R=1000 ) MSobj <- boxes( dmR, boxpos=TRUE, scale.R=1000, show.D=FALSE ) MSobj <- boxes( dmR, boxpos=TRUE, scale.R=1000, DR.sep=c(" (",")") ) class( MSobj ) boxes( MSobj ) MSobj$Boxes[1,c("col.txt","col.border")] <- "red" MSobj$Arrows[1:2,"col.arr"] <- "red" boxes( MSobj ) } \seealso{ \code{\link{tmat.Lexis}} } \keyword{survival} \keyword{hplot} \keyword{iplot} Epi/man/Lexis.diagram.Rd0000644000176200001440000001160213751040403014515 0ustar liggesusers\name{Lexis.diagram} \alias{Lexis.diagram} \title{Plot a Lexis diagram} \description{ Draws a Lexis diagram, optionally with life lines from a cohort, and with lifelines of a cohort if supplied. Intended for presentation purposes. } \usage{ Lexis.diagram( age = c( 0, 60), alab = "Age", date = c( 1940, 2000 ), dlab = "Calendar time", int = 5, lab.int = 2*int, col.life = "black", lwd.life = 2, age.grid = TRUE, date.grid = TRUE, coh.grid = FALSE, col.grid = gray(0.7), lwd.grid = 1, las = 1, entry.date = NA, entry.age = NA, exit.date = NA, exit.age = NA, risk.time = NA, birth.date = NA, fail = NA, cex.fail = 1.1, pch.fail = c(NA,16), col.fail = rep( col.life, 2 ), data = NULL, ... ) } \arguments{ \item{age}{Numerical vector of length 2, giving the age-range for the diagram} \item{alab}{Label on the age-axis.} \item{date}{Numerical vector of length 2, giving the calendar time-range for the diagram} \item{dlab}{label on the calendar time axis.} \item{int}{The interval between grid lines in the diagram. If a vector of length two is given, the first value will be used for spacing of age-grid and the second for spacing of the date grid.} \item{lab.int}{The interval between labelling of the grids.} \item{col.life}{Colour of the life lines.} \item{lwd.life}{Width of the life lines.} \item{age.grid}{Should grid lines be drawn for age?} \item{date.grid}{Should grid lines be drawn for date?} \item{coh.grid}{Should grid lines be drawn for birth cohorts (diagonals)?} \item{col.grid}{Colour of the grid lines.} \item{lwd.grid}{Width of the grid lines.} \item{las}{How are the axis labels plotted?} \item{entry.date, entry.age, exit.date, exit.age, risk.time, birth.date}{Numerical vectors defining lifelines to be plotted in the diagram. At least three must be given to produce lines. Not all subsets of three will suffice, the given subset has to define life lines. If insufficient data is given, no life lines are produced.} \item{fail}{Logical of event status at exit for the persons whose life lines are plotted.} \item{pch.fail}{Symbols at the end of the life lines for censorings (\code{fail==0}) and failures (\code{fail != 0}).} \item{cex.fail}{Expansion of the status marks at the end of life lines.} \item{col.fail}{Character vector of length 2 giving the colour of the failure marks for censorings and failures respectively.} \item{data}{Dataframe in which to interpret the arguments.} \item{...}{Arguments to be passed on to the initial call to plot.} } \value{ If sufficient information on lifelines is given, a data frame with one row per person and columns with entry ages and dates, birth date, risk time and status filled in. Side effect: a plot of a Lexis diagram is produced with the life lines in it is produced. This will be the main reason for using the function. If the primary aim is to illustrate follow-up of a cohort, then it is better to represent the follow-up in a \code{\link{Lexis}} object, and use the generic \code{\link{plot.Lexis}} function. } \details{ The default unit for supplied variables are (calendar) years. If any of the variables \code{entry.date}, \code{exit.date} or \code{birth.date} are of class "\code{Date}" or if any of the variables \code{entry.age}, \code{exit.age} or \code{risk.time} are of class "\code{difftime}", they will be converted to calendar years, and plotted correctly in the diagram. The returned dataframe will then have colums of classes "\code{Date}" and "\code{difftime}". } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com} } \examples{ Lexis.diagram( entry.age = c(3,30,45), risk.time = c(25,5,14), birth.date = c(1970,1931,1925.7), fail = c(TRUE,TRUE,FALSE) ) LL <- Lexis.diagram( entry.age = sample( 0:50, 17, replace=TRUE ), risk.time = sample( 5:40, 17, r=TRUE), birth.date = sample( 1910:1980, 17, r=TRUE ), fail = sample( 0:1, 17, r=TRUE ), cex.fail = 1.1, lwd.life = 2 ) # Identify the persons' entry and exits text( LL$exit.date, LL$exit.age, paste(1:nrow(LL)), col="red", font=2, adj=c(0,1) ) text( LL$entry.date, LL$entry.age, paste(1:nrow(LL)), col="blue", font=2, adj=c(1,0) ) data( nickel ) attach( nickel ) LL <- Lexis.diagram( age=c(10,100), date=c(1900,1990), entry.age=age1st, exit.age=ageout, birth.date=dob, fail=(icd \%in\% c(162,163)), lwd.life=1, cex.fail=0.8, col.fail=c("green","red") ) abline( v=1934, col="blue" ) nickel[1:10,] LL[1:10,] } \keyword{hplot} \keyword{dplot} \seealso{ \code{\link{Life.lines}}, \code{\link{Lexis.lines}} } Epi/man/cal.yr.Rd0000644000176200001440000000554513751040403013227 0ustar liggesusers\name{cal.yr} \alias{cal.yr} \alias{as.Date.cal.yr} \title{ Functions to convert character, factor and various date objects into a number, and vice versa. } \description{ Dates are converted to a numerical value, giving the calendar year as a fractional number. 1 January 1970 is converted to 1970.0, and other dates are converted by assuming that years are all 365.25 days long, so inaccuracies may arise, for example, 1 Jan 2000 is converted to 1999.999. Differences between converted values will be 1/365.25 of the difference between corresponding \code{\link{Date}} objects. } \usage{ cal.yr( x, format="\%Y-\%m-\%d", wh=NULL ) \method{as.Date}{cal.yr}( x, ... ) } \arguments{ \item{x}{A factor or character vector, representing a date in format \code{format}, or an object of class \code{\link{Date}}, \code{\link{POSIXlt}}, \code{\link{POSIXct}}, \code{\link{date}}, \code{dates} or \code{chron} (the latter two requires the \code{chron} package). If \code{x} is a data frame, all variables in the data-frame which are of one the classes mentioned are converted to class \code{cal.yr}. See arguemt \code{wh}, though.} \item{format}{Format of the date values if \code{x} is factor or character. If this argument is supplied and \code{x} is a datafame, all character variables are converted to class \code{cal.yr}. Factors in the dataframe will be ignored.} \item{wh}{Indices of the variables to convert if \code{x} is a data frame. Can be either a numerical or character vector.} \item{...}{Arguments passed on from other methods.} } \value{ \code{cal.yr} returns a numerical vector of the same length as \code{x}, of class \code{c("cal.yr","numeric")}. If \code{x} is a data frame a dataframe with some of the columns converted to class \code{"cal.yr"} is returned. \code{as.Date.cal.yr} returns a \code{\link{Date}} object. } \author{ Bendix Carstensen, Steno Diabetes Center \& Dept. of Biostatistics, University of Copenhagen, \email{b@bxc.dk}, \url{http://bendixcarstensen.com} } \seealso{ \code{\link{DateTimeClasses}}, \code{\link{Date}} } \examples{ # Character vector of dates: birth <- c("14/07/1852","01/04/1954","10/06/1987","16/05/1990", "12/11/1980","01/01/1997","01/01/1998","01/01/1999") # Proper conversion to class "Date": birth.dat <- as.Date( birth, format="\%d/\%m/\%Y" ) # Converson of character to class "cal.yr" bt.yr <- cal.yr( birth, format="\%d/\%m/\%Y" ) # Back to class "Date": bt.dat <- as.Date( bt.yr ) # Numerical calculation of days since 1.1.1970: days <- Days <- (bt.yr-1970)*365.25 # Blunt assignment of class: class( Days ) <- "Date" # Then data.frame() to get readable output of results: data.frame( birth, birth.dat, bt.yr, bt.dat, days, Days, round(Days) ) } \keyword{manip} \keyword{chron} Epi/man/stattable.Rd0000644000176200001440000001135313751040403014014 0ustar liggesusers\name{stat.table} \alias{stat.table} \alias{print.stat.table} \title{Tables of summary statistics} \description{ \code{stat.table} creates tabular summaries of the data, using a limited set of functions. A list of index variables is used to cross-classify summary statistics. It does NOT work inside \code{with()}! } \usage{ stat.table(index, contents = count(), data, margins = FALSE) \method{print}{stat.table}(x, width=7, digits,...) } \arguments{ \item{index}{A factor, or list of factors, used for cross-classification. If the list is named, then the names will be used when printing the table. This feature can be used to give informative labels to the variables.} \item{contents}{A function call, or list of function calls. Only a limited set of functions may be called (See Details below). If the list is named, then the names will be used when printing the table.} \item{data}{an optional data frame containing the variables to be tabulated. If this is omitted, the variables will be searched for in the calling environment.} \item{margins}{a logical scalar or vector indicating which marginal tables are to be calculated. If a vector, it should be the same length as the \code{index} argument: values corresponding to \code{TRUE} will be retained in marginal tables.} \item{x}{an object of class \code{stat.table}.} \item{width}{a scalar giving the minimum column width when printing.} \item{digits}{a scalar, or named vector, giving the number of digits to print after the decimal point. If a named vector is used, the names should correspond to one of the permitted functions (See Details below) and all results obtained with that function will be printed with the same precision.} \item{...}{further arguments passed to other print methods.} } \details{ This function is similar to \code{tapply}, with some enhancements: multiple summaries of multiple variables may be mixed in the same table; marginal tables may be calculated; columns and rows may be given informative labels; pretty printing may be controlled by the associated print method. This function is not a replacement for \code{tapply} as it also has some limitations. The only functions that may be used in the \code{contents} argument are: \code{\link{count}}, \code{\link{mean}}, \code{\link{weighted.mean}}, \code{\link{sum}}, \code{\link{quantile}}, \code{\link{median}}, \code{\link{IQR}}, \code{\link{max}}, \code{\link{min}}, \code{\link{ratio}}, \code{\link{percent}}, and \code{\link{sd}}. The \code{count()} function, which is the default, simply creates a contingency table of counts. The other functions are applied to each cell created by combinations of the \code{index} variables. } \value{ An object of class \code{stat.table}, which is a multi-dimensional array. A print method is available to create formatted one-way and two-way tables. } \author{Martyn Plummer} \note{ The permitted functions in the contents list %are overloaded functions that are defined inside \code{stat.table}. They have the same interface as the functions callable from the command line, except for two differences. If there is an argument \code{na.rm} then its default value is always \code{TRUE}. A second difference is that the \code{quantile} function can only produce a single quantile in each call. } \seealso{\code{\link{table}}, \code{\link{tapply}}, \code{\link{mean}}, \code{\link{weighted.mean}}, \code{\link{sum}}, \code{\link{quantile}}, \code{\link{median}}, \code{\link{IQR}}, \code{\link{max}}, \code{\link{min}}, \code{\link{ratio}}, \code{\link{percent}}, \code{\link{count}}, \code{\link{sd}}.} \examples{ data(warpbreaks) # A one-way table stat.table(tension,list(count(),mean(breaks)),data=warpbreaks) # The same table with informative labels stat.table(index=list("Tension level"=tension),list(N=count(), "mean number of breaks"=mean(breaks)),data=warpbreaks) # A two-way table stat.table(index=list(tension,wool),mean(breaks),data=warpbreaks) # The same table with margins over tension, but not wool stat.table(index=list(tension,wool),mean(breaks),data=warpbreaks, margins=c(TRUE, FALSE)) # A table of column percentages stat.table(list(tension,wool), percent(tension), data=warpbreaks) # Cell percentages, with margins stat.table(list(tension,wool),percent(tension,wool), margin=TRUE, data=warpbreaks) # A table with multiple statistics # Note how each statistic has its own default precision a <- stat.table(index=list(wool,tension), contents=list(count(),mean(breaks),percent (wool)), data=warpbreaks) print(a) # Print the percentages rounded to the nearest integer print(a, digits=c(percent=0)) } \keyword{iteration} \keyword{category} Epi/man/fit.mult.Rd0000644000176200001440000000360413751040403013573 0ustar liggesusers\name{fit.mult} \alias{fit.mult} \title{ Fits a multiplicative relative risk model to interval censored data. } \description{ Utility function. The model fitted assumes a piecewise constant baseline rate in intervals specified by the argument \code{breaks}, and a multiplicative relative risk function. } \usage{ fit.mult( y, rates.frame, cov.frame, start ) } \arguments{ \item{y}{Binary vector of outcomes} \item{rates.frame}{Dataframe expanded from the original data by \code{\link{expand.data}}, cooresponding to covariates for the rate parameters.} \item{cov.frame}{ do., but covariates corresponding to the \code{formula} argument of \code{\link{Icens}}} \item{start}{Starting values for the rate parameters. If not supplied, then starting values are generated.} } \details{ The model is fitted by alternating between two generalized linear models where one estimates the underlying rates in the intervals, and the other estimates the log-relative risks. } \value{ A list with three components: \item{rates}{A glm object from a binomial model with log-link, estimating the baseline rates.} \item{cov}{A glm object from a binomial model with complementary log-log link, estimating the log-rate-ratios} \item{niter}{Nuber of iterations, a scalar} } \references{ B Carstensen: Regression models for interval censored survival data: application to HIV infection in Danish homosexual men. Statistics in Medicine, 15(20):2177-2189, 1996. CP Farrington: Interval censored survival data: a generalized linear modelling approach. Statistics in Medicine, 15(3):283-292, 1996. } \author{ Martyn Plummer, \email{martyn.plummer@r-project.org}, Bendix Carstensen, \email{b@bxc.dk} } \seealso{ \code{\link{Icens}} \code{\link{fit.add}} } \examples{ data( HIV.dk ) } \keyword{ models } \keyword{ regression } \keyword{ survival } Epi/man/matshade.Rd0000644000176200001440000000776013751040403013626 0ustar liggesusers\name{matshade} \alias{matshade} \title{ Plot confidence intervals as shaded areas around lines. } \description{ Uses an x-vector and a matrix of 3*N columns with estimates and ci.s to produce the lines of estimates and confidence intervals as shaded areas in transparent colours around the lines of the estimates. } \usage{ matshade( x, y, lty = 1, col = 1:(ncol(y)/3), col.shade=col, alpha=0.15, plot = dev.cur()==1, ... ) } \arguments{ \item{x}{Numerical vector. Unlike \code{\link{matplot}} this can only be a vector. } \item{y}{A matrix with 3*N columns --- representing estimates and confidence bounds for N curves. Order of columns are assumed to be (est,lo,hi,est,lo,hi...) (or (est,hi,lo...)) } \item{lty}{Line types for the curves. } \item{col}{Color(s) of the estimated curves. } \item{col.shade}{Color(s) of the shaded areas. These are the colors that are made transparent by the \code{alpha} factor. Defaults to the same colors as the lines. } \item{alpha}{Number in [0,1] indicating the transparency of the colors for the confidence intervals. Larger values makes the shades darker. Can be a vector which then applies to the curves in turn. } \item{plot}{Logical. Should a new plot frame be started? If no device is active, the default is to start one, and plot all \code{y}s versus x in transparent color. On the rare occasion a device is open, but no plot have been called you will get an error telling that plot.new has not been called yet, in which case you should explicitly set \code{plot} to \code{TRUE}. } \item{\dots}{Arguments passed on to \code{\link{matplot}} (if \code{plot=TRUE}) and \code{\link{matlines}} for use when plotting the lines. Note that \code{lwd=0} will cause lines to be omitted and only the shades be plotted. } } \details{All shaded areas are plotted first, the curves added afterwards, so that lines are not 'overshadowed'. If there are NAs in \code{x} or \code{y} there will be separate shaded areas for each non-\code{NA} sequence. Applies separately to each set of confidence bands in \code{y}. Note that if you repeat the same command, you will get the curves and the shaded areas overplotted in the same frame, so the effect is to have the shades darker, because the transparent colors are plotted on top of those from the first command. } \value{NULL. Used for its side effects. } \author{Bendix Carstensen, \url{http://bendixcarstensen.com} } \seealso{\code{\link{pc.matshade}} } \examples{ # Follow-up data of Danish DM patients data( DMlate ) mL <- Lexis( entry=list(age=dodm-dobth,per=dodm), exit=list(per=dox), exit.status=factor(!is.na(dodth),labels=c("Alive","Dead")), data=DMlate ) # Split follow-up and model by splines sL <- splitLexis( mL, breaks=0:100, time.scale="age") \dontrun{ # the same thing with popEpi sL <- splitMulti( mL, age=0:100 ) } # Mortality rates separately for M and F: mort <- glm( (lex.Xst=="Dead") ~ sex*Ns(age,knots=c(15,3:8*10)), offset = log(lex.dur), family = poisson, data = sL ) \dontrun{ # The counterpart with gam library( mgcv ) mort <- gam( (lex.Xst=="Dead") ~ s(age,by=sex) + sex, offset = log(lex.dur), family = poisson, data = sL ) } # predict rates (per 1000 PY) for men and women ndM <- data.frame( age=10:90, sex="M", lex.dur=1 ) ndF <- data.frame( age=10:90, sex="F", lex.dur=1 ) # gam objects ignores the offset in prediction so # lex.dur=1000 in prediction frame wll not work. prM <- ci.pred( mort, ndM )*1000 prF <- ci.pred( mort, ndF )*1000 # predict rate-ratio MFr <- ci.exp( mort, ctr.mat=list(ndM,ndF) ) # plot lines with shaded confidence limits # for illustration we make a holes for the RRs: MFr[40:45,2] <- NA MFr[44:49,1] <- NA matshade( ndM$age, cbind( MFr, prF, prM ), col=c(1,2,4), lwd=3, log="y", xlab="Age", ylab="Mortality per 1000 PY (and RR)" ) abline( h=1 ) } \keyword{color} Epi/man/apc.LCa.Rd0000644000176200001440000000550713751040403013236 0ustar liggesusers\name{apc.LCa} \alias{apc.LCa} \alias{show.apc.LCa} \title{Fit Age-Period-Cohort models and Lee-Carter models with effects modeled by natural splines. } \description{ \code{apc.LCa} fits an Age-Period-Cohort model and sub-models (using \code{\link{apc.fit}}) as well as Lee-Carter models (using \code{\link{LCa.fit}}). \code{show.apc.LCa} plots the models in little boxes with their residual deviance with arrows showing their relationships. } \usage{ apc.LCa( data, keep.models = FALSE, ... ) show.apc.LCa( x, dev.scale = TRUE, top = "Ad", ... ) } \arguments{ \item{data}{A data frame that must have columns \code{A}, \code{P}, \code{D} and \code{Y}, see e.g. \code{\link{apc.fit}} } \item{keep.models}{Logical. Should the \code{apc} object and the 5 \code{LCa} objects be returned too? } \item{...}{Further parameters passed on to \code{\link{LCa.fit}} or \code{\link{boxes.matrix}}. } \item{x}{The result from a call to \code{apc.LCa}.} \item{dev.scale}{Should the vertical position of the boxes with the models be scales relative to the deviance between the Age-drift model and the extended Lee-Carter model?} \item{top}{The model presented at the top of the plot of boxes (together with any other model with larger deviance) when vertical position is scaled by deviances. Only "Ad", "AP", "AC", "APa" or "ACa" will make sense.} } \details{The function \code{apc.LCa} fits all 9 models (well, 10) available as extension and sub-models of the APC-model and compares them by returning deviance and residual df. } \value{A 9 by 2 matrix classified by model and deviance/df; optionally (if \code{models=TRUE}) a list with the matrix as \code{dev}, \code{apc}, an \code{apc} object (from \code{\link{apc.fit}}), and \code{LCa}, a list with 5 \code{LCa} objects (from \code{\link{LCa.fit}}). } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com} } \seealso{ \code{ \link{apc.fit}}, \code{\link{LCa.fit} } } \examples{ library( Epi ) clear() # Danish lung cancer incidence in 5x5x5 Lexis triangles data( lungDK ) lc <- subset( lungDK, Ax>40 )[,c("Ax","Px","D","Y")] names( lc )[1:2] <- c("A","P") head( lc ) al <- apc.LCa( lc, npar=c(9,6,6,6,10), keep.models=TRUE, maxit=500, eps=10e-3 ) show.apc.LCa( al, dev=TRUE ) # Danish mortality data \dontrun{ data( M.dk ) mdk <- subset( M.dk, sex==1 )[,c("A","P","D","Y")] head( mdk ) al <- apc.LCa( mdk, npar=c(15,15,20,6,6), maxit=50, eps=10e-3, quiet=FALSE, VC=FALSE ) show.apc.LCa( al, dev=FALSE ) show.apc.LCa( al, dev=TRUE ) show.apc.LCa( al, top="AP" ) # Fit a reasonable model to Danish mortality data and plot results mAPa <- LCa.fit( mdk, model="APa", npar=c(15,15,20,6,6), c.ref=1930, a.ref=70, quiet=FALSE, maxit=250 ) par( mfrow=c(1,3) ) plot( mAPa ) } } \keyword{regression} \keyword{models} Epi/man/thoro.Rd0000644000176200001440000000401113751040403013155 0ustar liggesusers\name{thoro} \alias{thoro} \docType{data} \title{Thorotrast Study} \description{ The \code{thoro} data frame has 2470 rows and 14 columns. Each row represents one patient that have had cerebral angiography (X-ray of the brain) with an injected contrast medium, either Thorotrast or another one (the controls). } \format{ This data frame contains the following columns: \describe{ \item{\code{id}}{Identification of person.} \item{\code{sex}}{Sex, 1: male / 2: female.} \item{\code{birthdat}}{Date of birth, \code{Date} variable.} \item{\code{contrast}}{Group, 1: Thorotrast / 2: Control.} \item{\code{injecdat}}{Date of contrast injection, \code{Date} variable.} \item{\code{volume}}{Injected volume of Thorotrast in ml. Control patients have a 0 in this variable.} \item{\code{exitdat}}{Date of exit from the study, \code{Date} variable.} \item{\code{exitstat}}{Status at exit, 1: dead / 2: alive, censored at closing of study, 20 February 1992 / 3: censored alive at some earlier date.} \item{\code{cause}}{Cause of death. See causes in the helpfile for \code{\link{gmortDK}}.} \item{\code{liverdat}}{Date of liver cancer diagnosis, \code{Date} variable.} \item{\code{liver}}{Indicator of liver cancer diagnosis. Not all livercancers are histologically verified, hence \code{liver >= hepcc + chola + hmang}} \item{\code{hepcc}}{Hepatocellular carcinoma at \code{liverdat}.} \item{\code{chola}}{Cholangiocellular carcinoma at \code{liverdat}.} \item{\code{hmang}}{Haemangisarcoma carcinoma at \code{liverdat}.} } } \source{ M Andersson, M Vyberg, J Visfeldt, B Carstensen & HH Storm: Primary liver tumours among Danish patients exposed to Thorotrast. Radiation Research, 137, pp. 262--273, 1994. M Andersson, B Carstensen HH Storm: Mortality and cancer incidence after cerebral angiography. Radiation Research, 142, pp. 305--320, 1995. } \examples{ data(thoro) str(thoro) } \seealso{\code{\link{mortDK}}, \code{\link{gmortDK}}} \keyword{datasets} Epi/man/clogistic.Rd0000644000176200001440000000656013751040403014015 0ustar liggesusers\name{clogistic} \alias{clogistic} \title{Conditional logistic regression} \description{ Estimates a logistic regression model by maximizing the conditional likelihood. The conditional likelihood calculations are exact, and scale efficiently to strata with large numbers of cases. } \usage{ clogistic(formula, strata, data, subset, na.action, init, model = TRUE, x = FALSE, y = TRUE, contrasts = NULL, iter.max=20, eps=1e-6, toler.chol = sqrt(.Machine$double.eps)) } \arguments{ \item{formula}{Model formula} \item{strata}{Factor describing membership of strata for conditioning} \item{data}{data frame containing the variables in the formula and strata arguments} \item{subset}{subset of records to use} \item{na.action}{missing value handling} \item{init}{initial values} \item{model}{ a logical value indicating whether \emph{model frame} should be included as a component of the returned value} \item{x,y}{ logical values indicating whether the response vector and model matrix used in the fitting process should be returned as components of the returned value. } \item{contrasts}{ an optional list. See the \code{contrasts.arg} of \code{model.matrix.default} } \item{iter.max}{maximum number of iterations} \item{eps}{ Convergence tolerance. Iteration continues until the relative change in the conditional log likelihood is less than \code{eps}. Must be positive. } \item{toler.chol}{ Tolerance used for detection of a singularity during a Cholesky decomposition of the variance matrix. This is used to detect redundant predictor variables. Must be less than \code{eps}. } } \value{ An object of class \code{"clogistic"}. This is a list containing the following components: \item{coefficients}{ the estimates of the log-odds ratio parameters. If the model is over-determined there will be missing values in the vector corresponding to the redundant columns in the model matrix. } \item{var}{ the variance matrix of the coefficients. Rows and columns corresponding to any missing coefficients are set to zero. } \item{loglik}{ a vector of length 2 containing the log-likelihood with the initial values and with the final values of the coefficients. } \item{iter}{ number of iterations used. } \item{n}{ number of observations used. Observations may be dropped either because they are missing, or because they belong to a homogeneous stratum. For more details on which observations were used, see \code{informative} below. } \item{informative}{ if \code{model=TRUE}, a logical vector of length equal to the number of rows in the model frame. This indicates whether an observation is informative. Strata that are homogeneous with respect to either the outcome variable or the predictor variables are uninformative, in the sense that they can be removed without modifying the estimates or standard errors. If \code{model=FALSE}, this is NULL. } The output will also contain the following, for documentation see the \code{glm} object: \code{terms}, \code{formula}, \code{call}, \code{contrasts}, \code{xlevels}, and, optionally, \code{x}, \code{y}, and/or \code{frame}. } \examples{ data(bdendo) clogistic(d ~ cest + dur, strata=set, data=bdendo) } \author{Martyn Plummer} \seealso{\code{\link{glm}}} \keyword{models} Epi/man/testisDK.Rd0000644000176200001440000000115413751040403013561 0ustar liggesusers\name{testisDK} \alias{testisDK} \docType{data} \title{Testis cancer incidence in Denmark, 1943--1996 } \description{Number of testiscancer cases and male person-years in the Danish population 1943--1996} \usage{data(testisDK)} \format{ A data frame with 4860 observations on the following 4 variables. \describe{ \item{\code{A}}{Age class, 0,1,2,...,89} \item{\code{P}}{Year, 1943,...,1996} \item{\code{D}}{Number of testis cancer cases} \item{\code{Y}}{Person years} } } \source{The Danish Cancer Registry } \examples{ data(testisDK) head(testisDK) } \keyword{datasets} Epi/man/expand.data.Rd0000644000176200001440000000334713751040403014224 0ustar liggesusers\name{expand.data} \alias{expand.data} \title{ Function to expand data for regression analysis of interval censored data. } \description{ This is a utility function. The original records with \code{first.well}, \code{last.well} and \code{first.ill} are expanded to multiple records; several for each interval where the person is known to be well and one where the person is known to fail. At the same time columns for the covariates needed to estimate rates and the response variable are generated. } \usage{ expand.data(fu, formula, breaks, data) } \arguments{ \item{fu}{A 3-column matrix with \code{first.well}, \code{last.well} and \code{first.ill} in each row.} \item{formula}{Model fromula, used to derive the model matrix.} \item{breaks}{Defines the intervals in which the baseline rate is assumed constant. All follow-up before the first and after the last break is discarded.} \item{data}{Datafrem in which \code{fu} and \code{formula} is interpreted.} } \value{ Returns a list with three components \item{rates.frame}{Dataframe of covariates for estimation of the baseline rates --- one per interval defined by \code{breaks}.} \item{cov.frame}{Dataframe for estimation of the covariate effects. A data-framed version of the designmatrix from \code{formula}.} \item{y}{Response vector.} } \references{ B Carstensen: Regression models for interval censored survival data: application to HIV infection in Danish homosexual men. Statistics in Medicine, 15(20):2177-2189, 1996. } \author{ Martyn Plummer, \email{martyn.plummer@r-project.org} } \seealso{ \code{\link{Icens}} \code{\link{fit.mult}} \code{\link{fit.add}} } \keyword{ models } \keyword{ regression } \keyword{ survival } Epi/man/start.Lexis.Rd0000644000176200001440000000543013751040403014250 0ustar liggesusers\name{entry.Lexis} \alias{entry} \alias{exit} \alias{status} \alias{dur} \alias{transient} \alias{absorbing} \alias{before} \alias{preceding} \alias{after} \alias{succeeding} \title{Time series and other methods for Lexis objects} \description{ Extract the entry time, exit time, status or duration of follow-up from a \code{Lexis} object. Classify states. } \usage{ entry( x, time.scale = NULL, by.id=FALSE ) exit( x, time.scale = NULL, by.id=FALSE ) status( x, at="exit" , by.id=FALSE ) dur( x, by.id=FALSE ) transient( x ) absorbing( x ) preceding( x, states ) before( x, states ) succeeding( x, states ) after( x, states ) } \arguments{ \item{x}{an object of class \code{Lexis}.} \item{time.scale}{a string or integer indicating the time scale. If omitted, all times scales are used.} \item{by.id}{Logical, if \code{TRUE}, only one record per unique value of \code{lex.id} is returned; either the first, the last, or for \code{dur}, the sum of \code{lex.dur}. If \code{TRUE}, the returned object have the \code{lex.id} as (row)names attribute.} \item{at}{string indicating the time point(s) at which status is to be measured. Possible values are "exit" or "entry".} \item{states}{Character vector of states.} } \value{ The \code{entry} and \code{exit} functions return a vector of entry times and exit times, respectively, on the requested time scale. If multiple time scales are requested, a matrix is returned. The \code{status} function returns a vector giving the status at "\code{at}" (either '\code{entry}' or '\code{exit}') and \code{dur} returns a vector with the lengths of the follow-up intervals. \code{entry}, \code{exit}, \code{status} and \code{dur} return vectors of length \code{nrow(x)} if \code{by.id=FALSE}; if \code{by.id=TRUE} a vector of length \code{length(unique(lex.id))}. The functions \code{transient} and \code{absorbing} return character vectors of the transient, resp. absorbing states in \code{x}. These are necessariy disjoint but the union may be a proper subset of \code{levels(x)}, since the latter may have levels that are never assumed by either \code{lex.Cst} or \code{lex.Xst}. \code{preceding} returns a character vector with names of the states of the Lexis object \code{x} from which one of the states in \code{states} can be reached directly - the preceding states. \code{before} is just a synonym for \code{preceding}. \code{succeeding} returns a character vector with names of the states of the Lexis object \code{x} that can be reached directly from one of the states in \code{states}. \code{after} is just a synonym for \code{succeeding}. } \author{Martyn Plummer & Bendix Carstensen} \seealso{\code{\link{Lexis}}} \keyword{survival} \keyword{ts} Epi/man/brv.Rd0000644000176200001440000000363213751040403012623 0ustar liggesusers\name{brv} \alias{brv} \docType{data} \title{Bereavement in an elderly cohort} \description{ The \code{brv} data frame has 399 rows and 11 columns. The data concern the possible effect of marital bereavement on subsequent mortality. They arose from a survey of the physical and mental health of a cohort of 75-year-olds in one large general practice. These data concern mortality up to 1 January, 1990 (although further follow-up has now taken place). Subjects included all lived with a living spouse when they entered the study. There are three distinct groups of such subjects: (1) those in which both members of the couple were over 75 and therefore included in the cohort, (2) those whose spouse was below 75 (and was not, therefore, part of the main cohort study), and (3) those living in larger households (that is, not just with their spouse). } \format{ This data frame contains the following columns: \describe{ \item{\code{id}}{subject identifier, a numeric vector} \item{\code{couple}}{couple identifier, a numeric vector} \item{\code{dob}}{date of birth, a date} \item{\code{doe}}{date of entry into follow-up study, a date} \item{\code{dox}}{date of exit from follow-up study, a date} \item{\code{dosp}}{date of death of spouse, a date (if the spouse was still alive at the end of follow-up,this was coded to January 1, 2000)} \item{\code{fail}}{status at end of follow-up, a numeric vector (0=alive,1=dead)} \item{\code{group}}{see Description, a numeric vector} \item{\code{disab}}{disability score, a numeric vector} \item{\code{health}}{perceived health status score, a numeric vector} \item{\code{sex}}{a factor with levels \code{Male} and \code{Female} } } } \source{ Jagger C, and Sutton CJ, Death after Marital Bereavement. Statistics in Medicine, 10:395-404, 1991. (Data supplied by Carol Jagger). } \examples{ data(brv) } \keyword{datasets} Epi/man/subset.Lexis.Rd0000644000176200001440000000225313766441333014435 0ustar liggesusers\name{subset.Lexis} \alias{subset.Lexis} \alias{[.Lexis} \alias{subset.stacked.Lexis} \title{Subsetting Lexis (and stacked.Lexis) objects} \description{ Return subsets of Lexis objects which meet conditions } \usage{ \method{subset}{Lexis}(x, ...) \method{[}{Lexis}(x, ...) \method{subset}{stacked.Lexis}(x, ...) } \arguments{ \item{x}{an object of class \code{Lexis}} \item{\dots}{additional arguments to be passed to \code{subset.data.frame}. This will normally be some logical expression selecting a subset of the rows. For details see \code{\link{subset.data.frame}}.} } \details{ The subset method for \code{Lexis} objects works exactly as the method for data frames. So does the "[" method. The special methods are needed in order to propagate the Lexis-specific attributes. The method for \code{stacked.Lexis} objects also shrinks the set of levels for \code{lex.Cst} and \code{lex.Xst} to those actually occurring in the resulting data frame. } \value{ A \code{Lexis} object with selected rows and columns. } \author{Martyn Plummer} \seealso{\code{\link{Lexis}}, \code{\link{merge.Lexis}}, \code{\link{bootLexis}}} \keyword{manip} Epi/man/stattable.funs.Rd0000644000176200001440000000332413751040403014765 0ustar liggesusers\name{stattable.funs} \alias{count} \alias{percent} \alias{ratio} \title{Special functions for use in stat.table} \description{ These functions may be used as \code{contents} arguments to the function \code{stat.table}. They are defined internally in \code{stat.table} and have no independent existence. } \usage{ count(id) ratio(d,y,scale=1, na.rm=TRUE) percent(...) } \arguments{ \item{id}{numeric vector in which identical values identify the same individual.} \item{d, y}{numeric vectors of equal length (\code{d} for Deaths, \code{y} for person-Years)} \item{scale}{a scalar giving a value by which the ratio should be multiplied} \item{na.rm}{a logical value indicating whether \code{NA} values should be stripped before computation proceeds.} \item{...}{a list of variables taken from the \code{index} argument to \code{\link{stat.table}}} } \value{ When used as a \code{contents} argument to \code{stat.table}, these functions create the following tables: \item{\code{count}}{If given without argument (\code{count()}) it returns a contingency table of counts. If given an \code{id} argument it returns a table of the number of different values of \code{id} in each cell, i.e. how many persons contribute in each cell.} \item{\code{ratio}}{returns a table of values \code{scale * sum(d)/sum(y)}} \item{\code{percent}}{returns a table of percentages of the classifying variables. Variables that are in the \code{index} argument to \code{stat.table} but not in the call to \code{percent} are used to define strata, within which the percentages add up to 100.} } \author{Martyn Plummer} \seealso{\code{\link{stat.table}}} \keyword{iteration} \keyword{category} Epi/man/time.band.Rd0000644000176200001440000000450113751040403013667 0ustar liggesusers\name{timeBand} \alias{timeBand} \alias{breaks} \title{Extract time band data from a split Lexis object} \description{ The break points of a \code{Lexis} object (created by a call to \code{splitLexis}) divide the follow-up intervals into time bands along a given time scale. The \code{breaks} function returns the break points, for a given time scale, and the \code{timeBand} classifies each row (=follow-up interval) into one of the time bands. } \usage{ timeBand(lex, time.scale, type="integer") breaks(lex, time.scale) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{lex}{an object of class \code{Lexis}} \item{time.scale}{a character or integer vector of length 1 identifying the time scale of interest} \item{type}{a string that determines how the time bands are labelled. See Details below} } \details{ Time bands may be labelled in various ways according to the \code{type} argument. The permitted values of the \code{type} argument, and the corresponding return values are: \describe{ \item{"integer"}{a numeric vector with integer codes starting from 0.} \item{"factor"}{a factor (unordered) with labels "(left,right]"} \item{"left"}{the left-hand limit of the time band} \item{"middle"}{the midpoint of the time band} \item{"right"}{the right-hand limit of the time band} } } \value{ The \code{breaks} function returns a vector of break points for the \code{Lexis} object, or NULL if no break points have been defined by a call to \code{splitLexis}. The \code{timeBand} function returns a numeric vector or factor, depending on the value of the \code{type} argument. } \author{Martyn Plummer} \note{ A newly created \code{Lexis} object has no break points defined. In this case, \code{breaks} will return NULL, and \code{timeBand} will a vector of zeros. } \examples{ data(diet) diet <- cal.yr(diet) diet.lex <- Lexis(entry=list(period=doe), exit=list(period=dox, age=dox-dob), exit.status=chd, data=diet) diet.split <- splitLexis(diet.lex, breaks=seq(40,70,5), "age" ) age.left <- timeBand(diet.split, "age", "left") table(age.left) age.fact <- timeBand(diet.split, "age", "factor") table(age.fact) age.mid <- timeBand(diet.split, "age", "mid") table(age.mid) } \seealso{\code{\link{Lexis}}} \keyword{attribute} Epi/man/lep.Rd0000644000176200001440000000233013751040403012604 0ustar liggesusers\name{lep} \alias{lep} \docType{data} \title{An unmatched case-control study of leprosy incidence} \description{ The \code{lep} data frame has 1370 rows and 7 columns. This was an unmatched case-control study in which incident cases of leprosy in a region of N. Malawi were compared with population controls. } \format{ This data frame contains the following columns: \tabular{rl}{ \code{id}: \tab subject identifier: a numeric vector \cr \code{d}: \tab case/control status: a numeric vector (1=case, 0=control) \cr \code{age}: \tab a factor with levels \code{5-9} \code{10-14} \code{15-19} \code{20-24} \code{25-29} \code{30-44} \code{45+} \cr \code{sex}: \tab a factor with levels \code{male}, \code{female} \cr \code{bcg}: \tab presence of vaccine scar, a factor with levels \code{no} \code{yes} \cr \code{school}: \tab schooling, a factor with levels \code{none} \code{1-5yrs} \code{6-8yrs} \code{sec/tert} \cr \code{house}: \tab housing, a factor with levels \code{brick} \code{sunbrick} \code{wattle} \code{temp} \cr } } \source{ The study is described in more detail in Clayton and Hills, Statistical Models in Epidemiology, Oxford University Press, Oxford:1993. } \examples{ data(lep) } \keyword{datasets} Epi/man/lines.apc.Rd0000644000176200001440000001054113751040403013703 0ustar liggesusers\name{apc.lines} \alias{lines.apc} \alias{apc.lines} \title{ Plot APC-estimates in an APC-frame. } \description{ When an APC-frame has been produced by \code{\link{apc.frame}}, this function draws a set of estimates from an APC-fit in the frame. An optional drift parameter can be added to the period parameters and subtracted from the cohort and age parameters. } \usage{ \method{lines}{apc}( x, P, C, scale = c("log","ln","rates","inc","RR"), frame.par = options()[["apc.frame.par"]], drift = 0, c0 = median( C[,1] ), a0 = median( A[,1] ), p0 = c0 + a0, ci = rep( FALSE, 3 ), lwd = c(3,1,1), lty = 1, col = "black", type = "l", knots = FALSE, shade = FALSE, ... ) apc.lines( x, P, C, scale = c("log","ln","rates","inc","RR"), frame.par = options()[["apc.frame.par"]], drift = 0, c0 = median( C[,1] ), a0 = median( A[,1] ), p0 = c0 + a0, ci = rep( FALSE, 3 ), lwd = c(3,1,1), lty = 1, col = "black", type = "l", knots = FALSE, shade = FALSE, ... ) } \arguments{ \item{x}{If an \code{apc}-object, (see \code{\link{apc.fit}}), then the arguments \code{P}, \code{C}, \code{c0}, \code{a0} and \code{p0} are ignored, and the estimates from \code{x} plotted. Can also be a 4-column matrix with columns age, age-specific rates, lower and upper c.i., in which case period and cohort effects are taken from the arguments \code{P} and \code{C}. } \item{P}{Period effects. Rate-ratios. Same form as for the age-effects.} \item{C}{Cohort effects. Rate-ratios. Same form as for the age-effects.} \item{scale}{Are effects given on a log-scale? Character variable, one of \code{"log"}, \code{"ln"}, \code{"rates"}, \code{"inc"}, \code{"RR"}. If \code{"log"} or \code{"ln"} it is assumed that effects are log(rates) and log(RRs) otherwise the actual effects are assumed given in \code{A}, \code{P} and \code{C}. If \code{A} is of class \code{apc}, it is assumed to be \code{"rates"}.} \item{frame.par}{2-element vector with the cohort-period offset and RR multiplicator. This will typically be the result from the call of \code{\link{apc.frame}}. See this for details.} \item{drift}{The drift parameter to be added to the period effect. If \code{scale="log"} this is assumed to be on the log-scale, otherwise it is assumed to be a multiplicative factor per unit of the first columns of \code{A}, \code{P} and \code{C} } \item{c0}{The cohort where the drift is assumed to be 0; the subtracted drift effect is \code{drift*(C[,1]-c0)}.} \item{a0}{The age where the drift is assumed to be 0.} \item{p0}{The period where the drift is assumed to be 0.} \item{ci}{Should confidence interval be drawn. Logical or character. If character, any occurrence of \code{"a"} or \code{"A"} produces confidence intervals for the age-effect. Similarly for period and cohort.} \item{lwd}{Line widths for estimates, lower and upper confidence limits.} \item{lty}{Linetypes for the three effects.} \item{col}{Colours for the three effects.} \item{type}{What type of lines / points should be used.} \item{knots}{Should knots from the model be shown?} \item{shade}{Should confidence intervals be plotted as shaded areas? If true, the setting of \code{ci} is ignored.} \item{...}{Further parameters to be transmitted to \code{points} \code{lines}, \code{matpoints} or \code{matlines} used for plotting the three sets of curves.} } \details{ There is no difference between the functions \code{apc.lines} and \code{lines.apc}, except the the latter is the \code{lines} method for \code{apc} objects. The drawing of three effects in an APC-frame is a rather trivial task, and the main purpose of the utility is to provide a function that easily adds the functionality of adding a drift so that several sets of lines can be easily produced in the same frame. } \value{ \code{apc.lines} returns (invisibly) a list of three matrices of the effects plotted. } \author{ Bendix Carstensen, Steno Diabetes Center, \url{http://bendixcarstensen.com} } \seealso{ \code{\link{apc.frame}}, \code{\link{pc.lines}}, \code{\link{apc.fit}}, \code{\link{apc.plot}} } \keyword{hplot} Epi/man/hivDK.Rd0000644000176200001440000000260413751040403013035 0ustar liggesusers\name{ hivDK } \alias{ hivDK } \docType{ data } \title{ hivDK: seroconversion in a cohort of Danish men} \description{ Data from a survey of HIV-positivity of a cohort of Danish men followed by regular tests from 1983 to 1989. } \usage{ data(hivDK) } \format{ A data frame with 297 observations on the following 7 variables. \describe{ \item{\code{id}}{ID of the person} \item{\code{entry}}{Date of entry to the study. Date variable.} \item{\code{well}}{Date last seen seronegative. Date variable.} \item{\code{ill}}{Date first seen seroconverted. Date variable.} \item{\code{bth}}{Year of birth minus 1950.} \item{\code{pyr}}{Annual number of sexual partners.} \item{\code{us}}{Indicator of wheter the person has visited the USA.} } } \source{ Mads Melbye, Statens Seruminstitut. } \references{ Becker N.G. and Melbye M.: Use of a log-linear model to compute the empirical survival curve from interval-censored data, with application to data on tests for HIV-positivity, Australian Journal of Statistics, 33, 125--133, 1990. Melbye M., Biggar R.J., Ebbesen P., Sarngadharan M.G., Weiss S.H., Gallo R.C. and Blattner W.A.: Seroepidemiology of HTLV-III antibody in Danish homosexual men: prevalence, transmission and disease outcome. British Medical Journal, 289, 573--575, 1984. } \examples{ data(hivDK) str(hivDK) } \keyword{ datasets } Epi/man/bootLexis.Rd0000644000176200001440000000601513751040403014000 0ustar liggesusers\name{bootLexis} \alias{nid} \alias{nid.Lexis} \alias{bootLexis} \title{ Create a bootstrap sample of persons (as identified by \code{lex.id}) from a Lexis object } \description{ \code{lex.id} is the person identifier in a \code{\link{Lexis}} object. This is used to sample persons from a Lexis object. If a person is sampled, all records from this persons is transported to the bootstrap sample. } \usage{ nid( Lx, \dots ) \method{nid}{Lexis}( Lx, by=NULL, \dots ) bootLexis( Lx, size = NULL, by = NULL, replace=TRUE ) } \arguments{ \item{Lx}{A \code{Lexis} object.} \item{\dots}{Parameters passed on to other methods.} \item{size}{Numeric. How many persons should be sampled from the \code{Lexis} object. Defaults to the number of persons in the \code{Lx}, or, if \code{by} is given, to the number of persons in each level of \code{by}. If \code{by} is given, \code{size} can have length \code{length(unique(by))}, to indicate how many are sampled from each level of \code{by}.} \item{by}{Character. Name of a variable (converted to factor) in the \code{Lexis} object. Bootstrap sampling is done within each level of by. Calculation of the number of persons (\code{lex.id}) is done within each level of \code{by}, and a vector returned. } \item{replace}{Should persons be sampled by replacement? Default is \code{TRUE}. Setting \code{replace} to \code{FALSE} enables selecting a random subset of persons from the Lexis object.} } \value{ \code{bootLexis} returns a Lexis object of the same structure as the input, with \emph{persons} bootstrapped. The variable \code{lex.id} in the resulting \code{Lexis} object has values 1,2,... The original values of \code{lex.id} from \code{Lx} are stored in the variable \code{old.id}. \code{nid} counts the number of persons in a Lexis object, possibly by \code{by}. If \code{by} is given, a named vector is returned. } \author{Bendix Carstensen, \url{http://bendixcarstensen.com}.} \seealso{\code{\link{Relevel.Lexis}},\code{\link{subset.Lexis}}} \examples{ # A small bogus cohort xcoh <- data.frame( id = c("A", "B", "C"), birth = c("1952-07-14", "1954-04-01", "1987-06-10"), entry = c("1965-08-04", "1972-09-08", "1991-12-23"), exit = c("1997-06-27", "1995-05-23", "1998-07-24"), fail = c(1, 0, 1), sex = c("M","F","M") ) # Convert to calendar years for( i in 2:4 ) xcoh[,i] <- cal.yr(xcoh[,i]) xcoh Lcoh <- Lexis( entry = list( per=entry ), exit = list( per=exit, age=exit-birth ), exit.status = fail, data = xcoh ) Lx <- Lcoh[sample(1:3,10,replace=TRUE),] Lx$per <- Lx$per + runif(10,0,10) Lx$lex.id <- 1:10 Lx <- splitLexis( Lx, breaks=0:10*10, "age" ) Lx nid( Lx ) nid( Lx, by="sex" ) Lb <- bootLexis( Lx ) head( Lb ) nid( bootLexis( Lx, size=7 ) ) Li <- bootLexis( Lx, by="id" ) # superfluous summary( Lx ) summary( Li ) L2 <- bootLexis( Lx, by="sex", size=c(2,5) ) nid( L2, by="sex" ) summary( L2 ) } \keyword{manip} Epi/man/N.dk.Rd0000644000176200001440000000141513751040403012621 0ustar liggesusers\name{N.dk} \alias{N.dk} \docType{data} \title{Population size in Denmark} \description{ The population size at 1st January in ages 0-99. } \usage{data(N.dk)} \format{ A data frame with 7200 observations on the following 4 variables. \describe{ \item{\code{sex}}{Sex, 1:males, 2:females} \item{\code{A}}{Age. 0:0, 1:1, ..., 98:98, 99:99+} \item{\code{P}}{Year} \item{\code{N}}{Number of persons alive at 1st January year \code{P}} } } \source{ \url{http://www.statistikbanken.dk/statbank5a/SelectTable/omrade0.asp?SubjectCode=02&PLanguage=1&ShowNews=OFF} } \examples{ data(N.dk) str(N.dk) with(N.dk,addmargins(tapply(N,list(P,sex),sum),2)) with(subset(N.dk,P==max(P)),addmargins(tapply(N,list(A,sex),sum))) } \keyword{datasets} Epi/man/pc.lines.Rd0000644000176200001440000000323413751040403013543 0ustar liggesusers\name{pc.lines} \alias{pc.points} \alias{pc.lines} \alias{pc.matpoints} \alias{pc.matlines} \alias{pc.matshade} \alias{cp.points} \alias{cp.lines} \alias{cp.matpoints} \alias{cp.matlines} \alias{cp.matshade} \title{ Plot period and cohort effects in an APC-frame. } \description{ When an APC-frame has been produced by \code{\link{apc.frame}}, this function draws curves or points in the period/cohort part of the frame. } \usage{ pc.points( x, y, ... ) pc.lines( x, y, ... ) pc.matpoints( x, y, ... ) pc.matlines( x, y, ... ) pc.matshade( x, y, ... ) cp.points( x, y, ... ) cp.lines( x, y, ... ) cp.matpoints( x, y, ... ) cp.matlines( x, y, ... ) cp.matshade( x, y, ... ) } \arguments{ \item{x}{vector of \code{x}-coordinates.} \item{y}{vector or matrix of \code{y}-coordinates.} \item{...}{Further parameters to be transmitted to points, lines, matpoints, matlines or matshade used for plotting curves in the calendar time realm of a graph generated by \code{\link{apc.frame}}} } \details{Since the Age-part of the frame is referred to by its real coordinates plotting in the calendar time part requires translation and scaling to put things correctly there, that is done by the functions \code{pc.points} etc. The functions \code{cp.points} etc. are just synonyms for these, in recognition of the fact that you can never remember whether it is "pc" or "cp". } \value{ The functions return nothing. } \author{ Bendix Carstensen, Steno Diabetes Center Copenhagen, \url{http://bendixcarstensen.com} } \seealso{ \code{\link{apc.frame}}, \code{\link{apc.fit}}, \code{\link{plot.apc}}, \code{\link{lines.apc}} } \keyword{hplot} Epi/man/Lexis.lines.Rd0000644000176200001440000000447713751040403014237 0ustar liggesusers\name{Lexis.lines} \alias{Lexis.lines} \title{Draw life lines in a Lexis diagram.} \description{ Add life lines to a Lexis diagram. } \usage{ Lexis.lines( entry.date = NA, exit.date = NA, birth.date = NA, entry.age = NA, exit.age = NA, risk.time = NA, col.life = "black", lwd.life = 2, fail = NA, cex.fail = 1, pch.fail = c(NA, 16), col.fail = col.life, data = NULL ) } \arguments{ \item{entry.date, entry.age, exit.date, exit.age, risk.time, birth.date}{Numerical vectors defining lifelines to be plotted in the diagram. At least three must be given to produce lines. Not all subsets of three will suffice, the given subset has to define life lines. If insufficient data is given, no life lines are produced.} \item{col.life}{Colour of the life lines.} \item{lwd.life}{Width of the life lines.} \item{fail}{Logical of event status at exit for the persons whose life lines are plotted.} \item{cex.fail}{The size of the status marks at the end of life lines.} \item{pch.fail}{The status marks at the end of the life lines.} \item{col.fail}{Colour of the marks for censorings and failures respectively.} \item{data}{Data frame in which to interpret values.} } \value{ If sufficient information on lifelines is given, a data frame with one row per person and columns with entry ages and dates, birth date, risk time and status filled in. Side effect: Life lines are added to an existing Lexis diagram. Lexis.lines adds life lines to an existing plot. } \author{ Bendix Carstensen, Steno Diabetes Center, \url{http://bendixcarstensen.com} } \examples{ Lexis.diagram( entry.age = c(3,30,45), risk.time = c(25,5,14), birth.date = c(1970,1931,1925.7), fail = c(TRUE,TRUE,FALSE) ) Lexis.lines( entry.age = sample( 0:50, 100, replace=TRUE ), risk.time = sample( 5:40, 100, r=TRUE), birth.date = sample( 1910:1980, 100, r=TRUE ), fail = sample(0:1,100,r=TRUE), cex.fail = 0.5, lwd.life = 1 ) } \keyword{ hplot } \keyword{ dplot } \seealso{ \code{\link{Lexis.diagram}}, \code{\link{Life.lines}} } Epi/man/effx.Rd0000644000176200001440000000732014002243074012757 0ustar liggesusers\name{effx} \alias{effx} \title{Function to calculate effects} \description{ The function calculates the effects of an exposure on a response, possibly stratified by a stratifying variable, and/or controlled for one or more confounding variables. } \usage{ effx( response, type = "metric", fup = NULL, exposure, strata = NULL, control = NULL, weights = NULL, eff = NULL, alpha = 0.05, base = 1, digits = 3, data = NULL ) } \arguments{ \item{response}{The \code{response} variable - must be numeric or logical. If logical, \code{TRUE} is considered the outcome.} \item{type}{The type of response\code{type} - must be one of "metric", "binary", "failure", or "count"} \item{fup}{The \code{fup} variable contains the follow-up time for a failure response. This must be numeric.} \item{exposure}{The \code{exposure} variable can be numeric or a factor} \item{strata}{The \code{strata} stratifying variable - must be a factor} \item{control}{The \code{control} variable(s) (confounders) - these are passed as a list if there are more than one.} \item{weights}{Frequency weights for binary response only} \item{eff}{How should effects be measured. If \code{response} is binomial, the default is "OR" (odds-ratio) with "RR" (relative risk) as an option. If \code{response} is failure, the default is "RR" (rate-ratio) with "RD" (rate difference) as an option.} \item{base}{Baseline for the effects of a categorical exposure, either a number or a name of the level. Defaults to 1} \item{digits}{Number of significant digits for the effects, default 3} \item{alpha}{1 - confidence level} \item{data}{\code{data} refers to the data used to evaluate the function} } \details{The function is a wrapper for glm. Effects are calculated as differences in means for a metric response, odds ratios/relative risks for a binary response, and rate ratios/rate differences for a failure or count response. The k-1 effects for a categorical exposure with k levels are relative to a baseline which, by default, is the first level. The effect of a metric (quantitative) exposure is calculated per unit of exposure. The exposure variable can be numeric or a factor, but if it is an ordered factor the order will be ignored.} \value{ % ~Describe the value returned % If it is a LIST, use \item{comp1 }{Effects of exposure} \item{comp2 }{Tests of significance} % ... } \author{Michael Hills (*1934-Jun-07, +2021-Jan-07)} %\note{ ~~further notes~~ } %\seealso{ ~~objects to See Also as \code{\link{~~fun~~}}, ~~~ } \examples{ library(Epi) data(births) births$hyp <- factor(births$hyp,labels=c("normal","hyper")) births$sex <- factor(births$sex,labels=c("M","F")) # bweight is the birth weight of the baby in gms, and is a metric # response (the default) # effect of hypertension on birth weight effx(bweight,exposure=hyp,data=births) # effect of hypertension on birth weight stratified by sex effx(bweight,exposure=hyp,strata=sex,data=births) # effect of hypertension on birth weight controlled for sex effx(bweight,exposure=hyp,control=sex,data=births) print( options('na.action') ) # effect of gestation time on birth weight effx(bweight,exposure=gestwks,data=births) # effect of gestation time on birth weight stratified by sex effx(bweight,exposure=gestwks,strata=sex,data=births) # effect of gestation time on birth weight controlled for sex effx(bweight,exposure=gestwks,control=sex,data=births) # lowbw is a binary response coded 1 for low birth weight and 0 otherwise # effect of hypertension on low birth weight effx(lowbw,type="binary",exposure=hyp,data=births) effx(lowbw,type="binary",exposure=hyp,eff="RR",data=births) } \keyword{ models } \keyword{ regression } Epi/man/merge.Lexis.Rd0000644000176200001440000000244613751040403014216 0ustar liggesusers\name{merge.Lexis} \alias{merge.Lexis} \title{Merge a Lexis object with a data frame} \description{ Merge additional variables from a data frame into a Lexis object. } \usage{ \method{merge}{Lexis}(x, y, id, by, ...) } \arguments{ \item{x}{an object of class \code{Lexis}} \item{y}{a data frame} \item{id}{the name of the variable in \code{y} to use for matching against the variable \code{lex.id} in \code{x}. } \item{by}{if matching is not done by id, a vector of variable names common to both \code{x} and \code{y}} \item{...}{optional arguments to be passed to \code{merge.data.frame}} } \details{ A \code{Lexis} object can be considered as an augmented data frame in which some variables are time-dependent variables representing follow-up. The \code{Lexis} function produces a minimal object containing only these time-dependent variables. Additional variables may be added to a \code{Lexis} object using the \code{merge} method. } \value{ A \code{Lexis} object with additional columns taken from the merged data frame. } \author{Martyn Plummer} \note{ The variable given as the \code{by.y} argument must not contain any duplicate values in the data frame \code{y}. } \seealso{\code{\link{merge.data.frame}}, \code{\link{subset.Lexis}}} \keyword{array} \keyword{manip} Epi/man/poisreg.Rd0000644000176200001440000000655413751040403013510 0ustar liggesusers\name{poisreg} \alias{poisreg} \title{Family Object for Poisson Regression} \usage{ poisreg(link = "log") } \arguments{ \item{link}{a specification for the model link function. The \code{poisreg} family accepts the links \code{identity}, \code{log} and \code{inverse}. } } \description{ The \code{poisreg} family allows Poisson regression models to be fitted using the \code{glm} function. In a Poisson regression model, we assume that the data arise from a Poisson process. We observe D disease events in follow up time Y and wish to estimate the incidence rate, which is assumed to be constant during the follow-up period for any individual. The incidence rate varies between individuals according to the predictor variables and the link function in the model specification. When using the \code{poisreg} family in the \code{glm} function, the response should be specified as a two-column matrix with the first column giving the number of events (D) and the second column giving the observation time (Y). This is similar to the \code{binomial} family for which a two-column outcome can be used representing the number of successes and the number of failures. } \note{ When using the log link, Poisson regression can also be carried out using the \code{poisson} family by including the log follow-up time \code{log(Y)} as an offset. However this approach does not generalize to other link functions. The \code{poisreg} family allows more general link functions including additive risk models with \code{poisreg(link = "identity")}. } \value{ An object of class \code{"family"}. See \code{\link[stats]{family}} for details. The family name, represented by the element \code{"family"} in the returned object, is \code{"poisson"} and not \code{"poisreg"}. This is necessary to prevent the \code{summary.glm} function from estimating an overdispersion parameter (which should be fixed at 1) and therefore giving incorrect standard errors for the estimates. } \examples{ ## Estimate incidence rate of diabetes in Denmark (1996-2015) by ## age and sex data(DMepi) DMepi$agegrp <- cut(DMepi$A, seq(from=0, to=100, by=5)) inc.diab <- glm(cbind(X, Y.nD) ~ -1 + agegrp + sex, family=poisreg, data=DMepi) ## The coefficients for agegrp are log incidence rates for men in each ## age group. The coefficient for sex is the log of the female:male ## incidence rate ratio. summary(inc.diab) ## Smooth function with non-constant M/F RR: requireNamespace("mgcv") library( mgcv ) gam.diab <- gam( cbind(X, Y.nD) ~ s(A,by=sex) + sex, family=poisreg, data=DMepi) ## There is no need/use for Y.nD in prediction data frames: nM <- data.frame( A=20:90, sex="M" ) nF <- data.frame( A=20:90, sex="F" ) ## Rates are returned in units of (1 year)^-1, so we must scale the ## rates by hand: matshade( nM$A, cbind( ci.pred(gam.diab, nM )*1000, ci.pred(gam.diab, nF )*1000, ci.exp( gam.diab,list(nM,nF)) ), plot=TRUE, col=c("blue","red","black"), log="y", xlab="Age", ylab="DM incidence rates per 1000 / M vs. F RR" ) abline(h=1) } \seealso{ \code{\link[stats]{glm}}, \code{\link[stats]{family}}. } \keyword{models} Epi/man/cutLexis.Rd0000644000176200001440000001776513763207003013652 0ustar liggesusers\name{cutLexis} \alias{cutLexis} \alias{countLexis} \title{ Cut follow-up at a specified date for each person. } \description{ Follow-up intervals in a Lexis object are divided into two sub-intervals: one before and one after an intermediate event. The intermediate event may denote a change of state, in which case the entry and exit status variables in the split Lexis object are modified. } \usage{ cutLexis( data, cut, timescale = 1, new.state = nlevels(data$lex.Cst)+1, new.scale = FALSE, split.states = FALSE, progressive = FALSE, precursor.states = transient(data), count = FALSE ) countLexis( data, cut, timescale = 1 ) } \arguments{ \item{data}{A \code{Lexis} object.} \item{cut}{A numeric vector with the times of the intermediate event. If a time is missing (\code{NA}) then the event is assumed to occur at time \code{Inf}. \code{cut} can also be a dataframe, see details.} \item{timescale}{The timescale that \code{cut} refers to. Numeric or character.} \item{new.state}{The state to which a transition occur at time \code{cut}. It may be a single value, which is then applied to all rows of \code{data}, or a vector with a separate value for each row} \item{new.scale}{Name of the timescale defined as "time since entry to new.state". If \code{TRUE} a name for the new scale is constructed. See details.} \item{split.states}{Should states that are not precursor states be split according to whether the intermediate event has occurred.} \item{progressive}{a logical flag that determines the changes to exit status. See details.} \item{precursor.states}{an optional vector of states to be considered as "less severe" than \code{new.state}. See Details below} \item{count}{logical indicating whether the \code{countLexis} options should be used. Specifying \code{count=TRUE} amounts to calling \code{countLexis}, in which case the arguments \code{new.state}, \code{progressive} and \code{precursor.states} will be ignored. } } \value{ A \code{Lexis} object, for which each follow-up interval containing the cutpoint is split in two: one before and one after the cutpoint. Any record representing follow up after the cutpoint has its value of \code{lex.Cst} updated to the new state. An extra time-scale is added; the time since the event at \code{cut}. This time scake will be\code{NA} for any follow-up prior to the intermediate event. The function \code{tsNA20} will replace all missing values in timescales with 0. This is commonly meeded when timescales defined as time since entry into an intermediate state are used in modeling. But you do not want to do that permanently in the cut data frame. } \note{ The \code{cutLexis} function superficially resembles the \code{splitLexis} function. However, the \code{splitLexis} function splits on a vector of common cut-points for all rows of the Lexis object, whereas the \code{cutLexis} function splits on a single time point, which may be distinct for each row, modifies the status variables, adds a new timescale and updates the attribute "time.since". This attribute is a character vector of the same length as the "time.scales" attribute, whose value is '""' if the corresponding timescale is defined for any piece of follow-up, and if the corresponding time scale is defined by say \code{cutLexis(obj,new.state="A",new.scale=TRUE)}, it has the value "A". } \details{ The \code{cutLexis} function allows a number of different ways of specifying the cutpoints and of modifying the status variable. If the \code{cut} argument is a dataframe it must have columns \code{lex.id}, \code{cut} and \code{new.state}. The values of \code{lex.id} must be unique. In this case it is assumed that each row represents a cutpoint (on the timescale indicated in the argument \code{timescale}). This cutpoint will be applied to all records in \code{data} with the corresponding \code{lex.id}. This makes it possible to apply \code{cutLexis} to a split \code{Lexis} object. If a \code{new.state} argument is supplied, the status variable is only modified at the time of the cut point. However, it is often useful to modify the status variable after the cutpoint when an important event occurs. There are three distinct ways of doing this. If the \code{progressive=TRUE} argument is given, then a "progressive" model is assumed, in which the status can either remain the same or increase during follow-up, but never decrease. This assumes that the state variables \code{lex.Cst} and \code{lex.Xst} are either numeric or ordered factors. In this case, if \code{new.state=X}, then any exit status with a value less than \code{X} is replaced with \code{X}. The Lexis object must already be progressive, so that there are no rows for which the exit status is less than the entry status. If \code{lex.Cst} and \code{lex.Xst} are factors they must be ordered factors if \code{progressive=TRUE} is given. As an alternative to the \code{progressive} argument, an explicit vector of precursor states, that are considered less severe than the new state, may be given. If \code{new.state=X} and \code{precursor.states=c(Y,Z)} then any exit status of \code{Y} or \code{Z} in the second interval is replaced with \code{X} and all other values for the exit status are retained. The \code{countLexis} function is a variant of \code{cutLexis} when the cutpoint marks a recurrent event, and the status variable is used to count the number of events that have occurred. Times given in \code{cut} represent times of new events. Splitting with \code{countLexis} increases the status variable by 1. If the current status is \code{X} and the exit status is \code{Y} before cutting, then after cutting the entry status is \code{X}, \code{X+1} for the first and second intervals, respectively, and the exit status is \code{X+1}, \code{Y+1} respectively. Moreover the values of the status is increased by 1 for all intervals for all intervals after the cut for the person in question. Hence, a call to \code{countLexis} is needed for as many times as the person with most events. But also it is immaterial in what order the cutpoints are entered. } \author{Bendix Carstensen, Steno Diabetes Center, \email{b@bxc.dk}, Martyn Plummer, \email{martyn.plummer@r-project.org} } \seealso{ \code{\link{mcutLexis}}, \code{\link{rcutLexis}}, \code{\link{addCov.Lexis}}, \code{\link{splitLexis}}, \code{\link{Lexis}}, \code{\link{summary.Lexis}}, \code{\link{timeSince}}, \code{\link{boxes.Lexis}} } \examples{ # A small artificial example xx <- Lexis( entry=list(age=c(17,24,33,29),per=c(1920,1933,1930,1929)), duration=c(23,57,12,15), exit.status=c(1,2,1,2) ) xx cut <- c(33,47,29,50) cutLexis(xx, cut, new.state=3, precursor=1) cutLexis(xx, cut, new.state=3, precursor=2) cutLexis(xx, cut, new.state=3, precursor=1:2) # The same as the last example cutLexis(xx, cut, new.state=3) # The same example with a factor status variable yy <- Lexis(entry = list(age=c(17,24,33,29),per=c(1920,1933,1930,1929)), duration = c(23,57,12,15), entry.status = factor(rep("alpha",4), levels=c("alpha","beta","gamma")), exit.status = factor(c("alpha","beta","alpha","beta"), levels=c("alpha","beta","gamma"))) cutLexis(yy,c(33,47,29,50),precursor="alpha",new.state="gamma") cutLexis(yy,c(33,47,29,50),precursor=c("alpha","beta"),new.state="aleph") ## Using a dataframe as cut argument rl <- data.frame( lex.id=1:3, cut=c(19,53,26), timescale="age", new.state=3 ) rl cutLexis( xx, rl ) cutLexis( xx, rl, precursor=1 ) cutLexis( xx, rl, precursor=0:2 ) ## It is immaterial in what order splitting and cutting is done xs <- splitLexis( xx, breaks=seq(0,100,10), time.scale="age" ) xs xsC <- cutLexis(xs, rl, precursor=0 ) xC <- cutLexis( xx, rl, pre=0 ) xC xCs <- splitLexis( xC, breaks=seq(0,100,10), time.scale="age" ) xCs str(xCs) } \keyword{survival} Epi/man/blcaIT.Rd0000644000176200001440000000127613751040403013172 0ustar liggesusers\name{blcaIT} \alias{blcaIT} \docType{data} \title{Bladder cancer mortality in Italian males} \description{ Number of deaths from bladder cancer and person-years in the Italian male population 1955--1979, in ages 25--79. } % \usage{data(blcaIT)} \format{ A data frame with 55 observations on the following 4 variables: \tabular{rl}{ \code{age}: \tab Age at death. Left endpoint of age class \cr \code{period}: \tab Period of death. Left endpoint of period \cr \code{D}: \tab Number of deaths \cr \code{Y}: \tab Number of person-years. } } % \source{ % Reference to a source... % } % \references{ % Reference to a publication... % } \examples{ data(blcaIT) } \keyword{datasets} Epi/man/S.typh.Rd0000644000176200001440000000421613751040403013216 0ustar liggesusers\name{S.typh} \alias{S.typh} \docType{data} \title{Salmonella Typhimurium outbreak 1996 in Denmark.} \description{ Matched case-control study of food poisoning. } \format{ A data frame with 136 observations on the following 15 variables: \tabular{rl}{ \code{id}: \tab Person identification \cr \code{set}: \tab Matched set indicator \cr \code{case}: \tab Case-control status (1:case, 0:control \cr \code{age}: \tab Age of individual \cr \code{sex}: \tab Sex of individual (1:male, 2:female) \cr \code{abroad}: \tab Within the last two weeks visited abroad (1:yes, 0:no) \cr \code{beef}: \tab Within the last two weeks eaten beef \cr \code{pork}: \tab Within the last two weeks eaten pork \cr \code{veal}: \tab Within the last two weeks eaten veal \cr \code{poultry}: \tab Within the last two weeks eaten poultry \cr \code{liverp}: \tab Within the last two weeks eaten liverpaste \cr \code{veg}: \tab Within the last two weeks eaten vegetables \cr \code{fruit}: \tab Within the last two weeks eaten fruit \cr \code{egg}: \tab Within the last two weeks eaten eggs \cr \code{plant7}: \tab Within the last two weeks eaten meat from plant no. 7 \cr } } \details{ In the fall of 1996 an unusually large number of Salmonella Typhimurium cases were recorded in Fyn county in Denmark. The Danish Zoonosis Centre set up a matched case-control study to find the sources. Cases and two age-, sex- and residency-matched controls were telephone interviewed about their food intake during the last two weeks. The participants were asked at which retailer(s) they had purchased meat. Retailers were independently of this linked to meat processing plants, and thus participants were linked to meat processing plants. This way persons could be linked to (amongst other) plant no 7.} \source{ Tine Hald. } \references{ Molbak K and Hald T: Salmonella Typhimurium outbreak in late summer 1996. A Case-control study. (In Danish: Salmonella typhimurium udbrud paa Fyn sensommeren 1996. En case-kontrol undersogelse.) Ugeskrift for Laeger., 159(36):5372-7, 1997. } \examples{ data(S.typh) } \keyword{datasets} Epi/man/nice.Rd0000644000176200001440000000141413751040403012744 0ustar liggesusers\name{nice} \alias{nice} \title{Nice breakpoints} \description{The function calls \code{\link{pretty}} for linear scale. For a log-scale nice are computed using a set of specified number in a decade. } \usage{ nice(x, log = F, lpos = c(1, 2, 5), ...) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{x}{Numerical vector to} \item{log}{Logical. Is the scale logartimic?} \item{lpos}{Numeric. Numbers between 1 and 10 giving the desired breakpoints in this interval.} \item{\dots}{Arguments passed on to \code{pretty} if \code{log}=FALSE} } \value{A vector of breakpoints.} \author{Bendix Carstensen, \email{b@bxc.dk}, \url{http://bendixcarstensen.com}} \seealso{pretty} \examples{ nice( exp( rnorm( 100 ) ), log=TRUE ) } \keyword{manip} Epi/man/apc.frame.Rd0000644000176200001440000001152213751040403013663 0ustar liggesusers\name{apc.frame} \alias{apc.frame} \title{ Produce an empty frame for display of parameter-estimates from Age-Period-Cohort-models. } \description{ A plot is generated where both the age-scale and the cohort/period scale is on the x-axis. The left vertical axis will be a logarithmic rate scale referring to age-effects and the right a logarithmic rate-ratio scale of the same relative extent as the left referring to the cohort and period effects (rate ratios). Only an empty plot frame is generated. Curves or points must be added with \code{points}, \code{lines} or the special utility function \code{\link{apc.lines}}. } \usage{ apc.frame( a.lab, cp.lab, r.lab, rr.lab = r.lab / rr.ref, rr.ref = r.lab[length(r.lab)/2], a.tic = a.lab, cp.tic = cp.lab, r.tic = r.lab, rr.tic = r.tic / rr.ref, tic.fac = 1.3, a.txt = "Age", cp.txt = "Calendar time", r.txt = "Rate per 100,000 person-years", rr.txt = "Rate ratio", ref.line = TRUE, gap = diff(range(c(a.lab, a.tic)))/10, col.grid = gray(0.85), sides = c(1,2,4) ) } \arguments{ \item{a.lab}{Numerical vector of labels for the age-axis.} \item{cp.lab}{Numerical vector of labels for the cohort-period axis.} \item{r.lab}{Numerical vector of labels for the rate-axis (left vertical)} \item{rr.lab}{Numerical vector of labels for the RR-axis (right vertical)} \item{rr.ref}{At what level of the rate scale is the RR=1 to be.} \item{a.tic}{Location of additional tick marks on the age-scale} \item{cp.tic}{Location of additional tick marks on the cohort-period-scale} \item{r.tic}{Location of additional tick marks on the rate-scale} \item{rr.tic}{Location of additional tick marks on the RR-axis.} \item{tic.fac}{Factor with which to diminish intermediate tick marks} \item{a.txt}{Text for the age-axis (left part of horizontal axis).} \item{cp.txt}{Text for the cohort/period axis (right part of horizontal axis).} \item{r.txt}{Text for the rate axis (left vertical axis).} \item{rr.txt}{Text for the rate-ratio axis (right vertical axis)} \item{ref.line}{Logical. Should a reference line at RR=1 be drawn at the calendar time part of the plot?} \item{gap}{Gap between the age-scale and the cohort-period scale} \item{col.grid}{Colour of the grid put in the plot.} \item{sides}{Numerical vector indicating on which sides axes should be drawn and annotated. This option is aimed for multi-panel displays where axes only are put on the outer plots.} } \details{ The function produces an empty plot frame for display of results from an age-period-cohort model, with age-specific rates in the left side of the frame and cohort and period rate-ratio parameters in the right side of the frame. There is a gap of \code{gap} between the age-axis and the calendar time axis, vertical grid lines at \code{c(a.lab,a.tic,cp.lab,cp.tic)}, and horizontal grid lines at \code{c(r.lab,r.tic)}. The function returns a numerical vector of length 2, with names \code{c("cp.offset","RR.fac")}. The y-axis for the plot will be a rate scale for the age-effects, and the x-axis will be the age-scale. The cohort and period effects are plotted by subtracting the first element (named \code{"cp.offset"}) of the returned result form the cohort/period, and multiplying the rate-ratios by the second element of the returned result (named \code{"RR.fac"}). } \value{ A numerical vector of length two, with names \code{c("cp.offset","RR.fac")}. The first is the offset for the cohort period-axis, the second the multiplication factor for the rate-ratio scale. Side-effect: A plot with axes and grid lines but no points or curves. Moreover, the option \code{apc.frame.par} is given the value \code{c("cp.offset","RR.fac")}, which is recognized by \code{\link{apc.plot}} and \code{\link{apc.lines}}. } \references{ B. Carstensen: Age-Period-Cohort models for the Lexis diagram. Statistics in Medicine, 26: 3018-3045, 2007. } \author{ Bendix Carstensen, Steno Diabetes Center, \url{http://bendixcarstensen.com} } \examples{ par( mar=c(4,4,1,4) ) res <- apc.frame( a.lab=seq(30,90,20), cp.lab=seq(1880,2000,30), r.lab=c(1,2,5,10,20,50), a.tic=seq(30,90,10), cp.tic=seq(1880,2000,10), r.tic=c(1:10,1:5*10), gap=27 ) res # What are the axes actually? par(c("usr","xlog","ylog")) # How to plot in the age-part: a point at (50,10) points( 50, 10, pch=16, cex=2, col="blue" ) # How to plot in the cohort-period-part: a point at (1960,0.3) points( 1960-res[1], 0.3*res[2], pch=16, cex=2, col="red" ) # or referring to the period-cohort part of the plot pc.points( 1960, 0.3, pch=16, cex=1, col="green" ) } \seealso{ \code{\link{apc.lines},\link{apc.fit}} } \keyword{hplot} Epi/man/rateplot.Rd0000644000176200001440000001723013751040403013663 0ustar liggesusers\name{rateplot} \alias{rateplot} \alias{Aplot} \alias{Pplot} \alias{Cplot} \title{ Functions to plot rates from a table classified by age and calendar time (period) } \description{ Produces plots of rates versus age, connected within period or cohort (\code{Aplot}), rates versus period connected within age-groups (\code{Pplot}) and rates and rates versus date of birth cohort (\code{Cplot}). \code{rateplot} is a wrapper for these, allowing to produce the four classical displays with a single call. } \usage{ rateplot( rates, which = c("ap","ac","pa","ca"), age = as.numeric( dimnames( rates )[[1]] ), per = as.numeric( dimnames( rates )[[2]] ), grid = FALSE, a.grid = grid, p.grid = grid, c.grid = grid, ygrid = grid, col.grid = gray( 0.9 ), a.lim = range( age, na.rm=TRUE ) + c(0,diff( range( age ) )/30), p.lim = range( per, na.rm=TRUE ) + c(0,diff( range( age ) )/30), c.lim = NULL, ylim = range( rates[rates>0], na.rm=TRUE ), at = NULL, labels = paste( at ), a.lab = "Age at diagnosis", p.lab = "Date of diagnosis", c.lab = "Date of birth", ylab = "Rates", type = "l", lwd = 2, lty = 1, log.ax = "y", las = 1, ann = FALSE, a.ann = ann, p.ann = ann, c.ann = ann, xannx = 1/20, cex.ann = 0.8, a.thin = seq( 1, length( age ), 2 ), p.thin = seq( 1, length( per ), 2 ), c.thin = seq( 2, length( age ) + length( per ) - 1, 2 ), col = par( "fg" ), a.col = col, p.col = col, c.col = col, ... ) Aplot( rates, age = as.numeric( dimnames( rates )[[1]] ), per = as.numeric( dimnames( rates )[[2]] ), grid = FALSE, a.grid = grid, ygrid = grid, col.grid = gray( 0.9 ), a.lim = range( age, na.rm=TRUE ), ylim = range( rates[rates>0], na.rm=TRUE ), at = NULL, labels = paste( at ), a.lab = names( dimnames( rates ) )[1], ylab = deparse( substitute( rates ) ), type = "l", lwd = 2, lty = 1, col = par( "fg" ), log.ax = "y", las = 1, c.col = col, p.col = col, c.ann = FALSE, p.ann = FALSE, xannx = 1/20, cex.ann = 0.8, c.thin = seq( 2, length( age ) + length( per ) - 1, 2 ), p.thin = seq( 1, length( per ), 2 ), p.lines = TRUE, c.lines = !p.lines, ... ) Pplot( rates, age = as.numeric( dimnames( rates )[[1]] ), per = as.numeric( dimnames( rates )[[2]] ), grid = FALSE, p.grid = grid, ygrid = grid, col.grid = gray( 0.9 ), p.lim = range( per, na.rm=TRUE ) + c(0,diff(range(per))/30), ylim = range( rates[rates>0], na.rm=TRUE ), p.lab = names( dimnames( rates ) )[2], ylab = deparse( substitute( rates ) ), at = NULL, labels = paste( at ), type = "l", lwd = 2, lty = 1, col = par( "fg" ), log.ax = "y", las = 1, ann = FALSE, cex.ann = 0.8, xannx = 1/20, a.thin = seq( 1, length( age ), 2 ), ... ) Cplot( rates, age = as.numeric( rownames( rates ) ), per = as.numeric( colnames( rates ) ), grid = FALSE, c.grid = grid, ygrid = grid, col.grid = gray( 0.9 ), c.lim = NULL, ylim = range( rates[rates>0], na.rm=TRUE ), at = NULL, labels = paste( at ), c.lab = names( dimnames( rates ) )[2], ylab = deparse( substitute( rates ) ), type = "l", lwd = 2, lty = 1, col = par( "fg" ), log.ax = "y", las = 1, xannx = 1/20, ann = FALSE, cex.ann = 0.8, a.thin = seq( 1, length( age ), 2 ), ... ) } \arguments{ \item{rates}{A two-dimensional table (or array) with rates to be plotted. It is assumed that the first dimension is age and the second is period.} \item{which}{A character vector with elements from \code{c("ap","ac","apc","pa","ca")}, indication which plots should be produced. One plot per element is produced. The first letter indicates the x-axis of the plot, the remaining which groups should be connected, i.e. \code{"pa"} will plot rates versus period and connect age-classes, and \code{"apc"} will plot rates versus age, and connect both periods and cohorts.} \item{age}{Numerical vector giving the means of the age-classes. Defaults to the rownames of \code{rates} as numeric.} \item{per}{Numerical vector giving the means of the periods. Defaults to the columnnames of \code{rates} as numeric.} \item{grid}{Logical indicating whether a background grid should be drawn.} \item{a.grid}{Logical indicating whether a background grid on the age-axis should be drawn. If numerical it indicates the age-coordinates of the grid.} \item{p.grid}{do. for the period.} \item{c.grid}{do. for the cohort.} \item{ygrid}{do. for the rate-dimension.} \item{col.grid}{The colour of the grid.} \item{a.lim}{Range for the age-axis.} \item{p.lim}{Range for the period-axis.} \item{c.lim}{Range for the cohort-axis.} \item{ylim}{Range for the y-axis (rates).} \item{at}{Position of labels on the y-axis (rates).} \item{labels}{Labels to put on the y-axis (rates).} \item{a.lab}{Text on the age-axis. Defaults to "Age".} \item{p.lab}{Text on the period-axis. Defaults to "Date of diagnosis".} \item{c.lab}{Text on the cohort-axis. Defaults to "Date of birth".} \item{ylab}{Text on the rate-axis. Defaults to the name of the rate-table.} \item{type}{How should the curves be plotted. Defaults to \code{"l"}.} \item{lwd}{Width of the lines. Defaults to 2.} \item{lty}{Which type of lines should be used. Defaults to 1, a solid line.} \item{log.ax}{Character with letters from \code{"apcyr"}, indicating which axes should be logarithmic. \code{"y"} and \code{"r"} both refer to the rate scale. Defaults to \code{"y"}.} \item{las}{see \code{par}.} \item{ann}{Should the curves be annotated?} \item{a.ann}{Logical indicating whether age-curves should be annotated.} \item{p.ann}{do. for period-curves.} \item{c.ann}{do. for cohort-curves.} \item{xannx}{The fraction that the x-axis is expanded when curves are annotated.} \item{cex.ann}{Expansion factor for characters annotating curves.} \item{a.thin}{Vector of integers indicating which of the age-classes should be labelled.} \item{p.thin}{do. for the periods.} \item{c.thin}{do. for the cohorts.} \item{col}{Colours for the curves.} \item{a.col}{Colours for the age-curves.} \item{p.col}{do. for the period-curves.} \item{c.col}{do. for the cohort-curves.} \item{p.lines}{Should rates from the same period be connected?} \item{c.lines}{Should rates from the same cohort be connected?} \item{...}{Additional arguments pssed on to \code{matlines} when plotting the curves.} } \details{ Zero values of the rates are ignored. They are neiter in the plot nor in the calculation of the axis ranges. } \value{ \code{NULL}. The function is used for its side-effect, the plot. } \author{ Bendix Carstensen, Steno Diabetes Center, \url{http://bendixcarstensen.com} } \seealso{ \code{\link{apc.frame}} } \examples{ data( blcaIT ) attach(blcaIT) # Table of rates: bl.rate <- tapply( D, list(age,period), sum ) / tapply( Y, list(age,period), sum ) bl.rate # The four classical plots: par( mfrow=c(2,2) ) rateplot( bl.rate*10^6 ) # The labels on the vertical axis could be nicer: rateplot( bl.rate*10^6, at=10^(-1:3), labels=c(0.1,1,10,100,1000) ) # More bells an whistles par( mfrow=c(1,3), mar=c(3,3,1,1), oma=c(0,3,0,0), mgp=c(3,1,0)/1.6 ) rateplot( bl.rate*10^6, ylab="", ann=TRUE, which=c("AC","PA","CA"), at=10^(-1:3), labels=c(0.1,1,10,100,1000), col=topo.colors(11), cex.ann=1.2 ) } \keyword{hplot} Epi/man/apc.fit.Rd0000644000176200001440000003020413751040403013351 0ustar liggesusers\name{apc.fit} \alias{apc.fit} \title{ Fit an Age-Period-Cohort model to tabular data. } \description{ Fits the classical five models to tabulated rate data (cases, person-years) classified by two of age, period, cohort: Age, Age-drift, Age-Period, Age-Cohort and Age-Period-Cohort. There are no assumptions about the age, period or cohort classes being of the same length, or that tabulation should be only by two of the variables. Only requires that mean age and period for each tabulation unit is given. } \usage{ apc.fit( data, A, P, D, Y, ref.c, ref.p, dist = c("poisson","binomial"), model = c("ns","bs","ls","factor"), dr.extr = "Y", parm = c("ACP","APC","AdCP","AdPC","Ad-P-C","Ad-C-P","AC-P","AP-C"), npar = c( A=5, P=5, C=5 ), scale = 1, alpha = 0.05, print.AOV = TRUE ) } \arguments{ \item{data}{Data frame with (at least) variables, \code{A} (age), \code{P} (period), \code{D} (cases, deaths) and \code{Y} (person-years). Cohort (date of birth) is computed as \code{P-A}. If this argument is given the arguments \code{A}, \code{P}, \code{D} and \code{Y} are ignored.} \item{A}{Age; numerical vector with mean age at diagnosis for each unit.} \item{P}{Period; numerical vector with mean date of diagnosis for each unit.} \item{D}{Cases, deaths; numerical vector.} \item{Y}{Person-years; numerical vector. Also used as denominator for binomial data, see the \code{dist} argument.} \item{ref.c}{Reference cohort, numerical. Defaults to median date of birth among cases. If used with \code{parm="AdCP"} or \code{parm="AdPC"}, the residual cohort effects will be 1 at \code{ref.c}} \item{ref.p}{Reference period, numerical. Defaults to median date of diagnosis among cases.} \item{dist}{Distribution (or more precisely: Likelihood) used for modeling. if a binomial model us used, \code{Y} is assumed to be the denominator; \code{"binomial"} gives a binomial model with logit link. The Age-effects returned are converted to the probability scale, Period and Cohort effects are still odds-ratios.} \item{model}{Type of model (covariate effects) fitted: \itemize{ \item \code{ns} fits a model with natural splines for each of the terms, with \code{npar} parameters for the terms. \item \code{bs} fits a model with B-splines for each of the terms, with \code{npar} parameters for the terms. \item \code{ls} fits a model with linear splines. \item \code{factor} fits a factor model with one parameter per value of \code{A}, \code{P} and \code{P-A}. \code{npar} is ignored in this case. } } \item{dr.extr}{Character or numeric. How the drift parameter should be extracted from the age-period-cohort model. Specifies the inner product used for definition of orthogonality of the period / cohort effects to the linear effects --- in terms of a diagonal matrix. \code{"Y"} (default) uses the no. person-time, \code{Y}, corresponding to the observed information about the square root of the rate. \code{"R"} or \code{"L"} uses \code{Y*Y/D} corresponding to the observed information about the rate (usually termed "lambda", hence the "\code{L}"). \code{"D"} or \code{"T"} uses the no. events as the weight in the inner product, corresponding to the information about the log-rate (usually termed "theta", hence the "\code{T}"). If given \code{"n"} (naive) (well, in fact any other character value) will induce the use of the standard inner product putting equal weight on all units in the dataset. If \code{dr.extr} is a numeric vector this is used as the diagonal of the matrix inducing the inner product. If \code{dr.extr} is a numeric scalar, \code{D + dr.extr*Y} is used as the diagonal of the matrix inducing the inner product. This family of inner products are the only ones that meet the split-observation invariance criterion. The setting of this parameter has no effect on the fit of the model, it only influences the parametrization returned in the \code{Age}, \code{Per} and \code{Coh} elements of the resulting list. } \item{parm}{Character. Indicates the parametrization of the effects. The first four refer to the ML-fit of the Age-Period-Cohort model, the last four give Age-effects from a smaller model and residuals relative to this. If one of the latter is chosen, the argument \code{dr.extr} is ignored. Possible values for \code{parm} are: \itemize{ \item \code{"ACP"}: ML-estimates. Age-effects as rates for the reference cohort. Cohort effects as RR relative to the reference cohort. Period effects constrained to be 0 on average with 0 slope. \item \code{"APC"}: ML-estimates. Age-effects as rates for the reference period. Period effects as RR relative to the reference period. Cohort effects constrained to be 0 on average with 0 slope. \item \code{"AdCP"}: ML-estimates. Age-effects as rates for the reference cohort. Cohort and period effects constrained to be 0 on average with 0 slope. In this case returned effects do not multiply to the fitted rates, the drift is missing and needs to be included to produce the fitted values. \item \code{"AdPC"}: ML-estimates. Age-effects as rates for the reference period. Cohort and period effects constrained to be 0 on average with 0 slope. In this case returned effects do not multiply to the fitted rates, the drift is missing and needs to be included to produce the fitted values. \item \code{"Ad-C-P"}: Age effects are rates for the reference cohort in the Age-drift model (cohort drift). Cohort effects are from the model with cohort alone, using log(fitted values) from the Age-drift model as offset. Period effects are from the model with period alone using log(fitted values) from the cohort model as offset. \item \code{"Ad-P-C"}: Age effects are rates for the reference period in the Age-drift model (period drift). Period effects are from the model with period alone, using log(fitted values) from the Age-drift model as offset. Cohort effects are from the model with cohort alone using log(fitted values) from the period model as offset. \item \code{"AC-P"}: Age effects are rates for the reference cohort in the Age-Cohort model, cohort effects are RR relative to the reference cohort. Period effects are from the model with period alone, using log(fitted values) from the Age-Cohort model as offset. \item \code{"AP-C"}: Age effects are rates for the reference period in the Age-Period model, period effects are RR relative to the reference period. Cohort effects are from the model with cohort alone, using log(fitted values) from the Age-Period model as offset. } } \item{npar}{The number of parameters/knots to use for each of the terms in the model. If it is vector of length 3, the numbers are taken as the no. of knots for Age, Period and Cohort, respectively. Unless it has a names attribute with values "A", "P" and "C" in which case these will be used. The knots chosen are the quantiles \code{(1:nk-0.5)/nk} of the events (i.e. of \code{rep(A,D)} and similarly for \code{P} and \code{C}). \code{npar} may also be a named list of three numerical vectors with names "A", "P" and "C", in which case these taken as the knots for the age, period and cohort effect, the smallest and largest element in each vector are used as the boundary knots.} \item{alpha}{The significance level. Estimates are given with (1-\code{alpha}) confidence limits.} \item{scale}{numeric(1), factor multiplied to the rate estimates before output.} \item{print.AOV}{Should the analysis of deviance table for the models be printed?} } \value{ An object of class "apc" (recognized by \code{\link{apc.plot}} and \code{\link{apc.lines}}) --- a list with components: \item{Type}{Text describing the model and parametrization returned.} \item{Model}{The model object(s) on which the parametrization is based.} \item{Age}{Matrix with 4 columns: \code{A.pt} with the ages (equals \code{unique(A)}) and three columns giving the estimated rates with c.i.s.} \item{Per}{Matrix with 4 columns: \code{P.pt} with the dates of diagnosis (equals \code{unique(P)}) and three columns giving the estimated RRs with c.i.s.} \item{Coh}{Matrix with 4 columns: \code{C.pt} with the dates of birth (equals \code{unique(P-A)}) and three columns giving the estimated RRs with c.i.s.} \item{Drift}{A 3 column matrix with drift-estimates and c.i.s: The first row is the ML-estimate of the drift (as defined by \code{drift}), the second row is the estimate from the Age-drift model. The first row name indicates which type of inner product were used for projections. For the sequential parametrizations, only the latter is given.} \item{Ref}{Numerical vector of length 2 with reference period and cohort. If ref.p or ref.c was not supplied the corresponding element is NA.} \item{Anova}{Analysis of deviance table comparing the five classical models.} \item{Knots}{If \code{model} is one of \code{"ns"} or \code{"bs"}, a list with three components: \code{Age}, \code{Per}, \code{Coh}, each one a vector of knots. The max and the min of the vectors are the boundary knots.} } \details{ Each record in the input data frame represents a subset of a Lexis diagram. The subsets need not be of equal length on the age and period axes, in fact there are no restrictions on the shape of these; they could be Lexis triangles for example. The requirement is that \code{A} and \code{P} are coded with the mean age and calendar time of observation in the subset. This is essential since \code{A} and \code{P} are used as quantitative variables in the models. This approach is different from to the vast majority of the uses of APC-models in the literature where a factor model is used for age, period and cohort effects. The latter can be obtained by using \code{model="factor"}. Note however that the cohort factor is defined from \code{A} and \code{P}, so that it is not possible in this framework to replicate the Boyle-Robertson fallacy. } \references{ The considerations behind the parametrizations used in this function are given in detail in: B. Carstensen: Age-Period-Cohort models for the Lexis diagram. Statistics in Medicine, 10; 26(15):3018-45, 2007. Various links to course material etc. is available through \url{http://bendixcarstensen.com/APC/} } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com} } \seealso{ \code{\link{apc.frame}}, \code{\link{apc.lines}}, \code{\link{apc.plot}}, \code{\link{LCa.fit}}, \code{\link{apc.LCa}}. } \examples{ library( Epi ) data(lungDK) # Taylor a dataframe that meets the requirements for variable names exd <- lungDK[,c("Ax","Px","D","Y")] names(exd)[1:2] <- c("A","P") # Three different ways of parametrizing the APC-model, ML ex.1 <- apc.fit( exd, npar=7, model="ns", dr.extr="1", parm="ACP", scale=10^5 ) ex.D <- apc.fit( exd, npar=7, model="ns", dr.extr="D", parm="ACP", scale=10^5 ) ex.Y <- apc.fit( exd, npar=7, model="ns", dr.extr="Y", parm="ACP", scale=10^5 ) # Sequential fit, first AC, then P given AC. ex.S <- apc.fit( exd, npar=7, model="ns", parm="AC-P", scale=10^5 ) # Show the estimated drifts ex.1[["Drift"]] ex.D[["Drift"]] ex.Y[["Drift"]] ex.S[["Drift"]] # Plot the effects lt <- c("solid","22")[c(1,1,2)] apc.plot( ex.1, lty=c(1,1,3) ) apc.lines( ex.D, col="red", lty=c(1,1,3) ) apc.lines( ex.Y, col="limegreen", lty=c(1,1,3) ) apc.lines( ex.S, col="blue", lty=c(1,1,3) ) } \keyword{models} \keyword{regression} Epi/man/twoby2.Rd0000644000176200001440000000352413751040403013260 0ustar liggesusers\name{twoby2} \alias{twoby2} \title{Analysis of a two by two table} \description{ Computes the usual measures of association in a 2 by 2 table with confidence intervals. Also produces asymtotic and exact tests. Assumes that comparison of probability of the first column level between levels of the row variable is of interest. Output requires that the input matrix has meaningful row and column labels. } \usage{ twoby2(exposure, outcome, alpha = 0.05, print = TRUE, dec = 4, conf.level = 1-alpha, F.lim = 10000) } \arguments{ \item{exposure}{If a table the analysis is based on the first two rows and first two columns of this. If a variable, this variable is tabulated against} \item{outcome}{as the second variable} \item{alpha}{Significance level} \item{print}{Should the results be printed?} \item{dec}{Number of decimals in the printout.} \item{conf.level}{1-\code{alpha}} \item{F.lim}{If the table total exceeds \code{F.lim}, Fisher's exact test is not computed} } \value{A list with elements: \item{table}{The analysed 2 x 2 table augmented with probabilities and confidence intervals. The confidence intervals for the probabilities are computed using the normal approximation to the log-odds. Confidence intervals for the difference of proportions are computed using method 10 from Newcombe, Stat.Med. 1998, 17, pp.873 ff.} \item{measures}{A table of Odds-ratios and relative risk with confidence intervals.} \item{p.value}{Exact p-value for the null hypothesis of OR=1} } \author{ Mark Myatt. Modified by Bendix Carstensen. } \examples{ Treat <- sample(c("A","B"), 50, rep=TRUE ) Resp <- c("Yes","No")[1+rbinom(50,1,0.3+0.2*(Treat=="A"))] twoby2( Treat, Resp ) twoby2( table( Treat, Resp )[,2:1] ) # Comparison the other way round } \keyword{univar} \keyword{htest} Epi/man/foreign.Lexis.Rd0000644000176200001440000000622313751040403014545 0ustar liggesusers\name{foreign.Lexis} \Rdversion{1.1} \alias{msdata} \alias{msdata.Lexis} \alias{etm} \alias{etm.Lexis} \title{Create a data structures suitable for use with packages \code{mstate} or \code{etm}. } \description{ The \code{mstate} package requires input in the form of a stacked dataset with specific variable names. This is provided by \code{msdata.Lexis}. The resulting dataframe contains the same information as the result of a call to \code{\link{stack.Lexis}}. The \code{etm} package requires input (almost) in the form of a \code{Lexis} object, but with specific column names etc. This is provided by \code{etm.Lexis}. } \usage{ msdata(obj, ...) \method{msdata}{Lexis}(obj, time.scale = timeScales(obj)[1], ... ) \method{etm}{Lexis}( data, time.scale = timeScales(data)[1], cens.name = "cens", s = 0, t = "last", covariance = TRUE, delta.na = TRUE, ... ) } \arguments{ \item{obj}{A \code{\link{Lexis}} object.} \item{data}{A \code{\link{Lexis}} object.} \item{time.scale}{Name or number of timescale in the \code{Lexis} object.} \item{cens.name}{Name of the code for censoring used by \code{etm}. It is only necessary to change this if one of the states in the \code{Lexis} object has name "\code{cens}".} \item{s}{Passed on to \code{etm}.} \item{t}{Passed on to \code{etm}.} \item{covariance}{Passed on to \code{etm}.} \item{delta.na}{Passed on to \code{etm}.} \item{\dots}{Further arguments.} } \value{ \code{msdata.Lexis} returns a dataframe with the \code{Lexis} specific variables stripped, and with the following added: \code{id}, \code{Tstart}, \code{Tstop}, \code{from}, \code{to}, \code{trans}, \code{status}, which are used in the \code{mstate} package. \code{etm.Lexis} transforms the \code{Lexis} object into a dataframe suitable for analysis by the function \code{etm} from the \code{etm} package, and actually calls this function, so returns an object of class \code{etm}. } \author{ Bendix Carstensen, \email{b@bxc.dk}, \url{http://bendixcarstensen.com} } \examples{ data(DMlate) str(DMlate) dml <- Lexis( entry = list(Per=dodm,Age=dodm-dobth,DMdur=0), exit = list(Per=dox), exit.status = factor(!is.na(dodth),labels=c("DM","Dead")), data = DMlate[1:1000,] ) dmi <- cutLexis( dml, cut=dml$doins, new.state="Ins", pre="DM" ) summary( dmi ) # Use the interface to the mstate package if( require(mstate) ) { ms.dmi <- msdata.Lexis( dmi ) # Check that all the transitions and person-years got across. with( ms.dmi, rbind( table(status,trans), tapply(Tstop-Tstart,trans,sum) ) ) } # Use the etm package directly with a Lexis object if( require(etm) ) { dmi <- subset(dmi,lex.id<1000) etm.D <- etm.Lexis( dmi, time.scale=3 ) str( etm.D ) plot( etm.D, col=rainbow(5), lwd=2, lty=1, xlab="DM duration" ) } } \seealso{ \code{\link{stack.Lexis}}, \code{\link[mstate:msprep]{msprep}}, \code{\link[etm:etm]{etm}} } \keyword{survival} Epi/man/DMlate.Rd0000644000176200001440000000437413751040403013204 0ustar liggesusers\name{DMlate} \Rdversion{1.1} \alias{DMlate} \alias{DMrand} \docType{data} \title{ The Danish National Diabetes Register. } \description{ These two datasets each contain a random sample of 10,000 persons from the Danish National Diabetes Register. \code{DMrand} is a random sample from the register, whereas \code{DMlate} is a random sample among those with date of diagnosis after 1.1.1995. All dates are radomly jittered by adding a U(-7,7) (days). } \usage{data(DMrand) data(DMlate)} \format{ A data frame with 10000 observations on the following 7 variables. \describe{ \item{\code{sex}}{Sex, a factor with levels \code{M} \code{F}} \item{\code{dobth}}{Date of birth} \item{\code{dodm}}{Date of inclusion in the register} \item{\code{dodth}}{Date of death} \item{\code{dooad}}{Date of 2nd prescription of OAD} \item{\code{doins}}{Date of 2nd insulin prescription} \item{\code{dox}}{Date of exit from follow-up.} } } \details{All dates are given in fractions of years, so 1998.000 corresponds to 1 January 1998 and 1998.997 to 31 December 1998. All dates are randomly perturbed by a small amount, so no real persons have any of the combinations of the 6 dates in the dataset. But results derived from the data will be quite close to those that would be obtained if the entire 'real' diabetes register were used. } \source{ Danish National Board of Health. } \references{ B Carstensen, JK Kristensen, P Ottosen and K Borch-Johnsen: The Danish National Diabetes Register: Trends in incidence, prevalence and mortality, Diabetologia, 51, pp 2187--2196, 2008. In partucular see the appendix at the end of the paper. } \examples{ data(DMlate) str(DMlate) dml <- Lexis( entry=list(Per=dodm, Age=dodm-dobth, DMdur=0 ), exit=list(Per=dox), exit.status=factor(!is.na(dodth),labels=c("DM","Dead")), data=DMlate ) # Cut the follow-up at insulin start, and introduce a new timescale, # and split non-precursor states system.time( dmi <- cutLexis( dml, cut = dml$doins, pre = "DM", new.state = "Ins", new.scale = "t.Ins", split.states = TRUE ) ) summary( dmi ) } \keyword{datasets} Epi/man/mod.Lexis.Rd0000644000176200001440000002130513751040403013671 0ustar liggesusers\name{mod.Lexis} \alias{glm.Lexis} \alias{gam.Lexis} \alias{coxph.Lexis} \title{Fit intensity models to follow-up data in Lexis objects } \description{ Modeling intensities based on Lexis objects, exploiting the structure of the Lexis objects where the events and risk time have predefined representations. This allows a simpler syntax than the traditional explicit modeling using \code{\link{glm}}, \code{\link{gam}} and \code{\link{coxph}}. Requires that \code{lex.Cst} and \code{lex.Xst} are defined as factors. But it is just a set of wrappers fro \code{glm}, \code{gam} and \code{coxph}. } \usage{ glm.Lexis( Lx, # Lexis object formula, # ~ model from = preceding(Lx,to), # 'from' states to = absorbing(Lx) , # 'to' states paired = FALSE, # only the pairwise link = "log", # link function scale = 1, # scaling of PY verbose = TRUE, # report what is done? \dots ) # further arguments to glm gam.Lexis( Lx, # Lexis object formula, # ~ model from = preceding(Lx,to), # 'from' states to = absorbing(Lx) , # 'to' states paired = FALSE, # only the pairwise link = "log", # link function scale = 1, # scaling of PY verbose = TRUE, # report what is done? \dots ) # further arguments to gam coxph.Lexis( Lx, # Lexis object formula, # timescale ~ model from = preceding(Lx,to), # 'from' states to = absorbing(Lx) , # 'to' states paired = FALSE, # only the pairwise verbose = TRUE, # report what is done? \dots ) # further arguments to coxph } \arguments{ \item{Lx}{A \code{\link{Lexis}} object representing cohort follow-up. } \item{formula}{Model formula describing the model for the intensity(-ies). For \code{glm} and \code{gam}, the formula should be one-sided; for \code{coxph} the formula should be two-sided and have the name of the time-scale used for baseline hazard as the l.h.s. } \item{from}{Character vector of states \bold{from} which transitions are considered. May also be an integer vector in which case the reference will be to the position of levels of \code{lex.Cst}. Defaults to the collection of transient states immediately preceding the absorbing states. } \item{to}{Character vector of states \bold{to} which a transition is considered an event. May also be an integer vector in which case the reference will be to the position of levels of \code{lex.Xst}. Defaults to the set of absorbing states. } \item{paired}{Logical. Should the states mentioned in \code{to}, rep. \code{from} be taken as pairs, indicating the only transitions modeled. If \code{FALSE} all transitions from any of the states in \code{from} to any states in \code{to} are modeled. } \item{link}{Character; name of the link function used, allowed values are \code{'log'} (the default), \code{'identity'} and \code{'sqrt'}, see the family \code{\link{poisreg}}. } \item{scale}{Scalar. \code{lex.dur} is divided by this number before analysis, so that you can get resulting rates on a scale of your wish. } \item{verbose}{Print information on the states modeled? } \item{\dots}{Further arguments passed on to \code{glm}, \code{glm} or \code{coxph} } } \details{ The \code{glm} and \code{gam} models are fitted using the family \code{\link{poisreg}} which is a bit faster than the traditional \code{poisson} family. The response variable for this family is a two-column vector of events and person-time respectively, so the predictions, for example using \code{\link{ci.pred}} does not require \code{lex.dur} (and would ignore this) as variable in the \code{newdata}. \code{ci.pred} will return the estimated rates in units of the \code{lex.dur} in the \code{Lexis} object, scaled by \code{scale}, which has a default value of 1. The default is to model all transitions into any absorbing state by the same model (how wise is that??). If only \code{from} is given, \code{to} is set to all states reachable from \code{from}, which may be a really goofy model and if so a warning is issued. If only \code{to} is given, \code{from} is set to the collection of states from which \code{to} can be reached directly --- see \code{\link{preceding}} and its cousins. This convention means that if you have a \code{\link{Lexis}} object representing a simple survival analysis, with states, say, "alive" and "dead", you can dispense with the \code{from} and \code{to} arguments. Occasionally you only want to model a subset of the possible transitions from states in \code{from} to states in \code{to}, in which case you specify \code{from} and \code{to} as character vectors of the same length and set \code{paired=TRUE}. Then only transitions \code{from[i]} to \code{to[i]}, \code{i}=1,2,... will be modeled. There is no working \code{update} functions for these objects (yet). Strictly speaking, it is a bit counter-intuitive to have the time-scale on the l.h.s. of the formula for the \code{coxph} since the time scale is also a predictor of the occurrence rate. On the other hand, calling \code{coxph} directly would also entail having the name of the time scale in the \code{Surv} object on the l.h.s. of the formula. So the inconsistency is merely carried over from \code{coxph}. } \value{\code{glm.Lexis} returns a \code{\link{glm}} object, which is also of class \code{glm.lex}, \code{gam.Lexis} returns a \code{\link[mgcv]{gam}} object, which is also of class \code{gam.lex}, and \code{coxph.Lexis} returns a \code{\link[survival]{coxph}} object, which is also of class \code{coxph.lex}. These extra class attributes are meant to facilitate the (still pending) implementation of an \code{update} function. The returned objects all have an extra attribute, \code{Lexis} which is a list with entries \code{data}, the name of the \code{Lexis} object modeled (note that it is \emph{not} the object, only the name of it, which may not be portable); \code{trans}, a character vector of transitions modeled; \code{formula}, the model formula; and \code{scale}, the scaling applied to \code{lex.dur} before modeling. Only the \code{glm} and \code{gam} objects have the \code{scale} element in the list; a scalar indicating the scaling of \code{lex.dur} before modeling. Note that the formula component of the \code{Lexis} attribute of a \code{coxph} object is a two-sided formula with the baseline time scale as the l.h.s. } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com}. } \seealso{ \code{\link{Lexis}}, \code{\link{cutLexis}}, \code{\link{mcutLexis}}, \code{\link{addCov.Lexis}}, \code{\link{absorbing}}, \code{\link{transient}} } \examples{ library( Epi ) library( survival ) data( DMlate ) # Lexis object of total follow-up mL <- Lexis( entry = list(age=dodm-dobth,per=dodm), exit = list(per=dox), exit.status = factor(!is.na(dodth),labels=c("Alive","Dead")), data = DMlate ) # Cut follow-up at start of insulin use cL <- cutLexis( mL, cut = mL$doins, timescale = "per", new.state = "Ins", precursor.states = "Alive" ) # Split follow-up on age-axis system.time( sL <- splitLexis( cL, breaks=0:25*4, time.scale="age") ) # ( consider splitMulti from the popEpi package ) summary( sL ) # glm models for rates based on the time-split dataset by insulin and sex # Proportional hazards model with insulin as time-dependent variable # - uses the defaul of modeling all transitions from both transient # states ("Alive" and "Ins") to the absorbing state ("Dead"). mt <- glm.Lexis( sL, ~ sex + lex.Cst + Ns(age,knots=c(15,3:8*10)) ) # prediction of mortality rates from "Alive" with and without PH assumption nA <- data.frame( age=40:70, sex="M", lex.Cst="Alive" ) nI <- data.frame( age=40:70, sex="M", lex.Cst="Ins" ) matshade( nA$age, cbind( ci.pred(mt,nA), ci.pred(mt,nI) )*1000, plot=TRUE, lwd=3, lty=1, log="y", col=c("black","blue","red"), xlab="Age", ylab="Mortality per 1000 PY" ) # gam models may take some time to run so we leave it out \dontrun{ mt.gam <- gam.Lexis( sL, ~ sex + lex.Cst + s(age), to="Dead", scale=1000 ) } # Fit a Cox model for mortality with age as baseline time scale and # insulin (lex.Cst) as time-dependent covariate mt.cox <- coxph.Lexis( sL, age ~ sex + lex.Cst, c("Alive","Ins"), "Dead" ) # Pretty much the same results for regression paramters as the glm: ci.exp( mt , subset="ex" ) # ci.exp( mt.gam, subset="ex" ) ci.exp( mt.cox, subset="ex" ) } \keyword{models} Epi/man/ftrend.Rd0000644000176200001440000000476613751040403013325 0ustar liggesusers\name{ftrend} \alias{ftrend} \title{Fit a floating trend to a factor in generalized linear model} \description{ Fits a "floating trend" model to the given factor in a glm in a generalized linear model by centering covariates. } \usage{ ftrend(object, ...) } \arguments{ \item{object}{fitted \code{lm} or \code{glm} object. The model must not have an intercept term} \item{...}{arguments to the \code{nlm} function} } \details{ \code{ftrend()} calculates "floating trend" estimates for factors in generalized linear models. This is an alternative to treatment contrasts suggested by Greenland et al. (1999). If a regression model is fitted with no intercept term, then contrasts are not used for the first factor in the model. Instead, there is one parameter for each level of this factor. However, the interpretation of these parameters, and their variance-covariance matrix, depends on the numerical coding used for the covariates. If an arbitrary constant is added to the covariate values, then the variance matrix is changed. The \code{ftrend()} function takes the fitted model and works out an optimal constant to add to the covariate values so that the covariance matrix is approximately diagonal. The parameter estimates can then be treated as approximately independent, thus simplifying their presentation. This is particularly useful for graphical display of dose-response relationships (hence the name). Greenland et al. (1999) originally suggested centring the covariates so that their weighted mean, using the fitted weights from the model, is zero. This heuristic criterion is improved upon by \code{ftrend()} which uses the same minimum information divergence criterion as used by Plummer (2003) for floating variance calculations. \code{ftrend()} calls \code{nlm()} to do the minimization and will pass optional arguments to control it. } \note{ The "floating trend" method is an alternative to the "floating absolute risk" method, which is implemented in the function \code{float()}. } \value{ A list with the following components \item{coef}{coefficients for model with adjusted covariates.} \item{vcov}{Variance-covariance matrix of adjusted coefficients.} } \references{ Greenland S, Michels KB, Robins JM, Poole C and Willet WC (1999) Presenting statistical uncertainty in trends and dose-response relations, \emph{American Journal of Epidemiology}, \bold{149}, 1077-1086. } \author{Martyn Plummer} \seealso{\code{\link{float}}} \keyword{regression} Epi/man/lls.Rd0000644000176200001440000000335213751040403012623 0ustar liggesusers\name{lls} \alias{lls} \alias{clear} \title{Functions to manage and explore the workspace } \description{These functions help you to find out what has gone wrong and to start afresh if needed. } \usage{ lls(pos = 1, pat = "", all=FALSE, print=TRUE ) clear() } \arguments{ \item{pos}{Numeric. What position in the search path do you want listed.} \item{pat}{Character. List only objects that have this string in their name.} \item{all}{Logical. Should invisible objects be printed too - see \code{\link{ls}} to which this argument is passed.} \item{print}{Logical. Should the result be printed?} } \details{\code{lls} is designed to give a quick overview of the name, mode, class and dimension of the object in your workspace. They may not always be what you think they are. \code{clear} clears all your objects from workspace, and all attached objects too --- it only leaves the loaded packages in the search path; thus allowing a fresh start without closing and restarting R. } \value{ \code{lls} returns a data frame with four character variables: code{name}, code{mode}, code{class} and code{size} and one row per object in the workspace (if \code{pos=1}). \code{size} is either the length or the dimension of the object. The data frame is by default printed with left-justified columns. } \author{\code{lls}: Unknown. Modified by Bendix Carstensen from a long forgotten snatch. \code{clear}: Michael Hills / David Clayton.} \examples{ x <- 1:10 y <- rbinom(10, 1, 0.5) m1 <- glm( y ~ x, family=binomial ) M <- matrix( 1:20, 4, 5 ) .M <- M dfr <- data.frame(x,y) attach( dfr ) lls() search() clear() search() lls() lls(all=TRUE) } \keyword{attributes}Epi/man/contr.cum.Rd0000644000176200001440000000306213751040403013737 0ustar liggesusers\name{contr.cum} \alias{contr.cum} \alias{contr.2nd} \alias{contr.diff} \alias{contr.orth} \title{ Contrast matrices } \description{ Return a matrix of contrasts for factor coding. } \usage{ contr.cum(n) contr.diff(n) contr.2nd(n) contr.orth(n) } \arguments{ \item{n}{A vector of levels for a factor, or the number of levels.} } \details{ These functions are used for creating contrast matrices for use in fitting regression models. The columns of the resulting matrices contain contrasts which can be used for coding a factor with \code{n} levels. \code{contr.cum} gives a coding corresponding to successive differences between factor levels. \code{contr.diff} gives a coding that correspond to the cumulative sum of the value for each level. This is not meaningful in a model where the intercept is included, therefore \code{n} columns ia always returned. \code{contr.2nd} gives contrasts corresponding to 2nd order differences between factor levels. Returns a matrix with \code{n-2} columns. \code{contr.orth} gives a matrix with \code{n-2} columns, which are mutually orthogonal and orthogonal to the matrix \code{cbind(1,1:n)} } \value{ A matrix with \code{n} rows and \code{k} columns, with \code{k}=\code{n} for \code{contr.diff} \code{k}=\code{n-1} for \code{contr.cum} \code{k}=\code{n-2} for \code{contr.2nd} and \code{contr.orth}. } \author{Bendix Carstensen} \seealso{ \code{\link{contr.treatment}} } \examples{ contr.cum(6) contr.2nd(6) contr.diff(6) contr.orth(6) } \keyword{design} \keyword{models} Epi/man/BrCa.Rd0000644000176200001440000000456213751040403012644 0ustar liggesusers\name{BrCa} \alias{BrCa} \docType{data} \title{Clinical status, relapse, metastasis and death in 2982 women with breast cancer. } \description{ This dataset is a transformation of the example dataset used by Crowther and Lambert in their multistate paper.} \usage{data(BrCa)} \format{ A data frame with 2982 observations on the following 17 variables: \describe{ \item{\code{pid}}{Person-id; numeric} \item{\code{year}}{Calendar year of diagnosis} \item{\code{age}}{Age at diagnosis} \item{\code{meno}}{Menopausal status; a factor with levels \code{pre} \code{post}} \item{\code{size}}{Tumour size; a factor with levels \code{<=20 mm} \code{>20-50 mm} \code{>50 mm}} \item{\code{grade}}{Tumour grade; a factor with levels \code{2} \code{3}} \item{\code{nodes}}{Number of positive lymph nodes, a numeric vector} \item{\code{pr}}{Progesteron receptor level} \item{\code{pr.tr}}{Transformed progesteron level} \item{\code{er}}{Estrogen receptor level} \item{\code{hormon}}{Hormon therapy at diagnosis; a factor with levels \code{no} \code{yes}} \item{\code{chemo}}{Chemotherapy treatment; a factor with levels \code{no} \code{yes}} \item{\code{tor}}{Time of relapse, years since diagnosis} \item{\code{tom}}{Time of metastasis, years since diagnosis} \item{\code{tod}}{Time of death, years since diagnosis} \item{\code{tox}}{Time of exit from study, years since diagnosis} \item{\code{xst}}{Vital status at exit; a factor with levels \code{Alive} \code{Dead}} } } \details{ The dataset has been modified to contain the times (since diagnosis) of the events of interest, to comply with the usual structure of data. } \source{ The original data were extracted from: \url{http://fmwww.bc.edu/repec/bocode/m/multistate_example.dta}, this is modified representation of the same amount of information. } \references{ The data were used as example in the paper by Crowther and Lambert: Parametric multistate survival models: Flexible modelling allowing transition-specific distributions with application to estimating clinically useful measures of effect differences; Stat Med 36 (29), pp 4719-4742, 2017. (No, it is not the paper, just the title.) A parallel analysis using the \code{\link{Lexis}} machinery is available as: \url{http://bendixcarstensen.com/AdvCoh/papers/bcMS.pdf} } \examples{ data(BrCa) } \keyword{datasets} Epi/man/time.scales.Rd0000644000176200001440000000241313751040403014235 0ustar liggesusers\name{timeScales} \alias{timeScales} \alias{timeSince} \alias{tsNA20} \title{The time scales of a Lexis object} \description{ Functions to get the names and type of the time scales of a \code{Lexis} object. } \usage{ timeScales(x) timeSince(x) tsNA20( x, all.scales=FALSE ) } \arguments{ \item{x}{an object of class \code{Lexis}.} \item{all.scales}{Should NAs in all timescales be replaced by 0? If \code{FALSE} (the default) only timescales defined as time since entry to a state get \code{NA}s replaced by 0s} } \value{ \code{timeScales} returns a character vector containing the names of the variables in \code{x} that represent the time scales. Extracted from the \code{time.scales} attribute of the object. \code{timeSince} returns a named character vector, the names being the names of the timescales and the content being the names of the states to which the corresponding timescale is defined as time since entry. For those time scales that are not defined as such an empty string is used. Hence, if none of the timescales are defined as time since entry to a state \code{timeSince} will return a vector of empty strings. } \author{Martyn Plummer, Bendix Carstensen} \seealso{\code{\link{Lexis}}, \code{\link{splitLexis}}} \keyword{attribute} Epi/man/gmortDK.Rd0000644000176200001440000000303113751040403013372 0ustar liggesusers\name{gmortDK} \alias{gmortDK} \docType{data} \title{Population mortality rates for Denmark in 5-years age groups.} \description{ The \code{gmortDK} data frame has 418 rows and 21 columns. } \format{ This data frame contains the following columns: \tabular{rl}{ \code{agr}: \tab Age group, 0:0--4, 5:5--9,..., 90:90+. \cr \code{per}: \tab Calendar period, 38: 1938--42, 43: 1943--47, ..., 88:1988-92. \cr \code{sex}: \tab Sex, 1: male, 2: female. \cr \code{risk}: \tab Number of person-years in the Danish population. \cr \code{dt}: \tab Number of deaths. \cr \code{rt}: \tab Overall mortality rate in cases per 1000 person-years, i.e. \code{rt=1000*dt/risk} \cr \tab Cause-specific mortality rates in cases per 1000 person-years: \cr \code{r1}: \tab Infections \cr \code{r2}: \tab Cancer. \cr \code{r3}: \tab Tumors, benign, unspecific nature. \cr \code{r4}: \tab Endocrine, metabolic. \cr \code{r5}: \tab Blood. \cr \code{r6}: \tab Nervous system, psychiatric. \cr \code{r7}: \tab Cerebrovascular. \cr \code{r8}: \tab Cardiac. \cr \code{r9}: \tab Respiratory diseases, excl. cancer. \cr \code{r10}: \tab Liver, excl. cancer. \cr \code{r11}: \tab Digestive, other. \cr \code{r12}: \tab Genitourinary. \cr \code{r13}: \tab Ill-defined symptoms. \cr \code{r14}: \tab All other, natural. \cr \code{r15}: \tab Violent. \cr } } \source{ Statistics Denmark, National board of health provided original data. Michael Andersson grouped the causes of death. } \examples{ data(gmortDK) } \seealso{\code{\link{thoro}}, \code{\link{mortDK}}} \keyword{datasets} Epi/man/in.span.Rd0000644000176200001440000000714213751040403013400 0ustar liggesusers\name{in.span} \alias{in.span} \alias{inSpan} \alias{id.span} \alias{idSpan} \alias{thinCol} \title{ Is \code{x} in the column span of matrix \code{A} and what columns are linearly dependent? } \description{ The function \code{in.span} checks if the vector \code{x} (or columns of the matrix \code{x}) is in the column span of the matrix \code{A}. If desired, it returns the coefficient matrix \code{B} so that \code{AB=x}. The function \code{thinCol} removes linearly dependent columns an returns a matrix of full rank. } \usage{ in.span( A, x, coef = FALSE, tol = 1e-08 ) inSpan( A, x, coef=FALSE, tol=1e-08 ) id.span( A, B, tol=1e-08 ) idSpan( A, B, tol=1e-08 ) thinCol( A, tol = 1e-06, col.num = FALSE ) } \details{\code{\link{thinCol}} is mainly a workhorse in \code{\link{detrend}}, but made available because of its general usefulness. \code{in.span} and \code{inSpan} are just different names for the same to accommodate different naming schools. \code{in.span} (\code{inSpan}) is handy in checking whether different parametrizations of a model are identical in the sense of spanning the same linear space. Equivalent to checking whether fitted values under different parametrizations are identical, but has the further use of checking if subspaces of models are equivalent. The function simply checks if the regression of (columns of) \code{x} on the columns of \code{A} produces residuals that are all 0. \code{id.span} (equivalent to \code{idSpan}) checks whether two matrices have the same column span. } \arguments{ \item{A}{A matrix.} \item{B}{A matrix.} \item{x}{A vector or matrix. \code{length(x)} (or \code{nrow(x)}) must be equal to \code{nrow(A)}.} \item{coef}{Logical. Should the coefficient matrix (\code{k}) be returned, so that \code{Ak=x}?} \item{tol}{Tolerance for identity of matrices in check (\code{in.span}) or QR decomposition (\code{thinCol})} \item{col.num}{Logical. Should the positions of dependent columns be returned instead of the full-rank matrix?} } \value{\code{in.span} returns a logical: is \code{x} is in \code{span(A)}? If \code{coef=TRUE} it returns a matrix \code{k} so that \code{Ak=x}. \code{k} is not necessarily unique (A may not have full rank). \code{id.span} returns a logical: is \code{span(A)} the same as \code{span(B)}? \code{thinCol} returns a matrix of full rank, formed from \code{A} by deleting columns linearly dependent on other. If \code{col.num=TRUE} (one possible set of) positions of columns forming a full rank basis for the column space of \code{A} is returned. } \author{Bendix Carstensen, \url{http://bendixcarstensen.com} with essential help from Lars Jorge Diaz and Peter Dalgaard. } \seealso{\code{\link{det}} } \examples{ # Matrices and vectors, x in span(A), z (hopefully) not A <- matrix(round(rnorm(15)*20),5,3) B <- matrix(round(rnorm(15)*20),5,3) B <- cbind( B, B\%*\%c(3,4,2) ) x <- A \%*\% c(3,4,2) z <- 5:9 # how they look data.frame( A=A, x=x, z=z, B=B ) # vectors in span(A)? in.span(A,x) in.span(x,A) in.span(A,x,coef=TRUE) in.span(A,z) in.span(A,z,coef=TRUE) # Do matrices span the same space ? in.span( A, B ) in.span( B, A ) # B is not in span of a subspace of B columns, but vice versa ( M <- matrix( rnorm(8)*7, 4, 2 ) ) in.span( B\%*\%M, B ) in.span( B, B\%*\%M ) id.span( B, B\%*\%M ) # But not unique for singular matrices: ( xx <- in.span( B, B\%*\%M, coef=TRUE ) ) cbind( B\%*\%M, B\%*\%xx ) cbind( xx, M ) # Easier for full rank matrices: ( K <- matrix( rnorm(9)*7, 3, 3 ) ) in.span( A\%*\%K, A ) in.span( A, A\%*\%K ) id.span( A, A\%*\%K ) in.span( A, A\%*\%K, coef=TRUE ) } \keyword{math} Epi/man/ncut.Rd0000644000176200001440000000310013751040403012771 0ustar liggesusers\name{ncut} \alias{ncut} \title{ Function to group a variable in intervals.} \description{ Cuts a continuous variable in intervals. As opposed to \code{cut} which returns a factor, \code{ncut} returns a numeric variable. } \usage{ ncut(x, breaks, type="left" ) } \arguments{ \item{x}{A numerical vector.} \item{breaks}{Vector of breakpoints. \code{NA} will results for values below \code{min(breaks)} if \code{type="left"}, for values above \code{max(breaks)} if \code{type="right"} and for values outside \code{range(breaks)} if \code{type="mid"}} \item{type}{Character: one of \code{c("left","right","mid")}, indicating whether the left, right or midpoint of the intervals defined in breaks is returned.} } \details{ The function uses the base function \code{findInterval}. } \value{ A numerical vector of the same length as \code{x}. } \author{ Bendix Carstensen, Steno Diabetes Center, \email{b@bxc.dk}, \url{http://bendixcarstensen.com}, with essential input from Martyn Plummer, \email{martyn.plummer@r-project.org} } \seealso{ \code{\link{cut}}, \code{\link{findInterval}} } \examples{ br <- c(-2,0,1,2.5) x <- c( rnorm( 10 ), br, -3, 3 ) cbind( x, l=ncut( x, breaks=br, type="l" ), m=ncut( x, breaks=br, type="m" ), r=ncut( x, breaks=br, type="r" ) )[order(x),] x <- rnorm( 200 ) plot( x, ncut( x, breaks=br, type="l" ), pch=16, col="blue", ylim=range(x) ) abline( 0, 1 ) abline( v=br ) points( x, ncut( x, breaks=br, type="r" ), pch=16, col="red" ) points( x, ncut( x, breaks=br, type="m" ), pch=16, col="green" ) } \keyword{manip} Epi/man/simLexis.Rd0000644000176200001440000003205613751040403013631 0ustar liggesusers\name{simLexis} \alias{simLexis} \alias{nState} \alias{pState} \alias{plot.pState} \alias{lines.pState} \title{Simulate a Lexis object representing follow-up in a multistate model.} \description{Based on a (pre-)\code{Lexis} object representing persons at given states and times, and full specification of transition intensities between states in the form of models for the transition rates, this function simulates transition times and -types for persons and returns a \code{Lexis} object representing the simulated cohort. The simulation scheme accommodates multiple timescales, including time since entry into an intermediate state, and accepts fitted Poisson models, Cox-models or just a function as specification of rates.} \usage{ simLexis( Tr, init, N = 1, lex.id, t.range = 20, n.int = 101, time.pts = seq(0,t.range,length.out=n.int) ) nState( obj, at, from, time.scale = 1 ) pState( nSt, perm = 1:ncol(nSt) ) \method{plot}{pState}( x, col = rainbow(ncol(x)), border = "transparent", xlab = "Time", ylim = 0:1, ylab = "Probability", ... ) \method{lines}{pState}( x, col = rainbow(ncol(x)), border = "transparent", ... ) } \arguments{ \item{Tr}{A named list of named lists. The names of the list are names of the transient states in the model. Each list element is again a named list. The names of the elements of this inner list are the names of the states reachable from the state with name equal to the list. Elements of the intter lists represent transitions. See details.} \item{init}{A (pre-)\code{\link{Lexis}} object representing the initial state of the persons whose trajectories through the multiple states we want to simulate. Must have attributes "time.scales" and "time.since" --- see details. Duplicate values of \code{lex.id} are not sensible and not accepted.} \item{N}{Numeric. How many persons should be simulated. \code{N} persons with covariate configuration of each row in \code{init} will be simulated. Either a scalar or a vector of length \code{nrow(init)}.} \item{lex.id}{Vector of ids of the simulated persons. Useful when simulating in chunks.} \item{t.range}{Numerical scalar. The range of time over which to compute the cumulative rates when simulating. Simulted times beyond this will result in an obervation censored at \code{t.range} after entry.} \item{n.int}{Number of intervals to use when computing (cumulative) rates.} \item{time.pts}{Numerical vector of times since start. Cumulative rates for transitions are computed at these times after stater and entry state. Simulation is only done till time \code{max(time.pts)} after start, where persons are censored. Must start with 0.} \item{obj}{A \code{Lexis} object.} \item{from}{The point on the time scale \code{time.scale} from which we start counting.} \item{time.scale}{The timescale to which \code{from} refer.} \item{at}{Time points (after \code{from}) where the number of persons in each state is to be computed.} \item{nSt}{A table obtained by \code{nState}.} \item{perm}{A permutation of columns used before cumulating row-wise and taking percentages.} \item{x}{An object of class \code{pState}, e.g. created by \code{pState}.} \item{col}{Colors for filling the areas between curves.} \item{border}{Colors for outline of the areas between curves.} \item{xlab}{Label on x-axis} \item{ylim}{Limits on y-axis} \item{ylab}{Label on y-axis} \item{...}{Further arguments passed on to \code{plot}.} } \details{The simulation command \code{simLexis} is not defined as a method for \code{Lexis} objects, because the input is not a \code{Lexis} object, the \code{Lexis}-like object is merely representing a prevalent population and a specification of which variables that are timescales. The variables \code{lex.dur} and \code{lex.Xst} are ignored (and overwritten) if present. The core input is the list \code{Tr} giving the transitions. The components of \code{Tr} represents the transition intensities between states. The transition from state \code{A} to \code{B}, say, is assumed stored in \code{Tr$A$B}. Thus names of the elements of \code{Tr} are names of transient states, and the names of the elements of each these are the names of states reachable from the corresponding transient state. The transition intensities are assumed modelled by either a glm with Poisson family or a Cox-model. In both cases the timescale(s) in the model must be using the names fo the timescales in a Lexis object representng the follow-up in a cohort, and the risk time must be taken from the variable \code{lex.dur} --- see the example. Alternatively, an element in \code{Tr} could be a function that from a data frame produces transition rates, or specifically cumulative transition rates over intervals of length \code{lex.dur}. The pre-\code{Lexis} object \code{init} must contain values of all variables used in any of the objects in \code{Tr}, as well as all timescales - even those not used in the models. Moreover, the attributes \code{time.scales} and \code{time.since} must be present. The attribute \code{time.since} is a character vector of the same length as \code{time.scales} and an element has value \code{"A"} if the corresponding time scale is defined as "time since entry into state \code{A}", otherwise the value is \code{""}. If not present it will be set to a vector of \code{""}s, which is only OK if no time scales are defined as time since entry to a state. Note that the variables pre-\code{Lexis} object \code{init} must have the same mode and class as in the dataset used for fitting the models --- hence the indexing of rows by brackets in the assignment of values used in the example below - this way the variables have their attributes preserved; using \code{init[,"var"] <-} or \code{init$var <-} replaces the variable, whereas \code{init[1:4,"var"] <-} or \code{init$var[1:4] <-} replaces values only and prevents you from entering non-existing factor levels etc. The function \code{\link{Lexis}} automatically generates an attribute \code{time.since}, and \code{\link{cutLexis}} updates it when new time scales are defined. Hence, the simplest way of defining a initial pre-\code{Lexis} object representing a current state of a (set of) persons to be followed through a multistate model is to take \code{NULL} rows of an existing Lexis object (normally the one used for estimation), and so ensuring that all relevant attributes and state levels are properly defined. See the example code. The prevalence function \code{nState} computes the distribution of individuals in different states at prespecified times. Only sensible for a simulated \code{Lexis} object. The function \code{pState} takes a matrix as output by \code{nState} and computes the row-wise cumulative probabilities across states, and leaves an object of class \code{pState}, suitable for plotting. } \value{\code{simLexis} returns a \code{\link{Lexis}} object representing the experience of a population starting as \code{init} followed through the states according to the transitions in \code{Tr}. The function \code{nState} returns a table of persons classified by states at each of the times in \code{at}. Note that this function can easily produce meaningless results, for example if applied to a \code{Lexis} object not created by simulation. If you apply it to a \code{Lexis} object generated by \code{simLexis}, you must make sure that you start (\code{from}) the point where you started the simulation on the correct timescale, and you will get funny results if you try to tabulate beyond the censoring time for the simulation. The resulting object has class \code{"table"}. The result from using \code{pState} on the result from \code{nState} has class \code{c("pState","matrix")}. } \author{Bendix Carstensen, \url{http://bendixcarstensen.com}.} \seealso{ \code{\link{Lexis}}, \code{\link{cutLexis}}, \code{\link{splitLexis}} } \examples{ data(DMlate) dml <- Lexis( entry = list(Per=dodm, Age=dodm-dobth, DMdur=0 ), exit = list(Per=dox), exit.status = factor(!is.na(dodth),labels=c("DM","Dead")), data = DMlate[runif(nrow(DMlate))<0.1,] ) # Split follow-up at insulin, introduce a new timescale, # and split non-precursor states dmi <- cutLexis( dml, cut = dml$doins, pre = "DM", new.state = "Ins", new.scale = "t.Ins", split.states = TRUE ) # Split the follow in 1-year intervals for modelling Si <- splitLexis( dmi, 0:30/2, "DMdur" ) # Define knots nk <- 4 ( ai.kn <- with( subset(Si,lex.Xst=="Ins"), quantile( Age+lex.dur, probs=(1:nk-0.5)/nk ) ) ) ( ad.kn <- with( subset(Si,lex.Xst=="Dead"), quantile( Age+lex.dur, probs=(1:nk-0.5)/nk ) ) ) ( di.kn <- with( subset(Si,lex.Xst=="Ins"), quantile( DMdur+lex.dur, probs=(1:nk-0.5)/nk ) ) ) ( dd.kn <- with( subset(Si,lex.Xst=="Dead"), quantile( DMdur+lex.dur, probs=(1:nk-0.5)/nk ) ) ) ( td.kn <- with( subset(Si,lex.Xst=="Dead(Ins)"), quantile( t.Ins+lex.dur, probs=(1:nk-0.5)/nk ) ) ) # Fit Poisson models to transition rates library( splines ) DM.Ins <- glm( (lex.Xst=="Ins") ~ Ns( Age , knots=ai.kn ) + Ns( DMdur, knots=di.kn ) + I(Per-2000) + sex, family=poisson, offset=log(lex.dur), data = subset(Si,lex.Cst=="DM") ) DM.Dead <- glm( (lex.Xst=="Dead") ~ Ns( Age , knots=ad.kn ) + Ns( DMdur, knots=dd.kn ) + I(Per-2000) + sex, family=poisson, offset=log(lex.dur), data = subset(Si,lex.Cst=="DM") ) Ins.Dead <- glm( (lex.Xst=="Dead(Ins)") ~ Ns( Age , knots=ad.kn ) + Ns( DMdur, knots=dd.kn ) + Ns( t.Ins, knots=td.kn ) + I(Per-2000) + sex, family=poisson, offset=log(lex.dur), data = subset(Si,lex.Cst=="Ins") ) # Stuff the models into an object representing the transitions Tr <- list( "DM" = list( "Ins" = DM.Ins, "Dead" = DM.Dead ), "Ins" = list( "Dead(Ins)" = Ins.Dead ) ) lapply( Tr, names ) # Define an initial object - note the subsetting that ensures that # all attributes are carried over ini <- Si[1,1:9][-1,] ini[1:2,"lex.Cst"] <- "DM" ini[1:2,"Per"] <- 1995 ini[1:2,"Age"] <- 60 ini[1:2,"DMdur"] <- 5 ini[1:2,"sex"] <- c("M","F") str(ini) # Simulate 200 of each sex using the estimated models in Tr simL <- simLexis( Tr, ini, time.pts=seq(0,11,0.5), N=200 ) summary( simL ) # Find the number of persons in each state at a set of times. # Note that the times are shirter than the time-span simulated. nSt <- nState( subset(simL,sex=="M"), at=seq(0,10,0.1), from=1995, time.scale="Per" ) nSt # Show the cumulative prevalences in a different order than that of the # state-level ordering and plot them using all defaults pp <- pState( nSt, perm=c(1,2,4,3) ) head( pp ) plot( pp ) # A more useful set-up of the graph clr <- c("orange2","forestgreen") par( las=1 ) plot( pp, col=clr[c(2,1,1,2)] ) lines( as.numeric(rownames(pp)), pp[,2], lwd=2 ) mtext( "60 year old male, diagnosed 1995", side=3, line=2.5, adj=0 ) mtext( "Survival curve", side=3, line=1.5, adj=0 ) mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[1] ) mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[2] ) axis( side=4 ) # Using a Cox-model for the mortality rates assuming the two mortality # rates to be proportional: # When we fit a Cox-model, lex.dur must be used in the Surv() function, # and the I() constrction must be used when specifying intermediate # states as covariates, since factors with levels not present in the # data will create NAs in the parameter vector returned by coxph, which # in return will crash the simulation machinery. library( survival ) Cox.Dead <- coxph( Surv( DMdur, DMdur+lex.dur, lex.Xst \%in\% c("Dead(Ins)","Dead")) ~ Ns( Age-DMdur, knots=ad.kn ) + I(lex.Cst=="Ins") + I(Per-2000) + sex, data = Si ) Cr <- list( "DM" = list( "Ins" = DM.Ins, "Dead" = Cox.Dead ), "Ins" = list( "Dead(Ins)" = Cox.Dead ) ) simL <- simLexis( Cr, ini, time.pts=seq(0,11,0.2), N=200 ) summary( simL ) nSt <- nState( subset(simL,sex=="M"), at=seq(0,10,0.2), from=1995, time.scale="Per" ) pp <- pState( nSt, perm=c(1,2,4,3) ) plot( pp ) } \keyword{survival} Epi/man/rbind.Lexis.Rd0000644000176200001440000000621113751040403014207 0ustar liggesusers\name{cbind.Lexis} \alias{cbind.Lexis} \alias{rbind.Lexis} %- Also NEED an '\alias' for EACH other topic documented here. \title{Combining a Lexis objects with data frames or other Lexis objects } \description{A Lexis object may be combined side-by-side with data frames. Or several Lexis objects may stacked, possibly increasing the number of states and time scales. } \usage{ \method{cbind}{Lexis}(...) \method{rbind}{Lexis}(...) } \arguments{ \item{\dots}{For \code{cbind} a sequence of data frames or vectors of which exactly one has class \code{Lexis}. For \code{rbind} a sequence of Lexis objects, supposedly representing follow-up in the same population.} } \details{ Arguments to \code{rbind.Lexis} must all be \code{\link{Lexis}} objects; except for possible NULL objects. The timescales in the resulting object will be the union of all timescales present in all arguments. Values of timescales not present in a contributing Lexis object will be set to \code{NA}. The \code{breaks} for a given time scale will be \code{NULL} if the \code{breaks} of the same time scale from two contributing Lexis objects are different. The arguments to \code{cbind.Lexis} must consist of at most one Lexis object, so the method is intended for amending a Lexis object with extra columns without losing the Lexis-specific attributes. } \value{ A \code{\link{Lexis}} object. \code{rbind} renders a \code{Lexis} object with timescales equal to the union of timescales in the arguments supplied. Values of a given timescale are set to \code{NA} for rows corresponding to supplied objects. \code{cbind} basically just adds columns to an existing Lexis object. } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com} } \seealso{ \code{\link{subset.Lexis}} } \examples{ # A small bogus cohort xcoh <- structure( list( id = c("A", "B", "C"), birth = c("14/07/1952", "01/04/1954", "10/06/1987"), entry = c("04/08/1965", "08/09/1972", "23/12/1991"), exit = c("27/06/1997", "23/05/1995", "24/07/1998"), fail = c(1, 0, 1) ), .Names = c("id", "birth", "entry", "exit", "fail"), row.names = c("1", "2", "3"), class = "data.frame" ) # Convert the character dates into numerical variables (fractional years) xcoh <- cal.yr( xcoh, format="\%d/\%m/\%Y", wh=2:4 ) # See how it looks xcoh str( xcoh ) # Define as Lexis object with timescales calendar time and age Lcoh <- Lexis( entry = list( per=entry ), exit = list( per=exit, age=exit-birth ), exit.status = fail, data = xcoh ) Lcoh cbind( Lcoh, zz=3:5 ) # Lexis object wit time since entry time scale Dcoh <- Lexis( entry = list( per=entry, tfe=0 ), exit = list( per=exit ), exit.status = fail, data = xcoh ) # A bit meningless to combie these two, really... rbind( Dcoh, Lcoh ) # Split different places sL <- splitLexis( Lcoh, time.scale="age", breaks=0:20*5 ) sD <- splitLexis( Dcoh, time.scale="tfe", breaks=0:50*2 ) sDL <- rbind( sD, sL ) } \keyword{survival} \keyword{manip} Epi/man/LCa.fit.Rd0000644000176200001440000003146213751040403013254 0ustar liggesusers\name{LCa.fit} \alias{LCa.fit} \alias{print.LCa} \alias{summary.LCa} \alias{plot.LCa} \alias{predict.LCa} \title{ Fit Lee-Carter-type models for rates to arbitrarily shaped observations of rates in a Lexis diagram. } \description{ The Lee-Carter model is originally defined as a model for rates observed in A-sets (age by period) of a Lexis diagram, as log(rate(x,t)) = a(x) + b(x)k(t), using one parameter per age(x) and period(t). This function uses natural splines for a(), b() and k(), placing knots for each effect such that the number of events is the same between knots. Also fits the continuous time counterparts of all models supported by the \code{\link[ilc]{lca.rh}} function from the \code{ilc} package (see details). } \usage{ LCa.fit( data, A, P, D, Y, model = "APa", # or one of "ACa", "APaC", "APCa" or "APaCa" a.ref, # age reference for the interactions pi.ref = a.ref, # age reference for the period interaction ci.ref = a.ref, # age reference for the cohort interaction p.ref, # period reference for the interaction c.ref, # cohort reference for the interactions npar = c(a = 6, # no. knots for main age-effect p = 6, # no. knots for period-effect c = 6, # no. knots for cohort-effect pi = 6, # no. knots for age in the period interaction ci = 6), # no. knots for age in the cohort interaction VC = TRUE, # numerical calculation of the Hessian? alpha = 0.05, # 1 minus confidence level eps = 1e-6, # convergence criterion maxit = 100, # max. no iterations quiet = TRUE ) # cut the crap \method{print}{LCa}( x, ... ) \method{summary}{LCa}( object, show.est=FALSE, ... ) \method{plot}{LCa}( x, ... ) \method{predict}{LCa}( object, newdata, alpha = 0.05, level = 1-alpha, sim = ( "vcov" \%in\% names(object) ), ... ) } \arguments{ \item{data}{ A data frame. Must have columns \code{A}(age), \code{P}(period, that is calendar time), \code{D}(no. of events) and \code{Y}(person-time, exposure). Alternatively these four quantities can be given as separate vectors: } \item{A}{ Vector of ages (midpoint of observation). } \item{P}{ Vector of period (midpoint of observation). } \item{D}{ Vector of no. of events. } \item{Y}{ Vector of person-time. Demographers would say "exposure", bewildering epidemiologists. } \item{a.ref}{ Reference age for the age-interaction term(s) \code{pi(x)} and/or \code{pi(x)}, where \code{pi(a.ref)=1} and \code{ci(a.ref)=1}. } \item{pi.ref}{ Same, but specifically for the interaction with period. } \item{ci.ref}{ Same, but specifically for the interaction with cohort. } \item{p.ref}{ Reference period for the time-interaction term \code{kp(t)} where \code{kp(p.ref)=0}. } \item{c.ref}{ Reference period for the time-interaction term \code{kp(t)} where \code{kc(c.ref)=0}. } \item{model}{ Character, either \code{"APa"} which is the classical Lee-Carter model for log-rates, other possibilities are \code{"ACa"}, \code{"APCa"}, \code{"APaC"} or \code{"APaCa"}, see details. } \item{npar}{ A (possibly named) vector or list, with either the number of knots or the actual vectors of knots for each term. If unnamed, components are taken to be in the order (a,b,t), if the model is "APaCa" in the order (a,p,c,pi,ci). If a vector, the three integers indicate the number of knots for each term; these will be placed so that there is an equal number of events (\code{D}) between each, and half as many below the first and above the last knot. If \code{npar} is a list of scalars the behavior is the same. If \code{npar} is a list of vectors, these are taken as the knots for the natural splines. See details for naming convention. } \item{VC}{ Logical. Should the variance-covariance matrix of the parameters be computed by numerical differentiation? See details. } \item{alpha}{ 1 minus the confidence level used when calculating confidence intervals for estimates in \code{LCa.fit} and for predictions by \code{predict.LCa}. } \item{eps}{ Convergence criterion for the deviance, we use the the relative difference between deviance from the two models fitted. } \item{maxit}{ Maximal number of iterations. } \item{quiet}{ Shall I shut up or talk extensively to you about iteration progression etc.? } \item{object}{An \code{LCa} object, see under "Value".} \item{show.est}{Logical. Should the estimates be printed?} \item{x}{An \code{LCa} object, see under "Value".} \item{newdata}{Prediction data frame, must have columns \code{A} and \code{P}. Any \code{Y} column is ignored, predictions are given in units of the \code{Y} supplied for the call that generated the \code{LCa} object.} \item{level}{Confidence level.} \item{sim}{Logical or numeric. If \code{TRUE}, prediction c.i.s will be based on 1000 simulations from the posterior parameters. If numeric, it will be based on that number of simulations.} \item{...}{Additional parameters passed on to the method.} } \details{ The Lee-Carter model is non-linear in age and time so does not fit in the classical glm-Poisson framework. But for fixed \code{b(x)} it is a glm, and also for fixed \code{a(x)}, \code{k(t)}. The function alternately fits the two versions until the same fit is produced (same deviance). The multiplicative age by period term could equally well have been a multiplicative age by cohort or even both. Thus the most extensive model has 5 continuous functions: \deqn{\log(\lambda(a,p)) = f(a) + b_p(a)k_p(p) + b_c(a)k_c(p-a)}{% log( lambda(a,p)) = f(a) + b_p(a)k_p(p) + b_c(a)k_c(p-a)} Each of these is fitted by a natural spline, with knots placed at the quantiles of the events along the age (a), calendar time (p) respective cohort (p-a) scales. Alternatively the knots can be specified explicitly in the argument \code{npar} as a named list, where \code{a} refers to \eqn{f(a)}{f(a)}, \code{p} refers to \eqn{k_p(p)}{k_p(p)}, \code{c} refers to \eqn{k_c(p-a)}{k_c(p-a)}, \code{pi} (\code{p}eriod code{i}nteraction) refers to \eqn{b_p(a)}{b_p(a)} and \code{ci} (\code{c}ohort \code{i}nteraction) refers to \eqn{b_c(p-a)}{b_c(p-a)}. The naming convention for the models is a capital \code{P} and/or \code{C} if the effect is in the model followed by a lower case \code{a} if there is an interaction with age. Thus there are 5 different models that can be fitted: \code{APa}, \code{ACa}, \code{APaC} \code{APCa} and \code{APaCa}. The standard errors of the parameters from the two separate model fits in the iterations are however wrong; they are conditional on a subset of the parameters having a fixed value. However, analytic calculation of the Hessian is a bit of a nightmare, so this is done numerically using the \code{hessian} function from the \code{numDeriv} package if \code{VC=TRUE}. The coefficients and the variance-covariance matrix of these are used in \code{predict.LCa} for a parametric bootstrap (that is, a simulation from a multivariate normal with mean equal to the parameter estimates and variance as the estimated variance-covariance) to get confidence intervals for the predictions if \code{sim} is \code{TRUE} --- which it is by default if they are part of the object. The \code{plot} for \code{LCa} objects merely produces between 3 and 5 panels showing each of the terms in the model. These are mainly for preliminary inspection; real reporting of the effects should use proper relative scaling of the effects.} \value{ \code{LCa.fit} returns an object of class \code{LCa} (smooth effects \code{L}ee-\code{Ca}rter model); it is a list with the following components: \item{model}{Character, either \code{APa}, \code{ACa}, \code{APaC}, \code{APCa} or \code{APaCa}, indicating the variable(s) interacting with age.} \item{ax}{3-column matrix of age-effects, c.i. from the age-time model. Row names are the unique occurring ages in the dataset. Estimates are rates.} \item{pi}{3-column matrix of age-period interaction effects, c.i. from the age model. Row names are the actually occurring ages in the dataset. Estimates are multipliers of the log-RRs in \code{kp}, centered at 1 at \code{pi.ref}.} \item{kp}{3-column matrix of period-effects, with c.i.s from the age-time model. Row names are the actually occurring times in the dataset. Estimates are rate-ratios centered at 1 at \code{p.ref}.} \item{ci}{3-column matrix of age-cohort interaction effects, c.i. from the age model. Row names are the actually occurring ages in the dataset. Estimates are multipliers of the log-RRs in \code{kc}, centered at 1 at \code{ci.ref}.} \item{kc}{3-column matrix of cohort-effects, with c.i.s from the age-time model. Row names are the actually occurring times in the dataset. Estimates are rate-ratios centered at 1 at \code{c.ref}.} \item{mod.at}{\code{glm} object with the final age-time model --- estimates the terms \code{ax}, \code{kp}, \code{kc}. Gives the same fit as the \code{mod.b} model after convergence.} \item{mod.b}{\code{glm} object with the final age model --- estimates the terms \code{pi}, \code{ci}. Gives the same fit as the \code{mod.at} model after convergence.} \item{coef}{All coefficients from both models, in the order \code{ax}, \code{kp}, \code{kc}, \code{pi}, \code{ci}. Only present if \code{LCa.fit} were called with \code{VC=TRUE} (the default).} \item{vcov}{Variance-covariance matrix of coefficients from both models, in the same order as in the \code{coef}. Only present if \code{LCa.fit} were called with \code{VC=TRUE}.} \item{knots}{List of vectors of knots used in for the age, period and cohort effects.} \item{refs}{List of reference points used for the age, period and cohort terms in the interactions.} \item{deviance}{Deviance of the model} \item{df.residual}{Residual degrees of freedom} \item{iter}{Number of iterations used to reach convergence.} \code{plot.LCa} plots the estimated effects in separate panels, using a log-scale for the baseline rates (\code{ax}) and the time-RR (\code{kt}). For the \code{APaCa} model 5 panels are plotted. \code{summary.LCa} returns (invisibly) a matrix with the parameters from the models and a column of the conditional se.s and additionally of the se.s derived from the numerically computed Hessian (if \code{LCa.fit} were called with \code{VC=TRUE}.) \code{predict.LCa} returns a matrix with one row per row in \code{newdata}. If \code{LCa.fit} were called with \code{VC=TRUE} there will be 3 columns, namely prediction (1st column) and c.i.s based on a simulation of parameters from a multivariate normal with mean \code{coef} and variance \code{vcov} using the median and \code{alpha}/2 quantiles from the \code{sim} simulations. If \code{LCa.fit} were called with \code{VC=FALSE} there will be 6 columns, namely estimates and c.i.s from age-time model (\code{mod.at}), and from the age-interaction model (\code{mod.b}), both using conditional variances, and therefore likely with too narrow confidence limits. } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com} This function was conceived while teaching a course on APC models at the Max Planck Institute of Demographic Research (MPIDR, \url{https://www.demogr.mpg.de/en/}) in Rostock in May 2016 (\url{http://bendixcarstensen.com/APC/MPIDR-2016/}), and finished during a week long research stay there, kindly sponsored by the MPIDR. } \seealso{ \code{\link{apc.fit}}, \code{\link{apc.LCa}}, \code{\link[ilc]{lca.rh}}, \code{\link[demography]{lca}} } \examples{ library( Epi ) # Load the testis cancer data by Lexis triangles data( testisDK ) tc <- subset( testisDK, A>14 & A<60 ) head( tc ) # We want to see rates per 100,000 PY tc$Y <- tc$Y / 10^5 # Fit the Lee-Carter model with age-period interaction (default) LCa.tc <- LCa.fit( tc, model="ACa", a.ref=30, p.ref=1980, quiet=FALSE, eps=10e-4, maxit=50 ) LCa.tc summary( LCa.tc ) # Inspect what we got names( LCa.tc ) # show the estimated effects par( mfrow=c(1,3) ) plot( LCa.tc ) # Prediction data frame for ages 15 to 60 for two time points: nd <- data.frame( A=15:60 ) # LCa predictions p70 <- predict.LCa( LCa.tc, newdata=cbind(nd,P=1970), sim=1000 ) p90 <- predict.LCa( LCa.tc, newdata=cbind(nd,P=1990), sim=1000 ) # Inspect the curves from the parametric bootstrap (simulation): par( mfrow=c(1,1) ) head( cbind(p70,p90) ) matplot( nd$A, cbind(p70,p90), type="l", lwd=c(6,3,3), lty=c(1,3,3), col=rep( 2:3, each=3 ), log="y", ylab="Testis cancer incidence per 100,000 PY in 1970 resp. 1990", xlab="Age" ) } \keyword{models} \keyword{regression} Epi/man/plot.Lexis.Rd0000644000176200001440000001160513751040403014072 0ustar liggesusers\name{plot.Lexis} \alias{plot.Lexis} \alias{points.Lexis} \alias{lines.Lexis} \alias{PY.ann} \alias{PY.ann.Lexis} \title{Lexis diagrams} \description{ The follow-up histories represented by a Lexis object can be plotted using one or two dimensions. The two dimensional plot is a Lexis diagram showing follow-up time simultaneously on two time scales. } \usage{ \method{plot}{Lexis}(x=Lexis( entry=list(Date=1900,Age=0), exit=list(Age=0) ), time.scale = NULL, type="l", breaks="lightgray", ...) \method{points}{Lexis}(x, time.scale = options()[["Lexis.time.scale"]] , ...) \method{lines}{Lexis}(x, time.scale = options()[["Lexis.time.scale"]], ...) \method{PY.ann}{Lexis}(x, time.scale = options()[["Lexis.time.scale"]], digits=1, ...) } \arguments{ \item{x}{An object of class \code{Lexis}. The default is a bogus \code{Lexis} object, so that \code{plot.Lexis} can be called without the first argument and still produce a(n empty) Lexis diagram. Unless arguments \code{xlim} and \code{ylim} are given in this case the diagram is looking pretty daft.} \item{time.scale}{A vector of length 1 or 2 giving the time scales to be plotted either by name or numerical order} \item{type}{Character indication what to draw: "n" nothing (just set up the diagram), "l" - liefelines, "p" - endpoints of follow-up, "b" - both lifelines and endpoints.} \item{breaks}{a string giving the colour of grid lines to be drawn when plotting a split Lexis object. Grid lines can be suppressed by supplying the value \code{NULL} to the \code{breaks} argument} \item{digits}{Numerical. How many digits after the demimal points should be when plotting the person-years.} \item{\dots}{Further graphical parameters to be passed to the plotting methods. Grids can be drawn (behind the life lines) using the following parameters in \code{plot}: \itemize{ \item \code{grid} If logical, a background grid is set up using the axis ticks. If a list, the first component is used as positions for the vertical lines and the last as positions for the horizontal. If a nunerical vector, grids on both axes are set up using the distance between the numbers. \item \code{col.grid="lightgray"} Color of the background grid. \item \code{lty.grid=2} Line type for the grid. \item \code{coh.grid=FALSE} Should a 45 degree grid be plotted?} } } \details{ The plot method for \code{Lexis} objects traces ``life lines'' from the start to the end of follow-up. The \code{points} method plots points at the end of the life lines. If \code{time.scale} is of length 1, the life lines are drawn horizontally, with the time scale on the X axis and the id value on the Y axis. If \code{time.scale} is of length 2, a Lexis diagram is produced, with diagonal life lines plotted against both time scales simultaneously. If \code{lex} has been split along one of the time axes by a call to \code{splitLexis}, then vertical or horizontal grid lines are plotted (on top of the life lines) at the break points. \code{PY.ann} writes the length of each (segment of) life line at the middle of the line. Not advisable to use with large cohorts. Another example is in the example file for \code{\link{occup}}. } \author{Martyn Plummer} \examples{ # A small bogus cohort xcoh <- structure( list( id = c("A", "B", "C"), birth = c("14/07/1952", "01/04/1957", "10/06/1987"), entry = c("04/08/1965", "08/09/1972", "23/12/1991"), exit = c("27/06/1997", "23/05/1995", "24/07/1998"), fail = c(1, 0, 1) ), .Names = c("id", "birth", "entry", "exit", "fail"), row.names = c("1", "2", "3"), class = "data.frame" ) # Convert the character dates into numerical variables (fractional years) xcoh$bt <- cal.yr( xcoh$birth, format="\%d/\%m/\%Y" ) xcoh$en <- cal.yr( xcoh$entry, format="\%d/\%m/\%Y" ) xcoh$ex <- cal.yr( xcoh$exit , format="\%d/\%m/\%Y" ) # See how it looks xcoh # Define as Lexis object with timescales calendar time and age Lcoh <- Lexis( entry = list( per=en ), exit = list( per=ex, age=ex-bt ), exit.status = fail, data = xcoh ) # Default plot of follow-up plot( Lcoh ) # Show follow-up time PY.ann( Lcoh ) # Show exit status plot( Lcoh, type="b" ) # Same but failures only plot( Lcoh, type="b", pch=c(NA,16)[Lcoh$fail+1] ) # With a grid and deaths as endpoints plot( Lcoh, grid=0:10*10, col="black" ) points( Lcoh, pch=c(NA,16)[Lcoh$lex.Xst+1] ) # With a lot of bells and whistles: plot( Lcoh, grid=0:20*5, col="black", xaxs="i", yaxs="i", xlim=c(1960,2010), ylim=c(0,50), lwd=3, las=1 ) points( Lcoh, pch=c(NA,16)[Lcoh$lex.Xst+1], col="red", cex=1.5 ) } \seealso{\code{\link{Lexis}}, \code{\link{splitLexis}}} \keyword{hplot} \keyword{aplot} Epi/man/mortDK.Rd0000644000176200001440000000301213751040403013222 0ustar liggesusers\name{mortDK} \alias{mortDK} \docType{data} \title{Population mortality rates for Denmark in 1-year age-classes.} \description{ The \code{mortDK} data frame has 1820 rows and 21 columns. } \format{ This data frame contains the following columns: \tabular{rl}{ \code{age}: \tab Age class, 0--89, 90:90+. \cr \code{per}: \tab Calendar period, 38: 1938--42, 43: 1943--47, ..., 88:1988-92. \cr \code{sex}: \tab Sex, 1: male, 2: female. \cr \code{risk}: \tab Number of person-years in the Danish population. \cr \code{dt}: \tab Number of deaths. \cr \code{rt}: \tab Overall mortality rate in cases per 1000 person-years, i.e. \code{rt=1000*dt/risk} \cr \tab Cause-specific mortality rates in cases per 1000 person-years: \cr \code{r1}: \tab Infections \cr \code{r2}: \tab Cancer. \cr \code{r3}: \tab Tumors, benign, unspecific nature. \cr \code{r4}: \tab Endocrine, metabolic. \cr \code{r5}: \tab Blood. \cr \code{r6}: \tab Nervous system, psychiatric. \cr \code{r7}: \tab Cerebrovascular. \cr \code{r8}: \tab Cardiac. \cr \code{r9}: \tab Respiratory diseases, excl. cancer. \cr \code{r10}: \tab Liver, excl. cancer. \cr \code{r11}: \tab Digestive, other. \cr \code{r12}: \tab Genitourinary. \cr \code{r13}: \tab Ill-defined symptoms. \cr \code{r14}: \tab All other, natural. \cr \code{r15}: \tab Violent. \cr } } \source{ Statistics Denmark, National board of health provided original data. Michael Andersson grouped the causes of death. } \examples{ data(mortDK) } \seealso{\code{\link{thoro}}, \code{\link{gmortDK}}} \keyword{datasets} Epi/man/M.dk.Rd0000644000176200001440000000315113751040403012617 0ustar liggesusers\name{M.dk} \alias{M.dk} \docType{data} \title{Mortality in Denmark 1974 ff.} \description{ Mortality in one-year classes of age (0-98,99+) and period (1974 ff.) in Denmark. } \usage{data(M.dk)} \format{ A data frame with 6400 observations on the following 6 variables. \describe{ \item{\code{A}}{Age-class, 0-98, 99:99+} \item{\code{sex}}{Sex. 1:males, 2:females} \item{\code{P}}{Period (year) of death} \item{\code{D}}{Number of deaths} \item{\code{Y}}{Number of person-years} \item{\code{rate}}{Mortality rate per 1000 person-years} } } \details{ Deaths in ages over 100 are in the class labelled 99. Risk time is computed by tabulation of the risk time in \code{\link{Y.dk}}, except for the class 99+ where the average of the population size in ages 99+ at the first and last date of the year is used.} \source{ \url{http://www.statistikbanken.dk/statbank5a/SelectTable/omrade0.asp?SubjectCode=02&PLanguage=1&ShowNews=OFF} } \examples{ data(M.dk) str(M.dk) zz <- xtabs( rate ~ sex+A+P, data=M.dk ) zz[zz==0] <- NA # 0s makes log-scale plots crash par(mfrow=c(1,2), mar=c(0,0,0,0), oma=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) for( i in 1:2 ) { matplot( dimnames(zz)[[2]], zz[i,,], lty=1, lwd=1, col=rev(heat.colors(37)), log="y", type="l", ylim=range(zz,na.rm=TRUE), ylab="", xlab="", yaxt="n" ) text( 0, max(zz,na.rm=TRUE), c("M","F")[i], font=2, adj=0:1, cex=2, col="gray" ) if( i==1 ) axis( side=2, las=1 ) } mtext( side=1, "Age", line=2, outer=TRUE ) mtext( side=2, "Mortality rate", line=2, outer=TRUE ) } \keyword{datasets} Epi/man/list.lex.Rd0000644000176200001440000000341013751040403013566 0ustar liggesusers\name{list.lex} \alias{list.lex} \title{Compact printing of Lexis object } \description{Often the number of digits after the decimal point ant not the sugnificant digits is relevant in printing timescales. } \usage{ list.lex( Lx, dig, sh="_" ) } \arguments{ \item{Lx}{A \code{\link{Lexis}} object.} \item{dig}{Scalar. How many digits should be printed after the decimal separator for the numerical variables.} \item{sh}{Replacement string for \code{lex.} in names when printing.} } \details{The function is designed to make a compact listing of a Lexis obejct. Variables are ordered with \code{lex.id}, time scales, \code{lex.dur} and state variables first. In order to avoid save between columns the \code{lex.} prefix is replaced by an underscore to shorten the names. } \value{NULL, the functions is used for its compact printing of a Lexis object. } \author{Bendix Carstensen } \examples{ # A small bogus cohort xcoh <- structure( list( id = c("A", "B", "C"), birth = c("14/07/1952", "01/04/1954", "10/06/1987"), entry = c("04/08/1965", "08/09/1972", "23/12/1991"), exit = c("27/06/1997", "23/05/1995", "24/07/1998"), fail = c(1, 0, 1) ), .Names = c("id", "birth", "entry", "exit", "fail"), row.names = c("1", "2", "3"), class = "data.frame" ) # Convert the character dates into numerical variables (fractional years) xcoh <- cal.yr( xcoh, format="\%d/\%m/\%Y", wh=2:4 ) # Make a Lexis obejct Lcoh <- Lexis( entry = list( per=entry ), exit = list( per=exit, age=exit-birth ), exit.status = fail, data = xcoh ) Lcoh list.lex( Lcoh, 2 ) } \keyword{manip} Epi/man/plot.apc.Rd0000644000176200001440000000352413751040403013552 0ustar liggesusers\name{plot.apc} \alias{plot.apc} \alias{apc.plot} \title{Plot the estimates from a fitted Age-Period-Cohort model} \description{ This function plots the estimates created by \code{\link{apc.fit}} in a single graph. It just calls \code{\link{apc.frame}} after computing some sensible values of the parameters, and subsequently plots the estimates using \code{\link{apc.lines}}. } \usage{ \method{plot}{apc}( x, r.txt="Rate", ...) apc.plot( x, r.txt="Rate", ...) } \arguments{ \item{x}{ An object of class \code{apc}. } \item{r.txt}{ The text to put on the vertical rate axis. } \item{\dots}{ Additional arguments passed on to \code{\link{apc.lines}}. } } \value{ A numerical vector of length two, with names \code{c("cp.offset","RR.fac")}. The first is the offset for the cohort period-axis, the second the multiplication factor for the rate-ratio scale. Therefore, if you want to plot at \code{(x,y)} in the right panel, use \code{(x-res["cp.offset"],y/res["RR.fac"])} \code{=(x-res[1],y/res[2])}. This vector should be supplied for the parameter \code{frame.par} to \code{\link{apc.lines}} if more sets of estimates is plotted in the same graph, however see \code{\link{cp.points}}. } \details{\code{plot.apc} is just a wrapper for \code{apc.plot}.} \author{ Bendix Carstensen, Steno Diabetes Center, \url{http://bendixcarstensen.com} } \seealso{ \code{\link{apc.lines}}, \code{\link{lines.apc}}, \code{\link{apc.frame}}, \code{\link{apc.fit}} } \examples{ data( lungDK ) apc1 <- apc.fit( transform( lungDK, A = Ax, P = Px, Y = Y/10^5 ), ref.c = 1920 ) fp <- apc.plot( apc1 ) apc.lines( apc1, frame.par=fp, drift=1.01, col="red" ) for( i in 1:11 ) apc.lines( apc1, frame.par=fp, drift=1+(i-6)/100, col=rainbow(12)[i] ) } \keyword{hplot} Epi/man/summary.Lexis.Rd0000644000176200001440000000521513751040403014611 0ustar liggesusers\name{summary.Lexis} \alias{summary.Lexis} \alias{print.summary.Lexis} \title{ Summarize transitions and risk time from a Lexis object } \description{ A two-way table of records and transitions classified by states (\code{lex.Cst} and \code{lex.Xst}), as well the risk time in each state. } \usage{ \method{summary}{Lexis}( object, simplify=TRUE, scale=1, by=NULL, Rates=FALSE, timeScales=FALSE, ... ) \method{print}{summary.Lexis}( x, ..., digits=2 ) } \arguments{ \item{object}{A Lexis object.} \item{simplify}{Should rows with 0 follow-up time be dropped?} \item{scale}{Scaling factor for the rates. The calculated rates are multiplied by this number.} \item{by}{Character vector of name(s) of variable(s) in \code{object}. Used to give a separate summaries for subsets of \code{object}. If longer than than 1, the interaction between that variables is used to stratify the summary. It is also possible to supply a vector of length \code{nrow(object)}, and the distinct values of this will be used to stratify the summary.} \item{Rates}{Should a component with transition rates be returned (and printed) too?} \item{timeScales}{Should the names of the timescales and the indication of since which entry also be given?} \item{x}{A \code{summary.Lexis} object.} \item{digits}{How many digits should be used for printing?} \item{ ... }{Other parameters - ignored} } \value{ An object of class \code{summary.Lexis}, a list with two components, \code{Transitions} and \code{Rates}, each one a matrix with rows classified by states where persons spent time, and columns classified by states to which persons transit. The \code{Transitions} contains number of transitions and has 4 extra columns with number of records, total number of events, total risk time and number of person contributing attached. The \code{Rates} contains the transitions rates. If the argument \code{Rates} is FALSE (the default), then only the first component of the list is returned. } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com} } \examples{ data( nickel ) # Lung cancer deaths and other deaths are coded 1 and 2 nic <- Lexis( data=nickel, entry=list(age=agein), exit=list(age=ageout,cal=ageout+dob,tfh=ageout-age1st), exit.status=factor( (icd > 0) + (icd \%in\% c(162,163)), labels=c("Alive","Other","Lung") ) ) str( nic ) head( nic ) summary( nic ) # More detailed summary, by exposure level summary( nic, by=nic$exposure>5, Rates=TRUE, scale=100 ) } \keyword{survival}Epi/man/ci.lin.Rd0000644000176200001440000003542313751040403013211 0ustar liggesusers\name{ci.lin} \alias{ci.lin} \alias{ci.mat} \alias{ci.exp} \alias{ci.pred} \alias{ci.ratio} \alias{Wald} \title{ Compute linear functions of parameters with standard errors and confidence limits, optionally transforming to a different scale. } \description{ For a given model object the function computes a linear function of the parameters and the corresponding standard errors, p-values and confidence intervals. } \usage{ ci.lin( obj, ctr.mat = NULL, subset = NULL, subint = NULL, xvars = NULL, diffs = FALSE, fnam = !diffs, vcov = FALSE, alpha = 0.05, df = Inf, Exp = FALSE, sample = FALSE ) ci.exp( ..., Exp = TRUE, pval = FALSE ) Wald( obj, H0=0, ... ) ci.mat( alpha = 0.05, df = Inf ) ci.pred( obj, newdata, Exp = NULL, alpha = 0.05 ) ci.ratio( r1, r2, se1 = NULL, se2 = NULL, log.tr = !is.null(se1) & !is.null(se2), alpha = 0.05, pval = FALSE ) } \arguments{ \item{obj}{A model object (in general of class \code{glm}, but for \code{ci.lin} and \code{ci.exp} it may also be of class \code{lm}, \code{coxph}, \code{survreg}, \code{clogistic}, \code{cch}, \code{lme}, \code{mer}, \code{lmerMod}, \code{gls}, \code{nls}, \code{gnlm}, \code{MIresult}, \code{mipo}, \code{polr}, or \code{rq}). } \item{ctr.mat}{Matrix, data frame or list (of two or four data frames). If \code{ctr.mat} is a matrix, it should be a contrast matrix to be multiplied to the parameter vector, i.e. the desired linear function of the parameters. If it is a data frame it should have columns corresponding to a prediction frame, see details. If it is a list, it must contain two or four data frames that are (possibly partial) prediction frames for \code{obj}, see argument \code{xvars} and details.} \item{xvars}{Character vector. If quantitative variables in the model are omitted from data frames supplied in a list to \code{ctr.mat}, they should be listed here. Omitted factors need not be mentioned here.} \item{subset}{The subset of the parameters to be used. If given as a character vector, the elements are in turn matched against the parameter names (using \code{grep}) to find the subset. Repeat parameters may result from using a character vector. This is considered a facility.} \item{subint}{Character. \code{sub}set selection, but where each element of the character vector is used to select a subset of parameters and only the \code{int}ersection of these is returned.} \item{diffs}{If TRUE, all differences between parameters in the subset are computed, and the \code{subset} argumnt is required. The argument \code{ctr.mat} is ignored. If \code{obj} inherits from \code{lm}, and \code{subset} is given as a string \code{subset} is used to search among the factors in the model and differences of all factor levels for the first match are shown. If \code{subset} does not match any of the factors in the model, all pairwise differences between parameters matching are returned.} \item{fnam}{Should the common part of the parameter names be included with the annotation of contrasts? Ignored if \code{diffs==T}. If a string is supplied this will be prefixed to the labels.} \item{vcov}{Should the covariance matrix of the set of parameters be returned? If this is set, \code{Exp} is ignored. See details.} \item{alpha}{Significance level for the confidence intervals.} \item{df}{Integer. Number of degrees of freedom in the t-distribution used to compute the quantiles used to construct the confidence intervals.} \item{Exp}{For \code{ci.lin}, if \code{TRUE} columns 5:6 are replaced with exp( columns 1,5,6 ). For \code{ci.exp}, if \code{FALSE}, the untransformed parameters are returned. For \code{ci.pred} it indicates whether the predictions should be exponentiated - the default (\code{Exp=NULL}) is to make a prediction with a Wald CI on the scale of the linear predictor and back-transform it by the inverse link function; if \code{FALSE}, the prediction on the link scale is returned.} \item{sample}{Logical or numerical. If \code{TRUE} or numerical a sample of size \code{as.numeric(sample)} is drawn from the multivariate normal with mean equal to the (\code{subset} defined) coefficients and variance equal to the estimated variance-covariance of these. These are then transformed by \code{ctr.mat} and returned.} \item{pval}{Logical. Should a column of P-values be included with the estimates and confidence intervals output by \code{ci.exp}.} \item{H0}{Numeric. The null values for the selected/transformed parameters to be tested by a Wald test. Must have the same length as the selected parameter vector.} \item{\ldots}{Parameters passed on to \code{ci.lin}.} \item{newdata}{Data frame of covariates where prediction is made.} \item{r1,r2}{Estimates of rates in two independent groups, with confidence limits. Can be either 3-column matrices or data frames with estimates and confindece intervals or 2 two column structures with confidence limits. Only the confidence limits} \item{se1,se2}{Standard errors of log-rates in the two groups. If given, it is assumed that \code{r1} and \code{r2} represent log-rates.} \item{log.tr}{Logical, if true, it is assumed that \code{r1} and \code{r2} represent log-rates with confidence intervals.} } \value{ \code{ci.lin} returns a matrix with number of rows and row names as \code{ctr.mat}. The columns are Estimate, Std.Err, z, P, 2.5\% and 97.5\% (or according to the value of \code{alpha}). If \code{vcov=TRUE} a list of length 2 with components \code{coef} (a vector), the desired functional of the parameters and \code{vcov} (a square matrix), the variance covariance matrix of this, is returned but not printed. If \code{Exp==TRUE} the confidence intervals for the parameters are replaced with three columns: exp(estimate,c.i.). \code{ci.exp} returns only the exponentiated parameter estimates with confidence intervals. It is merely a wrapper for \code{ci.lin}, fishing out the last 3 columns from \code{ci.lin(...,Exp=TRUE)}. If you just want the estimates and confidence limits, but not exponentiated, use \code{ci.exp(...,Exp=FALSE)}. If \code{ctr.mat} is a data frame, the model matrix corresponding to this is constructed and supplied. This is only supported for objects of class \code{lm}, \code{glm}, \code{gam} and \code{coxph}. So the default behaviour will be to produce the same as \code{ci.pred}, apparently superfluous. The purpose of this is to allow the use of the arguments \code{vcov} that produces the variance-covariance matrix of the predictions, and \code{sample} that produces a sample of predictions using sampling from the multivariate normal with mean equal to parameters and variance equal to the hessian. If \code{ctr.mat} is a list of two data frames, the difference of the predictions from using the first versus the last as newdata arguments to predict is computed. Columns that would be identical in the two data frames can be omitted (see below), but names of numerical variables omitted must be supplied in a character vector \code{xvars}. Factors omitted need not be named. If the second data frame has only one row, this is replicated to match the number of rows in the first. This facility is primarily aimed at teasing out RRs that are non-linear functions of a quantitative variable without setting up contrast matrices using the same code as in the model. Note however if splines are used with computed knots stored in a vector such as \code{Ns(x,knots=kk)} then the \code{kk} must be available in the (global) environment; it will not be found inside the model object. In practical terms it means that if you save model objects for later prediction you should save the knots used in the spline setups too. If \code{ctr.mat} is a list of four data frames, the difference of the difference of predictions from using the first and second versus difference of predictions from using the third and fourth is computed. Simply \code{(pr1-pr2) - (pr3-pr4)} with obvious notation. Useful to derive esoteric interaction effects. Finally, only arguments \code{Exp}, \code{vcov}, \code{alpha} and \code{sample} from \code{ci.lin} are honored when \code{ctr.mat} is a data frame or a list of two data frames. You can leave out variables (columns) from the two data frames that would be identical, basically variables not relevant for the calculation of the contrast. In many cases \code{ci.lin} (really \code{Epi:::ci.dfr}) can figure out the names of the omitted columns, but occasionally you will have to supply the names of the omitted variables in the \code{xvars} argument. Factors omitted need not be listed in \code{xvars}, although no harm is done doing so. \code{Wald} computes a Wald test for a subset of (possibly linear combinations of) parameters being equal to the vector of null values as given by \code{H0}. The selection of the subset of parameters is the same as for \code{ci.lin}. Using the \code{ctr.mat} argument makes it possible to do a Wald test for equality of parameters. \code{Wald} returns a named numerical vector of length 3, with names \code{Chisq}, \code{d.f.} and \code{P}. \code{ci.mat} returns a 2 by 3 matrix with rows \code{c(1,0,0)} and \code{c(0,-1,1)*1.96}, devised to post-multiply to a p by 2 matrix with columns of estimates and standard errors, so as to produce a p by 3 matrix of estimates and confidence limits. Used internally in \code{ci.lin} and \code{ci.cum}. The 1.96 is replaced by the appropriate quantile from the normal or t-distribution when arguments \code{alpha} and/or \code{df} are given. \code{ci.pred} returns a 3-column matrix with estimates and upper and lower confidence intervals as columns. This is just a convenience wrapper for \code{predict.glm(obj,se.fit=TRUE)} which returns a rather unhandy structure. The prediction with c.i. is made in the \code{link} scale, and by default transformed by the inverse link, since the most common use for this is for multiplicative Poisson or binomial models with either log or logit link. \code{ci.ratio} returns the rate-ratio of two independent set of rates given with confidence intervals or s.e.s. If \code{se1} and \code{se2} are given and \code{log.tr=FALSE} it is assumed that \code{r1} and \code{r2} are rates and \code{se1} and \code{se2} are standard errors of the log-rates. } \author{ Bendix Carstensen, \url{http://bendixcarstensen.com} & Michael Hills } \seealso{See also \code{\link{ci.cum}} for a function computing cumulative sums of (functions of) parameter estimates, and \code{\link{ci.surv}} for a function computing confidence intervals for survival functions based on smoothed rates. The example code for \code{\link{matshade}} has an application of predicting a rate-ratio using a list of two prediction frame in the \code{ctr.mat} argument.} \examples{ # Bogus data: f <- factor( sample( letters[1:5], 200, replace=TRUE ) ) g <- factor( sample( letters[1:3], 200, replace=TRUE ) ) x <- rnorm( 200 ) y <- 7 + as.integer( f ) * 3 + 2 * x + 1.7 * rnorm( 200 ) # Fit a simple model: mm <- lm( y ~ x + f + g ) ci.lin( mm ) ci.lin( mm, subset=3:6, diff=TRUE, fnam=FALSE ) ci.lin( mm, subset=3:6, diff=TRUE, fnam=TRUE ) ci.lin( mm, subset="f", diff=TRUE, fnam="f levels:" ) print( ci.lin( mm, subset="g", diff=TRUE, fnam="gee!:", vcov=TRUE ) ) # Use character defined subset to get ALL contrasts: ci.lin( mm, subset="f", diff=TRUE ) # Suppose the x-effect differs across levels of g: mi <- update( mm, . ~ . + g:x ) ci.lin( mi ) # RR a vs. b by x: nda <- data.frame( x=-3:3, g="a", f="b" ) ndb <- data.frame( x=-3:3, g="b", f="b" ) # ci.lin( mi, list(nda,ndb) ) # Same result if f column is omitted because "f" columns are identical ci.lin( mi, list(nda[,-3],ndb[,-3]) ) # However, crashes if knots in spline is supplied, and non-factor omitted xk <- -1:1 xi <- c(-0.5,0.5) ww <- rnorm(200) mi <- update( mm, . ~ . -x + ww + Ns(x,knots=xk) + g:Ns(x,knots=xi) ) # Will crash try( cbind( nda$x, ci.lin( mi, list(nda,ndb) ) ) ) # Must specify num vars (not factors) omitted from nda, ndb cbind( nda$x, ci.lin( mi, list(nda,ndb), xvars="ww" ) ) # A Wald test of whether the g-parameters are 0 Wald( mm, subset="g" ) # Wald test of whether the three first f-parameters are equal: ( CM <- rbind( c(1,-1,0,0), c(1,0,-1,0)) ) Wald( mm, subset="f", ctr.mat=CM ) # or alternatively ( CM <- rbind( c(1,-1,0,0), c(0,1,-1,0)) ) Wald( mm, subset="f", ctr.mat=CM ) # Confidence intervals for ratio of rates # Rates and ci supplied, but only the range (lower and upper ci) is used ci.ratio( cbind(10,8,12.5), cbind(5,4,6.25) ) ci.ratio( cbind(8,12.5), cbind(4,6.25) ) # Beware of the offset when making predictions with ci.pred and ci.exp \dontrun{ library( mgcv ) data( mortDK ) m.arg <- glm( dt ~ age , offset=log(risk) , family=poisson, data=mortDK ) m.form <- glm( dt ~ age + offset(log(risk)), family=poisson, data=mortDK ) a.arg <- gam( dt ~ age , offset=log(risk) , family=poisson, data=mortDK ) a.form <- gam( dt ~ age + offset(log(risk)), family=poisson, data=mortDK ) nd <- data.frame( age=60:65, risk=100 ) round( ci.pred( m.arg , nd ), 4 ) round( ci.pred( m.form, nd ), 4 ) round( ci.exp ( m.arg , nd ), 4 ) round( ci.exp ( m.form, nd ), 4 ) round( ci.pred( a.arg , nd ), 4 ) round( ci.pred( a.form, nd ), 4 ) round( ci.exp ( a.arg , nd ), 4 ) round( ci.exp ( a.form, nd ), 4 ) nd <- data.frame( age=60:65 ) try( ci.pred( m.arg , nd ) ) try( ci.pred( m.form, nd ) ) try( ci.exp ( m.arg , nd ) ) try( ci.exp ( m.form, nd ) ) try( ci.pred( a.arg , nd ) ) try( ci.pred( a.form, nd ) ) try( ci.exp ( a.arg , nd ) ) try( ci.exp ( a.form, nd ) ) } # The offset may be given as an argument (offset=log(risk)) # or as a term (+offset(log)), and depending on whether we are using a # glm or a gam Poisson model and whether we use ci.pred or ci.exp to # predict rates the offset is either used or ignored and either # required or not; the state of affairs can be summarized as: # # offset # ------------------------------------- # usage required? # ------------------ --------------- # function model argument term argument term # --------------------------------------------------------- # ci.pred glm used used yes yes # gam ignored used no yes # # ci.exp glm ignored ignored no yes # gam ignored ignored no yes # --------------------------------------------------------- } \keyword{models} \keyword{regression} Epi/man/pctab.Rd0000644000176200001440000000222413751040403013117 0ustar liggesusers\name{pctab} \alias{pctab} \title{Create percentages in a table} \description{ Computes percentages and a margin of totals along a given margin of a table. } \usage{ pctab(TT, margin = length(dim(TT)), dec=1) } \arguments{ \item{TT}{A table or array object} \item{margin}{Which margin should be the the total?} \item{dec}{How many decimals should be printed? If 0 or \code{FALSE} nothing is printed} } \value{ A table of percentages, where all dimensions except the one specified \code{margin} has two extra levels named "All" (where all entries are 100) and "N". The function prints the table with \code{dec} decimals. } \author{ Bendix Carstensen, Steno Diabetes Center, \url{http://bendixcarstensen.com}. } \seealso{ \code{\link{addmargins}} } \examples{ Aye <- sample( c("Yes","Si","Oui"), 177, replace=TRUE ) Bee <- sample( c("Hum","Buzz"), 177, replace=TRUE ) Sea <- sample( c("White","Black","Red","Dead"), 177, replace=TRUE ) A <- table( Aye, Bee, Sea ) A ftable( pctab( A ) ) ftable( pctab( addmargins( A, 1 ), 3 ) ) round( ftable( pctab( addmargins( A, 1 ), 3 ), row.vars=3 ), 1) } \keyword{ manip } \keyword{ methods } \keyword{ array } Epi/man/DMepi.Rd0000644000176200001440000000556213751040403013034 0ustar liggesusers\name{DMepi} \alias{DMepi} \docType{data} \title{Epidemiological rates for diabetes in Denmark 1996--2015} \description{Register based counts and person-years for incidence of diabetes and mortality with and without diabetes. } \usage{data("DMepi")} \format{ A data frame with 4200 observations on the following 8 variables. \describe{ \item{\code{sex}}{a factor with levels \code{M}, \code{F}} \item{\code{A}}{Age class, 0--99} \item{\code{P}}{Calendar year, 1996--2016} \item{\code{X}}{Number of new diagnoses of diabetes among persons without diabetes} \item{\code{D.nD}}{Number of deaths among persons without diabetes} \item{\code{Y.nD}}{Person-years among persons without diabetes} \item{\code{D.DM}}{Number of deaths among persons with diabetes} \item{\code{Y.DM}}{Person-years among persons with diabetes} } } \details{Based on registers of the Danish population. Only included for illustrative purposes. Cannot be used as scientifically validated data, since small numbers are randomly permuted between units. } \examples{ data(DMepi) # Total deaths and person-years in the Danish population ftable( addmargins( xtabs( cbind( Deaths=D.nD+D.DM, PYrs=Y.nD+Y.DM ) ~ P + sex, data=DMepi ), 2 ), row.vars = 1 ) # Deaths and person-years in the population of diabetes patients round( ftable( addmargins( xtabs( cbind( Deaths=D.DM, PYrs=Y.DM ) ~ P + sex, data=DMepi ), 2 ), row.vars = 1 ) ) # Model for age-specific incidence rates; inc <- glm( X ~ sex + Ns( A, knots=seq(30,80,10) ) + P, offset = log(Y.nD), family = poisson, data = DMepi ) # Predict for men and women separately in 2010: ndm <- data.frame( sex="M", A=20:90, P=2010, Y.nD=1000 ) ndf <- data.frame( sex="F", A=20:90, P=2010, Y.nD=1000 ) prM <- ci.pred( inc, ndm ) prF <- ci.pred( inc, ndf ) matplot( ndm$A, cbind(prM,prF), type="l", lty=1, lwd=c(3,1,1), col=rep(c("blue","red"),each=3), log="y", xlab="Age", ylab="DM incidence per 1000 PY" ) # This is a proportional hazards model - add sex-age interaction int <- update( inc, . ~ . + sex:Ns( A, knots=seq(30,80,10) ) ) prM <- ci.pred( int, ndm ) prF <- ci.pred( int, ndf ) matplot( ndm$A, cbind(prM,prF), type="l", lty=1, lwd=c(3,1,1), col=rep(c("blue","red"),each=3), log="y", xlab="Age", ylab="DM incidence per 1000 PY" ) # The rate-ratio is teased out using the ci.exp: RRp <- ci.exp( inc, list(ndm,ndf) ) RRi <- ci.exp( int, list(ndm,ndf) ) # and added to the plot matlines( ndm$A, cbind(RRi,RRp), type="l", lty=1, lwd=c(3,1,1), col=gray(rep(c(0.3,0.7),each=3)) ) abline(h=1) axis(side=4) mtext( "Male/Female IRR", side=4, line=2 ) } \keyword{datasets} Epi/DESCRIPTION0000644000176200001440000000267014016527043012504 0ustar liggesusersPackage: Epi Version: 2.44 Date: 2021-02-28 Title: Statistical Analysis in Epidemiology Authors@R: c(person("Bendix", "Carstensen", role = c("aut", "cre"), email = "b@bxc.dk"), person("Martyn", "Plummer", role = "aut", email = "Martyn.Plummer@warwick.ac.uk"), person("Esa", "Laara", role = "ctb"), person("Michael", "Hills", role = "ctb")) Depends: R (>= 3.5.0), utils Imports: cmprsk, etm, splines, MASS, survival, purrr, plyr, dplyr, Matrix, numDeriv, data.table, zoo, mgcv Suggests: mstate, nlme, lme4, popEpi Description: Functions for demographic and epidemiological analysis in the Lexis diagram, i.e. register and cohort follow-up data, in particular representation, manipulation and simulation of multistate data - the Lexis suite of functions, which includes interfaces to 'mstate', 'etm' and 'cmprsk' packages. Also contains functions for Age-Period-Cohort and Lee-Carter modeling and a function for interval censored data and some useful functions for tabulation and plotting, as well as a number of epidemiological data sets. License: GPL-2 URL: http://BendixCarstensen.com/Epi/ NeedsCompilation: yes Packaged: 2021-02-27 19:39:55 UTC; bendix Author: Bendix Carstensen [aut, cre], Martyn Plummer [aut], Esa Laara [ctb], Michael Hills [ctb] Maintainer: Bendix Carstensen Repository: CRAN Date/Publication: 2021-02-27 20:40:03 UTC Epi/src/0000755000176200001440000000000013052766107011565 5ustar liggesusersEpi/src/init.c0000644000176200001440000000066413052766107012702 0ustar liggesusers#include #include #include // for NULL #include extern SEXP clogit(SEXP, SEXP, SEXP, SEXP, SEXP, SEXP, SEXP); static const R_CallMethodDef CallEntries[] = { {"C_clogit", (DL_FUNC) &clogit, 7}, {NULL, NULL, 0} }; void R_init_Epi(DllInfo *dll) { R_registerRoutines(dll, NULL, CallEntries, NULL, NULL); R_useDynamicSymbols(dll, FALSE); R_forceSymbols(dll, TRUE); } Epi/src/cholesky2.c0000644000176200001440000000317713052766107013644 0ustar liggesusers/* $Id: cholesky2.c 11357 2009-09-04 15:22:46Z therneau $ ** ** subroutine to do Cholesky decompostion on a matrix: C = FDF' ** where F is lower triangular with 1's on the diagonal, and D is diagonal ** ** arguments are: ** n the size of the matrix to be factored ** **matrix a ragged array containing an n by n submatrix to be factored ** toler the threshold value for detecting "singularity" ** ** The factorization is returned in the lower triangle, D occupies the ** diagonal and the upper triangle is left undisturbed. ** The lower triangle need not be filled in at the start. ** ** Return value: the rank of the matrix (non-negative definite), or -rank ** it not SPD or NND ** ** If a column is deemed to be redundant, then that diagonal is set to zero. ** ** Terry Therneau * * Copied from the survival package by Terry Therneau, version 2.35-7 */ #include int attribute_hidden cholesky2(double **matrix, int n, double toler) { double temp; int i,j,k; double eps, pivot; int rank; int nonneg; nonneg=1; eps =0; for (i=0; i eps) eps = matrix[i][i]; for (j=(i+1); j void attribute_hidden chsolve2(double **matrix, int n, double *y) { register int i,j; register double temp; /* ** solve Fb =y */ for (i=0; i=0; i--) { if (matrix[i][i]==0) y[i] =0; else { temp = y[i]/matrix[i][i]; for (j= i+1; j #include #include /* Utility functions by Terry Therneau from the survival package These are specially adapted to work with information matrices that are not of full rank. */ extern int cholesky2(double **matrix, int m, double toler); extern void chsolve2(double **matrix, int m, double *y); extern void chinv2(double **matrix, int m); /* Efficient calculation of the conditional log likelihood, along with the score and information matrix, for a single stratum. Input parameters: X T x m matrix of covariate values y T-vector that indicates if an individual is a case (y[t]==1) or control (y[t]==0) T Number of individuals in the stratum m Number of covariates offset Vector of offsets for the linear predictor beta m-vector of log odds ratio parameters Output parameters: loglik The conditional log-likelihood (scalar) score The score function (m-vector) info The information matrix (m x m matrix) The contribution from this stratum will be *added* to the output parameters, so they must be correctly initialized before calling cloglik. */ static void cloglik_stratum(double const *X, int const *y, double const *offset, int T, int m, double const *beta, double *loglik, double *score, double *info) { double *f, *g, *h, *xt, *xmean; int i,j,k,t; int K = 0, Kp; int iscase = 1; double sign = 1; double lpmax; /* Calculate number of cases */ for (t = 0; t < T; ++t) { if (y[t] != 0 && y[t] != 1) { error("Invalid outcome in conditional log likelihood"); } K += y[t]; } if (K==0 || K==T) { return; /* Non-informative stratum */ } /* If there are more cases than controls then define cases to be those with y[t] == 0, and reverse the sign of the covariate values. */ if (2 * K > T ) { K = T - K; iscase = 0; sign = -1; } /* Calculate the maximum value of the linear predictor (lpmax) within the stratum. This is subtracted from the linear predictor when taking exponentials for numerical stability. Note that we must correct the log-likelihood for this, but not the score or information matrix. */ lpmax = sign * offset[0]; for (i = 0; i < m; ++i) { lpmax += sign * beta[i] * X[T*i]; } for (t = 1; t < T; ++t) { double lp = sign * offset[t]; for (i = 0; i < m; ++i) { lp += sign * beta[i] * X[t + T*i]; } if (lp > lpmax) { lpmax = lp; } } /* Calculate the mean value of the covariates within the stratum. This is used to improve the numerical stability of the score and information matrix. */ xmean = Calloc(m, double); for (i = 0; i < m; ++i) { xmean[i] = 0; for (t = 0; t < T; ++t) { xmean[i] += sign * X[t + T*i]; } xmean[i] /= T; } /* Contribution from cases */ for (t = 0; t < T; ++t) { if (y[t] == iscase) { loglik[0] += sign * offset[t]; for (i = 0; i < m; ++i) { loglik[0] += sign * X[t + i*T] * beta[i]; score[i] += sign * X[t + i*T] - xmean[i]; } loglik[0] -= lpmax; } } /* Allocate and initialize workspace for recursive calculations */ Kp = K + 1; f = Calloc(Kp, double); g = Calloc(m * Kp, double); h = Calloc(m * m * Kp, double); xt = Calloc(m, double); for (k = 0; k < Kp; ++k) { f[k] = 0; for (i = 0; i < m; ++i) { g[k+Kp*i] = 0; for (j = 0; j < m; ++j) { h[k + Kp*(i + m*j)] = 0; } } } f[0] = 1; /* Recursively calculate contributions over all possible case sets of size K. */ for (t = 0; t < T; ++t) { double Ct = offset[t]; for (i = 0; i < m; ++i) { xt[i] = sign * X[t + T*i] - xmean[i]; Ct += sign * beta[i] * X[t + T*i]; } Ct = exp(Ct - lpmax); for (k = imin2(K,t+1); k > 0; --k) { for (i = 0; i < m; ++i) { double const *gpi = g + Kp*i; for (j = 0; j < m; ++j) { double const *gpj = g + Kp*j; double *hp = h + Kp*(i + m*j); hp[k] += Ct * (hp[k-1] + xt[i] * gpj[k-1] + xt[j] * gpi[k-1] + xt[i] * xt[j] * f[k-1]); } } for (i = 0; i < m; ++i) { double *gp = g + Kp*i; gp[k] += Ct * (gp[k-1] + xt[i] * f[k-1]); } f[k] += Ct * f[k-1]; } } /* Add contributions from this stratum to the output parameters */ loglik[0] -= log(f[K]); for (i = 0; i < m; ++i) { double const *gpi = g + Kp*i; score[i] -= gpi[K] / f[K]; for (j = 0; j < m; ++j) { double const *gpj = g + Kp*j; double const *hp = h + Kp*(i + m*j); info[i + m*j] += hp[K]/f[K] - (gpi[K]/f[K]) * (gpj[K]/f[K]); } } Free(f); Free(g); Free(h); Free(xt); Free(xmean); } /* * Calculate the conditional log likelihood summed over all strata, * along with the score and information matrix. * * Input parameters: * * X - list of matrices of covariate values. One element of the list * corresponds to a single stratum * Y - list of vectors of outcomes, corresponding to X, * beta - vector of log odds ratio parameters * m - number of parameters * * Output parameters * * loglik - contains the conditional log-likelihood on exit (scalar) * score - contains the score function on exit (m - vector) * info - contains the information matrix on exit (m*m - vector) */ static void cloglik(SEXP X, SEXP y, SEXP offset, int m, double *beta, double *loglik, double *score, double *info) { int i; int M = m*m; /* Output parameters of cloglik_stratum must be initialized to zero */ loglik[0] = 0; for (i = 0; i < m; ++i) { score[i] = 0; } for (i = 0; i < M; ++i) { info[i] = 0; } for (i = 0; i < length(X); ++i) { SEXP Xi = VECTOR_ELT(X,i); SEXP yi = VECTOR_ELT(y,i); SEXP oi = VECTOR_ELT(offset, i); cloglik_stratum(REAL(Xi), INTEGER(yi), REAL(oi), nrows(Xi), m, beta, loglik, score, info); } } /* The chinv2 function only works on the lower triangle of the matrix. This wrapper function copies the lower to the upper triangle */ static void invert_info(double **imat, int m) { int i,j; chinv2(imat, m); for (i = 1; i < m; i++) { for (j = 0; j < i; j++) { imat[i][j] = imat[j][i]; } } } /* Find maximum likelihood estimate of conditional logistic regression model by Newton-Raphson. The algorithm is copied from coxph.fit from the survival package by Terry Therneau. The variable u is used to store both the score function and the step for the next iteration. Likewise info contains both the information matrix and its Cholesky decomposition. If flag > 0 then the arrays hold the score and variance-covariance matrix respectively. */ static void clogit_fit(SEXP X, SEXP y, SEXP offset, int m, double *beta, double *loglik, double *u, double *info, int *flag, int *maxiter, double const *eps, double const * tol_chol) { int i, iter = 0; Rboolean halving = FALSE; double *oldbeta = Calloc(m, double); double **imat = Calloc(m, double*); /* Set up ragged array representation of information matrix for use by cholesky2, chsolve2, and invert_info functions */ for (i = 0; i < m; ++i) { imat[i] = info + m*i; } /* Initial iteration */ cloglik(X, y, offset, m, beta, loglik, u, info); if (*maxiter > 0) { *flag = cholesky2(imat, m, *tol_chol); if (*flag > 0) { chsolve2(imat, m, u); for (i = 0; i < m; i++) { oldbeta[i] = beta[i]; beta[i] += u[i]; } } else { /* Bad information matrix. Don't go into the main loop */ *maxiter = 0; } } /* Main loop */ for (iter = 1; iter <= *maxiter; iter++) { double oldlik = *loglik; cloglik(X, y, offset, m, beta, loglik, u, info); if (fabs(1 - (oldlik / *loglik)) <= *eps && !halving) { /* Done */ break; } else if (iter == *maxiter) { /* Out of time */ *flag = 1000; break; } else if (*loglik < oldlik) { /* Not converging: halve step size */ halving = TRUE; for (i = 0; i < m; i++) { beta[i] = (beta[i] + oldbeta[i]) /2; } } else { /* Normal update */ halving = FALSE; oldlik = *loglik; *flag = cholesky2(imat, m, *tol_chol); if (*flag > 0) { chsolve2(imat, m, u); for (i = 0; i < m; i++) { oldbeta[i] = beta[i]; beta[i] += u[i]; } } else { break; /* Bad information matrix */ } } } *maxiter = iter; if (*flag > 0) { cholesky2(imat, m, *tol_chol); invert_info(imat, m); } Free(oldbeta); Free(imat); } /* R interface */ SEXP clogit(SEXP X, SEXP y, SEXP offset, SEXP init, SEXP maxiter, SEXP eps, SEXP tol_chol) { int i; int n = length(X); int m = length(init); int M = m*m; int flag = 0; int niter = INTEGER(maxiter)[0]; double loglik[2], *score, *info, *beta; SEXP ans, a, names, dims; if (!isNewList(X)) error("'X' must be a list"); if (!isNewList(y)) error("'y' must be a list"); if (!isNewList(offset)) error("'offset' must be a list"); if (length(X) != length(y)) error("length mismatch between X and y"); if (length(X) != length(offset)) error("length mismatch between X and offset"); for (i = 0; i < n; ++i) { int T = nrows(VECTOR_ELT(X,i)); int xcols = ncols(VECTOR_ELT(X,i)); int ylen = length(VECTOR_ELT(y,i)); int olen = length(VECTOR_ELT(offset, i)); if (xcols != m) { error("Element %d of X has %d columns; expected %d", i, xcols, m); } if (ylen != T) { error("Element %d of y has length %d; expected %d", i, ylen, T); } if (olen != T) { error("Element %d of offset has length %d; expected %d", i, ylen, T); } } beta = (double *) R_alloc(m, sizeof(double)); for (i = 0; i < m; ++i) { beta[i] = REAL(init)[i]; } score = (double *) R_alloc(m, sizeof(double)); info = (double *) R_alloc(M, sizeof(double)); /* Calculate initial loglikelihood */ cloglik(X, y, offset, m, beta, &loglik[0], score, info); /* Maximize the likelihood */ clogit_fit(X, y, offset, m, beta, &loglik[1], score, info, &flag, &niter, REAL(eps), REAL(tol_chol)); /* Construct return list */ PROTECT(ans = allocVector(VECSXP, 5)); PROTECT(names = allocVector(STRSXP, 5)); /* Estimates */ PROTECT(a = allocVector(REALSXP, m)); for (i = 0; i < m; ++i) { REAL(a)[i] = beta[i]; } SET_VECTOR_ELT(ans, 0, a); SET_STRING_ELT(names, 0, mkChar("coefficients")); UNPROTECT(1); /* Log likelihood */ PROTECT(a = allocVector(REALSXP, 2)); REAL(a)[0] = loglik[0]; REAL(a)[1] = loglik[1]; SET_VECTOR_ELT(ans, 1, a); SET_STRING_ELT(names, 1, mkChar("loglik")); UNPROTECT(1); /* Information matrix */ PROTECT(a = allocVector(REALSXP, M)); PROTECT(dims = allocVector(INTSXP, 2)); for (i = 0; i < M; ++i) { REAL(a)[i] = info[i]; } INTEGER(dims)[0] = m; INTEGER(dims)[1] = m; setAttrib(a, R_DimSymbol, dims); SET_VECTOR_ELT(ans, 2, a); SET_STRING_ELT(names, 2, mkChar("var")); UNPROTECT(2); /* Flag */ PROTECT(a = ScalarInteger(flag)); SET_VECTOR_ELT(ans, 3, a); SET_STRING_ELT(names, 3, mkChar("flag")); UNPROTECT(1); /* Number of iterations */ PROTECT(a = ScalarInteger(niter)); SET_VECTOR_ELT(ans, 4, a); SET_STRING_ELT(names, 4, mkChar("iter")); UNPROTECT(1); setAttrib(ans, R_NamesSymbol, names); UNPROTECT(2); return(ans); } Epi/src/chinv2.c0000644000176200001440000000301713052766107013123 0ustar liggesusers/* $Id: chinv2.c 11357 2009-09-04 15:22:46Z therneau $ ** ** matrix inversion, given the FDF' cholesky decomposition ** ** input **matrix, which contains the chol decomp of an n by n ** matrix in its lower triangle. ** ** returned: the upper triangle + diagonal contain (FDF')^{-1} ** below the diagonal will be F inverse ** ** Terry Therneau ** ** Copied from the survival package by Terry Therneau, version 2.35-7 */ #include void attribute_hidden chinv2(double **matrix , int n) { register double temp; register int i,j,k; /* ** invert the cholesky in the lower triangle ** take full advantage of the cholesky's diagonal of 1's */ for (i=0; i0) { matrix[i][i] = 1/matrix[i][i]; /*this line inverts D */ for (j= (i+1); j options( width=90 ) > library( Epi ) > print( sessionInfo(), l=F ) \end{Sinput} \begin{Soutput} R version 3.6.3 (2020-02-29) Platform: x86_64-pc-linux-gnu (64-bit) Running under: Ubuntu 14.04.6 LTS Matrix products: default BLAS: /usr/lib/openblas-base/libopenblas.so.0 LAPACK: /usr/lib/lapack/liblapack.so.3.0 attached base packages: [1] utils datasets graphics grDevices stats methods base other attached packages: [1] Epi_2.43 loaded via a namespace (and not attached): [1] Rcpp_1.0.3 magrittr_1.5 splines_3.6.3 MASS_7.3-53 [5] tidyselect_0.2.5 lattice_0.20-41 R6_2.4.1 rlang_0.4.4 [9] plyr_1.8.5 dplyr_0.8.4 cmprsk_2.2-7 tools_3.6.3 [13] parallel_3.6.3 grid_3.6.3 data.table_1.12.0 nlme_3.1-149 [17] mgcv_1.8-33 survival_3.2-7 assertthat_0.2.1 tibble_2.1.3 [21] etm_1.0.4 numDeriv_2016.8-1 crayon_1.3.4 Matrix_1.2-18 [25] purrr_0.3.0 glue_1.3.1 compiler_3.6.3 pillar_1.4.3 [29] zoo_1.8-4 pkgconfig_2.0.3 \end{Soutput} \end{Schunk} First we load the diabetes data and set up a simple illness-death model: \begin{Schunk} \begin{Sinput} > data(DMlate) > dml <- Lexis( entry = list(Per=dodm, Age=dodm-dobth, DMdur=0 ), + exit = list(Per=dox), + exit.status = factor(!is.na(dodth),labels=c("DM","Dead")), + data = DMlate ) \end{Sinput} \begin{Soutput} NOTE: entry.status has been set to "DM" for all. NOTE: Dropping 4 rows with duration of follow up < tol \end{Soutput} \end{Schunk} This is just data for a simple survival model with states \texttt{DM} and \texttt{Dead}. Now we cut the follow-up at insulin start, which for the majority of patients (T2D) is a clinical indicator of deterioration of disease regulation. We therefore also introduce a new timescale, and split the non-precursor states, so that we can address the question of ever having been on insulin: \begin{Schunk} \begin{Sinput} > dmi <- cutLexis( dml, cut = dml$doins, + pre = "DM", + new.state = "Ins", + new.scale = "t.Ins", + split.states = TRUE ) > summary( dmi, timeScales=T ) \end{Sinput} \begin{Soutput} Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 6157 1694 2048 0 9899 3742 45885.49 9899 Ins 0 1340 0 451 1791 451 8387.77 1791 Sum 6157 3034 2048 451 11690 4193 54273.27 9996 Timescales: Per Age DMdur t.Ins "" "" "" "Ins" \end{Soutput} \end{Schunk} Note that we show the time scales in the \texttt{Lexis} object, and that it is indicated that the time scale \texttt{t.Ins} is defined as time since entry into stat state \texttt{Ins.} We can show how many person-years we have and show the number of transitions and transition rates (per 1000), using the \texttt{boxes.Lexis} function to display the states and the number of transitions between them: \begin{Schunk} \begin{Sinput} > boxes( dmi, boxpos = list(x=c(20,20,80,80), + y=c(80,20,80,20)), + scale.R = 1000, show.BE = TRUE ) \end{Sinput} \end{Schunk} \insfig{boxes}{0.8}{Data overview for the \textrm{\tt dmi} dataset. Numbers in the boxes are person-years and the number of persons who begin, resp. end their follow-up in each state, and numbers on the arrows are no. of transitions and rates (transition intensities) per 1000 PY.} \section{Analysis of rates} In the \texttt{Lexis} object (which is just a data frame) each person is represented by one record for each transient state occupied, thus in this case either 1 or 2 records; those who have a recorded time both without and with insulin have two records. In order to be able to fit Poisson models with occurrence rates varying by the different time-scales, we split the follow-up in 3-month intervals for modeling: \begin{Schunk} \begin{Sinput} > Si <- splitLexis( dmi, seq(0,20,1/4), "DMdur" ) > summary( Si ) \end{Sinput} \begin{Soutput} Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 184986 1694 2048 0 188728 3742 45885.49 9899 Ins 0 34707 0 451 35158 451 8387.77 1791 Sum 184986 36401 2048 451 223886 4193 54273.27 9996 \end{Soutput} \begin{Sinput} > print( subset( Si, lex.id==97 )[,1:10], digits=6 ) \end{Sinput} \begin{Soutput} lex.id Per Age DMdur t.Ins lex.dur lex.Cst lex.Xst sex dobth 2142 97 1997.55 58.9268 0.00000 NA 0.2500000 DM DM F 1938.62 2143 97 1997.80 59.1768 0.25000 NA 0.2500000 DM DM F 1938.62 2144 97 1998.05 59.4268 0.50000 NA 0.2500000 DM DM F 1938.62 2145 97 1998.30 59.6768 0.75000 NA 0.2500000 DM DM F 1938.62 2146 97 1998.55 59.9268 1.00000 NA 0.2500000 DM DM F 1938.62 2147 97 1998.80 60.1768 1.25000 NA 0.2500000 DM DM F 1938.62 2148 97 1999.05 60.4268 1.50000 NA 0.2500000 DM DM F 1938.62 2149 97 1999.30 60.6768 1.75000 NA 0.2500000 DM DM F 1938.62 2150 97 1999.55 60.9268 2.00000 NA 0.1793292 DM Ins F 1938.62 2151 97 1999.72 61.1061 2.17933 0.0000000 0.0706708 Ins Ins F 1938.62 2152 97 1999.80 61.1768 2.25000 0.0706708 0.2500000 Ins Ins F 1938.62 2153 97 2000.05 61.4268 2.50000 0.3206708 0.2500000 Ins Ins F 1938.62 2154 97 2000.30 61.6768 2.75000 0.5706708 0.2500000 Ins Ins F 1938.62 2155 97 2000.55 61.9268 3.00000 0.8206708 0.0116359 Ins Dead(Ins) F 1938.62 \end{Soutput} \end{Schunk} Note that when we split the follow-up, each person's follow up now consists of many records, each with the \emph{current} values of the timescales at the start of the interval represented by the record. In the modeling we shall assume that the rates are constant within each 6-month interval, but the \emph{size} of these rates we model as smooth functions of the time scales (that is the values at the beginning of each interval). The approach often used in epidemiology where one parameter is attached to each interval of time (or age) is not feasible when more than one time scale is used, because intervals are not classified the same way on all timescales. We shall use natural splines (restricted cubic splines) for the analysis of rates, and hence we must allocate knots for the splines. This is done for each of the time-scales, and separately for the transition out of states \texttt{DM} and \texttt{Ins}. For age, we place the knots so that the number of events is the same between each pair of knots, but only half of this beyond each of the boundary knots, whereas for the timescales \texttt{DMdur} and \texttt{tIns} where we have observation from a well-defined 0, we put knots at 0 and place the remaining knots so that the number of events is the same between each pair of knots as well as outside the boundary knots. \begin{Schunk} \begin{Sinput} > nk <- 5 > ( ai.kn <- with( subset(Si,lex.Xst=="Ins" & lex.Cst!=lex.Xst ), + quantile( Age+lex.dur , probs=(1:nk-0.5)/nk ) ) ) \end{Sinput} \begin{Soutput} 10% 30% 50% 70% 90% 23.23751 48.82218 58.63244 67.79028 78.88542 \end{Soutput} \begin{Sinput} > ( ad.kn <- with( subset(Si,lex.Xst=="Dead"), + quantile( Age+lex.dur , probs=(1:nk-0.5)/nk ) ) ) \end{Sinput} \begin{Soutput} 10% 30% 50% 70% 90% 61.91951 72.52731 78.43121 83.32348 90.15195 \end{Soutput} \begin{Sinput} > ( di.kn <- with( subset(Si,lex.Xst=="Ins" & lex.Cst!=lex.Xst ), + c(0,quantile( DMdur+lex.dur, probs=(1:(nk-1))/nk ) )) ) \end{Sinput} \begin{Soutput} 20% 40% 60% 80% 0.00000000 0.06570842 0.45448323 3.28761123 6.63764545 \end{Soutput} \begin{Sinput} > ( dd.kn <- with( subset(Si,lex.Xst=="Dead"), + c(0,quantile( DMdur+lex.dur, probs=(1:(nk-1))/nk ) )) ) \end{Sinput} \begin{Soutput} 20% 40% 60% 80% 0.0000000 0.7687885 2.1327858 4.0465435 6.5232033 \end{Soutput} \begin{Sinput} > ( ti.kn <- with( subset(Si,lex.Xst=="Dead(Ins)"), + c(0,quantile( t.Ins+lex.dur, probs=(1:(nk-1))/nk ) )) ) \end{Sinput} \begin{Soutput} 20% 40% 60% 80% 0.0000000 0.3093771 1.1307324 2.5489391 4.9117043 \end{Soutput} \end{Schunk} Note that when we tease out the event records for transition to \emph{transient} states (in this case \texttt{Ins}, that is \verb|lex.Xst=="Ins"|), we should add \verb|lex.Cst!=lex.Xst|, to include only transition records and avoiding including records of sojourn time in the transient state. We then fit Poisson models to transition rates, using the wrapper \texttt{Ns} from the \texttt{Epi} package to simplify the specification of the rates: \begin{Schunk} \begin{Sinput} > library( splines ) > DM.Ins <- glm( (lex.Xst=="Ins") ~ Ns( Age , knots=ai.kn ) + + Ns( DMdur, knots=di.kn ) + + I(Per-2000) + sex, + family=poisson, offset=log(lex.dur), + data = subset(Si,lex.Cst=="DM") ) > ci.exp( DM.Ins ) \end{Sinput} \begin{Soutput} exp(Est.) 2.5% 97.5% (Intercept) 1.37516629 1.21414923 1.55753699 Ns(Age, knots = ai.kn)1 0.23411761 0.19185266 0.28569349 Ns(Age, knots = ai.kn)2 0.23166177 0.19576557 0.27414000 Ns(Age, knots = ai.kn)3 0.02835009 0.02284379 0.03518363 Ns(Age, knots = ai.kn)4 0.38067392 0.32945713 0.43985278 Ns(DMdur, knots = di.kn)1 0.04462626 0.03373451 0.05903459 Ns(DMdur, knots = di.kn)2 0.22388988 0.19028663 0.26342723 Ns(DMdur, knots = di.kn)3 0.03379141 0.02574708 0.04434907 Ns(DMdur, knots = di.kn)4 0.47100646 0.40783317 0.54396529 I(Per - 2000) 0.97381513 0.96082049 0.98698552 sexF 0.73757407 0.66886782 0.81333785 \end{Soutput} \begin{Sinput} > class( DM.Ins ) \end{Sinput} \begin{Soutput} [1] "glm" "lm" \end{Soutput} \end{Schunk} We can also fit this model with a slightly simpler syntax using the \texttt{glm.Lexis} function: \begin{Schunk} \begin{Sinput} > DM.Ins <- glm.Lexis( Si, from = "DM", to = "Ins", + formula = ~ Ns( Age , knots=ai.kn ) + + Ns( DMdur, knots=di.kn ) + + I(Per-2000) + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object Si with log link: Rates for the transition: DM->Ins \end{Soutput} \begin{Sinput} > ci.exp( DM.Ins ) \end{Sinput} \begin{Soutput} exp(Est.) 2.5% 97.5% (Intercept) 1.37516630 1.21415038 1.55753552 Ns(Age, knots = ai.kn)1 0.23411761 0.19185214 0.28569426 Ns(Age, knots = ai.kn)2 0.23166177 0.19576473 0.27414118 Ns(Age, knots = ai.kn)3 0.02835009 0.02284374 0.03518371 Ns(Age, knots = ai.kn)4 0.38067392 0.32945601 0.43985427 Ns(DMdur, knots = di.kn)1 0.04462625 0.03373347 0.05903639 Ns(DMdur, knots = di.kn)2 0.22388988 0.19028599 0.26342813 Ns(DMdur, knots = di.kn)3 0.03379141 0.02574705 0.04434912 Ns(DMdur, knots = di.kn)4 0.47100646 0.40783201 0.54396683 I(Per - 2000) 0.97381513 0.96082027 0.98698574 sexF 0.73757407 0.66886641 0.81333956 \end{Soutput} \begin{Sinput} > class( DM.Ins ) \end{Sinput} \begin{Soutput} [1] "glm.lex" "glm" "lm" \end{Soutput} \end{Schunk} So we have a slightly simpler syntax, and we get an informative message of which transition(s) we are modeling. However we do not have \texttt{update} method for these objects. \begin{Schunk} \begin{Sinput} > DM.Dead <- glm.Lexis( Si, from = "DM", to = "Dead", + formula = ~ Ns( Age , knots=ad.kn ) + + Ns( DMdur, knots=dd.kn ) + + I(Per-2000) + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object Si with log link: Rates for the transition: DM->Dead \end{Soutput} \begin{Sinput} > Ins.Dead <- glm.Lexis( Si, from = "Ins", + formula = ~ Ns( Age , knots=ad.kn ) + + Ns( DMdur, knots=dd.kn ) + + Ns( t.Ins, knots=ti.kn ) + + I(Per-2000) + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object Si with log link: Rates for the transition: Ins->Dead(Ins) \end{Soutput} \end{Schunk} Note the similarity of the code used to fit the three models, is is mainly redefining the response variable (\texttt{to} state) and the subset of the data used (\texttt{from} state). Also note that the last model need no specification of \texttt{to}, the default is to model all transitions from the \texttt{from} state, and his case there is only one. \section{The mortality rates} This section discusses in some detail how to extract ad display the mortality rates from the models fitted. But it is not necessary for understanding how to use \texttt{simLexis} in practice. \subsection{Proportionality of mortality rates} Note that we have fitted separate models for the three transitions, there is no assumption of proportionality between the mortality rates from \texttt{DM} and \texttt{Ins}. However, there is nothing that prevents us from testing this assumption; we can just fit a model for the mortality rates in the entire data frame \texttt{Si}, and compare the deviance from this with the sum of the deviances from the separate models using the \texttt{glm.Lexis} function: \begin{Schunk} \begin{Sinput} > All.Dead <- glm.Lexis( Si, to = c("Dead(Ins)","Dead"), + formula = ~ Ns( Age , knots=ad.kn ) + + Ns( DMdur, knots=dd.kn ) + + lex.Cst + + I(Per-2000) + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object Si with log link: Rates for transitions: Ins->Dead(Ins), DM->Dead \end{Soutput} \begin{Sinput} > round( ci.exp( All.Dead ), 3 ) \end{Sinput} \begin{Soutput} exp(Est.) 2.5% 97.5% (Intercept) 0.057 0.049 0.065 Ns(Age, knots = ad.kn)1 4.101 3.462 4.858 Ns(Age, knots = ad.kn)2 4.661 4.064 5.346 Ns(Age, knots = ad.kn)3 15.434 13.548 17.583 Ns(Age, knots = ad.kn)4 7.509 6.695 8.421 Ns(DMdur, knots = dd.kn)1 0.466 0.384 0.565 Ns(DMdur, knots = dd.kn)2 0.642 0.563 0.731 Ns(DMdur, knots = dd.kn)3 0.229 0.165 0.318 Ns(DMdur, knots = dd.kn)4 0.796 0.713 0.888 lex.CstIns 2.168 1.947 2.415 I(Per - 2000) 0.965 0.954 0.977 sexF 0.665 0.614 0.721 \end{Soutput} \end{Schunk} Incidentally we could have dispensed with the \texttt{to=} argument too, because the default is to take \texttt{to} to be all absorbing states in the model. From the parameter values we would in a simple setting just claim that start of insulin-treatment was associated with a slightly more than doubling of mortality. The model \texttt{All.dead} assumes that the age- and DM-duration effects on mortality in the \texttt{DM} and \texttt{Ins} states are the same, and moreover that there is no effect of insulin duration, but merely a mortality that is larger by a multiplicative constant not depending on insulin duration. The model \texttt{DM.Dead} has 8 parameters to describe the dependency on age and DM duration, the model \texttt{Ins.Dead} has 12 for the same plus the insulin duration (a natural spline with $k$ knots gives $k-1$ parameters, and we chose $k=5$ above). We can compare the fit of the simple proportional hazards model with the fit of the separate models for the two mortality rates, by adding up the deviances and d.f. from these: \begin{Schunk} \begin{Sinput} > what <- c("null.deviance","df.null","deviance","df.residual") > ( rD <- unlist( DM.Dead[what] ) ) \end{Sinput} \begin{Soutput} null.deviance df.null deviance df.residual 22535.77 188727.00 20412.81 188717.00 \end{Soutput} \begin{Sinput} > ( rI <- unlist( Ins.Dead[what] ) ) \end{Sinput} \begin{Soutput} null.deviance df.null deviance df.residual 4867.127 35157.000 4211.735 35143.000 \end{Soutput} \begin{Sinput} > ( rA <- unlist( All.Dead[what] ) ) \end{Sinput} \begin{Soutput} null.deviance df.null deviance df.residual 27415.21 223885.00 24705.70 223874.00 \end{Soutput} \begin{Sinput} > round( c( dd <- rA-(rI+rD), "pVal"=1-pchisq(dd[3],dd[4]+1) ), 3 ) \end{Sinput} \begin{Soutput} null.deviance df.null deviance df.residual pVal.deviance 12.314 1.000 81.154 14.000 0.000 \end{Soutput} \end{Schunk} Thus we see there is a substantial non-proportionality of mortality rates from the two states; but a test provides no clue whatsoever to the particular \emph{shape} of the non-proportionality. To this end, we shall explore the predicted mortalities under the two models quantitatively in more detail. Note that the reason that there is a difference in the null deviances (and a difference of 1 in the null d.f.) is that the null deviance of \texttt{All.Dead} refer to a model with a single intercept, that is a model with constant and \emph{identical} mortality rates from the states \texttt{DM} and \texttt{Ins}, whereas the null models for \texttt{DM.Dead} and \texttt{Ins.Dead} have constant but \emph{different} mortality rates from the states \texttt{DM} and \texttt{Ins}. This is however irrelevant for the comparison of the \emph{residual} deviances. \subsection{How the mortality rates look} If we want to see how the mortality rates are modelled in \texttt{DM.Dead} and \texttt{Ins.Dead} in relation to \texttt{All.Dead}, we make a prediction of rates for say men diagnosed in different ages and going on insulin at different times after this. So we consider men diagnosed in ages 40, 50, 60 and 70, and who either never enter insulin treatment or do it 0, 2 or 5 years after diagnosis of DM. To this end we create a prediction data frame where we have observation times from diagnosis and 12 years on (longer would not make sense as this is the extent of the data). But we start by setting up an array to hold the predicted mortality rates, classified by diabetes duration, age at diabetes onset, time of insulin onset, and of course type of model. What we want to do is to plot the age-specific mortality rates for persons not on insulin, and for persons starting insulin at different times after DM. The mortality curves start at the age where the person gets diabetes and continues 12 years; for persons on insulin they start at the age when they initiate insulin. \begin{Schunk} \begin{Sinput} > pr.rates <- NArray( list( DMdur = seq(0,12,0.1), + DMage = 4:7*10, + r.Ins = c(NA,0,2,5), + model = c("DM/Ins","All"), + what = c("rate","lo","hi") ) ) > str( pr.rates ) \end{Sinput} \begin{Soutput} logi [1:121, 1:4, 1:4, 1:2, 1:3] NA NA NA NA NA NA ... - attr(*, "dimnames")=List of 5 ..$ DMdur: chr [1:121] "0" "0.1" "0.2" "0.3" ... ..$ DMage: chr [1:4] "40" "50" "60" "70" ..$ r.Ins: chr [1:4] NA "0" "2" "5" ..$ model: chr [1:2] "DM/Ins" "All" ..$ what : chr [1:3] "rate" "lo" "hi" \end{Soutput} \end{Schunk} For convenience the \texttt{Epi} package contains a function that computes predicted (log-)rates with c.i. --- it is merely a wrapper for \texttt{predict.glm}. So we set up the prediction data frame and modify it in loops over ages at onset and insulin onset in order to collect the predicted rates in different scenarios: \begin{Schunk} \begin{Sinput} > nd <- data.frame( DMdur = as.numeric( dimnames(pr.rates)[[1]] ), + lex.Cst = factor( 1, levels=1:4, + labels=levels(Si$lex.Cst) ), + sex = factor( 1, levels=1:2, labels=c("M","F")) ) \end{Sinput} \end{Schunk} Note that we did \emph{not} insert \texttt{lex.dur} as covariate in the prediction frame. This would be required if we used the \texttt{poisson} family with the \texttt{glm}, but the wrapper \texttt{glm.Lexis} uses the \texttt{poisreg} family, so \texttt{lex.dur} is ignored and predictions always comes in the (inverse) units of \texttt{lex.dur}. So we get rates per 1 person-year in the predictions. \begin{Schunk} \begin{Sinput} > for( ia in dimnames(pr.rates)[[2]] ) + { + dnew <- transform( nd, Age = as.numeric(ia)+DMdur, + Per = 1998+DMdur ) + pr.rates[,ia,1,"DM/Ins",] <- ci.pred( DM.Dead, newdata = dnew ) + pr.rates[,ia,1,"All" ,] <- ci.pred( All.Dead, newdata = dnew ) + for( ii in dimnames(pr.rates)[[3]][-1] ) + { + dnew = transform( dnew, lex.Cst = factor( 2, levels=1:4, + labels=levels(Si$lex.Cst) ), + t.Ins = ifelse( (DMdur-as.numeric(ii)) >= 0, + DMdur-as.numeric(ii), NA ) ) + pr.rates[,ia, ii ,"DM/Ins",] <- ci.pred( Ins.Dead, newdata = dnew ) + pr.rates[,ia, ii ,"All" ,] <- ci.pred( All.Dead, newdata = dnew ) + } + } \end{Sinput} \end{Schunk} So for each age at DM onset we make a plot of the mortality as function of current age both for those with no insulin treatment and those that start insulin treatment 0, 2 and 5 years after diabetes diagnosis, thus 4 curves (with c.i.). These curves are replicated with a different color for the simplified model. \begin{Schunk} \begin{Sinput} > par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1 ) > plot( NA, xlim=c(40,82), ylim=c(5,300), bty="n", + log="y", xlab="Age", ylab="Mortality rate per 1000 PY" ) > abline( v=seq(40,80,5), h=outer(1:9,10^(0:2),"*"), col=gray(0.8) ) > for( aa in 4:7*10 ) for( ii in 1:4 ) + matshade( aa+as.numeric(dimnames(pr.rates)[[1]]), + cbind( pr.rates[,paste(aa),ii,"DM/Ins",], + pr.rates[,paste(aa),ii,"All" ,] )*1000, + type="l", lty=1, lwd=2, + col=c("red","limegreen") ) \end{Sinput} \end{Schunk} \insfig{mort-int}{0.9}{Estimated mortality rates for male diabetes patients with no insulin (lower sets of curves) and insulin (upper curves), with DM onset in age 40, 50, 60 and 70. The red curves are from the models with separate age effects for persons with and without insulin, and a separate effect of insulin duration. The green curves are from the model with common age-effects and only a time-dependent effect of insulin, assuming no effect of insulin duration (the classical time-dependent variable approach). Hence the upper green curve is common for any time of insulin inception.} From figure \ref{fig:mort-int} we see that there is a substantial insulin-duration effect which is not accommodated by the simple model with only one time-dependent variable to describe the insulin effect. Note that the simple model (green curves) for those on insulin does not depend in insulin duration, and hence the mortality curves for those on insulin are just parallel to the mortality curves for those not on insulin, regardless of diabetes duration (or age) at the time of insulin initiation. This is the proportional hazards assumption. Thus the effect of insulin initiation is under-estimated for short duration of insulin and over-estimated for long duration of insulin. This is the major discrepancy between the two models, and illustrates the importance of being able to accommodate different time scales, but there is also a declining overall insulin effect by age which is not accommodated by the proportional hazards approach. Finally, this plot illustrates an important feature in reporting models with multiple timescales; all timescales must be represented in the predicted rates, only reporting the effect of one timescale, conditional on a fixed value of other timescales is misleading since all timescales by definition advance at the same pace. For example, the age-effect for a fixed value of insulin duration really is a misnomer since it does not correspond to any real person's follow-up, but to the mortality of persons in different ages but with the same duration of insulin use. \section{Input to the \texttt{simLexis} function} We want to estimate the cumulative probability of being in each of the 4 states, so that we can assess the fraction of diabetes pateints that go on insulin In order to simulate from the multistate model with the estimated transition rates, and get the follow-up of a hypothetical cohort, we must supply \emph{both} the transition rates and the structure of the model \emph{as well as} the initial cohort status to \texttt{simLexis}. \subsection{The transition object} We first put the models into an object representing the transitions; note this is a list of lists, the latter having \texttt{glm} objects as elements: \begin{Schunk} \begin{Sinput} > Tr <- list( "DM" = list( "Ins" = DM.Ins, + "Dead" = DM.Dead ), + "Ins" = list( "Dead(Ins)" = Ins.Dead ) ) \end{Sinput} \end{Schunk} Now we have the description of the rates and of the structure of the model. The \texttt{Tr} object defines the states and models for all transitions between them; the object \verb|Tr$A$B| is the model for the transition intensity from state \texttt{A} to state \texttt{B}. \subsection{The initial cohort} We now define an initial \texttt{Lexis} object of persons with all relevant covariates defined. Note that we use \texttt{NULL} as row indicator in the \texttt{Lexis} object we used for modeling; this conserves the \texttt{time.scale} and \texttt{time.since} attributes which are needed for the simulation: \begin{Schunk} \begin{Sinput} > str( ini <- Si[NULL,1:9] ) \end{Sinput} \begin{Soutput} Classes ‘Lexis’ and 'data.frame': 0 obs. of 9 variables: $ lex.id : int $ Per : num $ Age : num $ DMdur : num $ t.Ins : num $ lex.dur: num $ lex.Cst: Factor w/ 4 levels "DM","Ins","Dead",..: $ lex.Xst: Factor w/ 4 levels "DM","Ins","Dead",..: $ sex : Factor w/ 2 levels "M","F": - attr(*, "time.scales")= chr "Per" "Age" "DMdur" "t.Ins" - attr(*, "time.since")= chr "" "" "" "Ins" - attr(*, "breaks")=List of 4 ..$ Per : NULL ..$ Age : NULL ..$ DMdur: num 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 ... ..$ t.Ins: NULL \end{Soutput} \end{Schunk} We now have an empty \texttt{Lexis} object with attributes reflecting the timescales in the multistate model we want to simulate from. But we must enter some data to represent the initial state of the persons whose follow-up we want to simulate through the model; so fill in data for one man and one woman: \begin{Schunk} \begin{Sinput} > ini[1:2,"lex.id"] <- 1:2 > ini[1:2,"lex.Cst"] <- "DM" > ini[1:2,"Per"] <- 1995 > ini[1:2,"Age"] <- 60 > ini[1:2,"DMdur"] <- 5 > ini[1:2,"sex"] <- c("M","F") > ini \end{Sinput} \begin{Soutput} lex.id Per Age DMdur t.Ins lex.dur lex.Cst lex.Xst sex 1 1 1995 60 5 NA NA DM M 2 2 1995 60 5 NA NA DM F \end{Soutput} \end{Schunk} So the persons starts in age 60 in 1995 with 5 years of diabetes duration. Note that the \texttt{t.Ins} is \texttt{NA}, because this is a timescale that first comes alive if a transtion to \texttt{Ins} is simulated. \section{Simulation of the follow-up} Now we simulate life-courses of a 1000 of each of these persons using the estimated model. The \texttt{t.range} argument gives the times range where the integrated intensities (cumulative rates) are evaluated and where linear interpolation is used when simulating transition times. Note that this must be given in the same units as \texttt{lex.dur} in the \texttt{Lexis} object used for fitting the models for the transitions. It is not a parameter that can be easily determined from the \texttt{TR} object, hence it must be supplied by the user. \begin{Schunk} \begin{Sinput} > set.seed( 52381764 ) > Nsim <- 5000 > system.time( simL <- simLexis( Tr, + ini, + t.range = 12, + N = Nsim ) ) \end{Sinput} \begin{Soutput} user system elapsed 17.936 1.015 17.934 \end{Soutput} \end{Schunk} The result is a \texttt{Lexis} object --- a data frame representing the simulated follow-up of 10000 persons (5000 identical men and 5000 identical women) according to the rates we estimated from the original dataset. \begin{Schunk} \begin{Sinput} > summary( simL, by="sex" ) \end{Sinput} \begin{Soutput} $M Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 1438 2048 1514 0 5000 3562 36620.95 5000 Ins 0 1363 0 685 2048 685 10935.47 2048 Sum 1438 3411 1514 685 7048 4247 47556.41 5000 $F Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 2186 1689 1125 0 5000 2814 42181.63 5000 Ins 0 1321 0 368 1689 368 9535.20 1689 Sum 2186 3010 1125 368 6689 3182 51716.83 5000 \end{Soutput} \end{Schunk} \subsection{Using other models for simulation} \subsubsection{Proportional hazards Poisson model} We fitted a proportional mortality model \texttt{All.Dead} (which fitted worse than the other two), this is a model for \emph{both} the transition from \texttt{DM} to \texttt{Death} \emph{and} from \texttt{Ins} to \texttt{Dead(Ins)}, assuming that they are proportional. But it can easily be used in the simulation set-up, because the state is embedded in the model via the term \texttt{lex.Cst}, which is updated during the simulation. Simulation using this instead just requires that we supply a different transition object: \begin{Schunk} \begin{Sinput} > Tr.p <- list( "DM" = list( "Ins" = DM.Ins, + "Dead" = All.Dead ), + "Ins" = list( "Dead(Ins)" = All.Dead ) ) > system.time( simP <- simLexis( Tr.p, + ini, + t.range = 12, + N = Nsim ) ) \end{Sinput} \begin{Soutput} user system elapsed 19.197 1.137 19.298 \end{Soutput} \begin{Sinput} > summary( simP, by="sex" ) \end{Sinput} \begin{Soutput} $M Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 1633 1984 1383 0 5000 3367 37674.18 5000 Ins 0 1135 0 849 1984 849 9807.38 1984 Sum 1633 3119 1383 849 6984 4216 47481.56 5000 $F Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 2285 1695 1020 0 5000 2715 42892.52 5000 Ins 0 1191 0 504 1695 504 8833.70 1695 Sum 2285 2886 1020 504 6695 3219 51726.21 5000 \end{Soutput} \end{Schunk} \subsubsection{Proportional hazards Cox model} A third possibility would be to replace the two-time scale proportional mortality model by a one-time-scale Cox-model, using diabetes duration as time scale, and age at diagnosis of DM as (fixed) covariate: \begin{Schunk} \begin{Sinput} > library( survival ) > Cox.Dead <- coxph( Surv( DMdur, DMdur+lex.dur, + lex.Xst %in% c("Dead(Ins)","Dead")) ~ + Ns( Age-DMdur, knots=ad.kn ) + + I(lex.Cst=="Ins") + + I(Per-2000) + sex, + data = Si ) > round( ci.exp( Cox.Dead ), 3 ) \end{Sinput} \begin{Soutput} exp(Est.) 2.5% 97.5% Ns(Age - DMdur, knots = ad.kn)1 4.172 3.535 4.923 Ns(Age - DMdur, knots = ad.kn)2 4.502 3.824 5.301 Ns(Age - DMdur, knots = ad.kn)3 16.077 14.087 18.348 Ns(Age - DMdur, knots = ad.kn)4 7.479 6.501 8.605 I(lex.Cst == "Ins")TRUE 2.170 1.948 2.418 I(Per - 2000) 0.965 0.954 0.977 sexF 0.667 0.616 0.723 \end{Soutput} \end{Schunk} Note that in order for this model to be usable for simulation, it is necessary that we use the components of the \texttt{Lexis} object to specify the survival. Each record in the data frame \texttt{Si} represents follow up from \texttt{DMdur} to \texttt{DMdur+lex.dur}, so the model is a Cox model with diabetes duration as underlying timescale and age at diagnosis, \texttt{Age-DMdur}, as covariate. Also note that we used \texttt{I(lex.Cst=="Ins")} instead of just \texttt{lex.Cst}, because \texttt{coxph} assigns design matrix columns to all levels of \texttt{lex.Cst}, also those not present in data, which would give \texttt{NA}s among the parameter estimates and \texttt{NA}s as mortality outcomes. We see that the effect of insulin and the other covariates are pretty much the same as in the two-time-scale model. We can simulate from this model too; there is no restrictions on what type of model can be used for different transitions \begin{Schunk} \begin{Sinput} > Tr.c <- list( "DM" = list( "Ins" = Tr$DM$Ins, + "Dead" = Cox.Dead ), + "Ins" = list( "Dead(Ins)" = Cox.Dead ) ) > system.time( simC <- simLexis( Tr.c, + ini, + t.range = 12, + N = Nsim ) ) \end{Sinput} \begin{Soutput} user system elapsed 20.557 1.208 20.873 \end{Soutput} \begin{Sinput} > summary( simC, by="sex" ) \end{Sinput} \begin{Soutput} $M Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 1714 2039 1247 0 5000 3286 37280.04 5000 Ins 0 1348 0 691 2039 691 9990.38 2039 Sum 1714 3387 1247 691 7039 3977 47270.42 5000 $F Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 2332 1702 966 0 5000 2668 42168.20 5000 Ins 0 1313 0 389 1702 389 9083.14 1702 Sum 2332 3015 966 389 6702 3057 51251.34 5000 \end{Soutput} \end{Schunk} \section{Reporting the simulation results} We can now tabulate the number of persons in each state at a predefined set of times on a given time scale. Note that in order for this to be sensible, the \texttt{from} argument would normally be equal to the starting time for the simulated individuals. \begin{Schunk} \begin{Sinput} > system.time( + nSt <- nState( subset(simL,sex=="M"), + at=seq(0,11,0.2), from=1995, time.scale="Per" ) ) \end{Sinput} \begin{Soutput} user system elapsed 0.776 0.000 0.776 \end{Soutput} \begin{Sinput} > nSt[1:10,] \end{Sinput} \begin{Soutput} State when DM Ins Dead Dead(Ins) 1995 5000 0 0 0 1995.2 4932 38 29 1 1995.4 4843 93 62 2 1995.6 4773 137 87 3 1995.8 4702 179 116 3 1996 4621 226 148 5 1996.2 4547 269 179 5 1996.4 4469 309 212 10 1996.6 4407 342 237 14 1996.8 4322 386 275 17 \end{Soutput} \end{Schunk} We see that as time goes by, the 5000 men slowly move away from the starting state (\texttt{DM}). Based on this table (\texttt{nSt} is a table) we can now compute the fractions in each state, or, rather more relevant, the cumulative fraction across the states in some specified order, so that a plot of the stacked probabilities can be made, using either the default rather colorful layout, or a more minimalist version (both in figure \ref{fig:pstate0}): \begin{Schunk} \begin{Sinput} > pM <- pState( nSt, perm=c(1,2,4,3) ) > head( pM ) \end{Sinput} \begin{Soutput} State when DM Ins Dead(Ins) Dead 1995 1.0000 1.0000 1.0000 1 1995.2 0.9864 0.9940 0.9942 1 1995.4 0.9686 0.9872 0.9876 1 1995.6 0.9546 0.9820 0.9826 1 1995.8 0.9404 0.9762 0.9768 1 1996 0.9242 0.9694 0.9704 1 \end{Soutput} \begin{Sinput} > par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) > plot( pM ) > plot( pM, border="black", col="transparent", lwd=3 ) > text( rep(as.numeric(rownames(pM)[nrow(pM)-1]),ncol(pM)), + pM[nrow(pM),]-diff(c(0,pM[nrow(pM),]))/5, + colnames( pM ), adj=1 ) > box( col="white", lwd=3 ) > box() \end{Sinput} \end{Schunk} \insfig{pstate0}{1.0}{Default layout of the \textrm{\tt plot.pState} graph (left), and a version with the state probabilities as lines and annotation of states.} A more useful set-up of the graph would include a more through annotation and sensible choice of colors, as seen in figure \ref{fig:pstatex}: \begin{Schunk} \begin{Sinput} > clr <- c("limegreen","orange") > # expand with a lighter version of the two chosen colors > clx <- c( clr, rgb( t( col2rgb( clr[2:1] )*2 + rep(255,3) ) / 3, max=255 ) ) > par( mfrow=c(1,2), las=1, mar=c(3,3,4,2), mgp=c(3,1,0)/1.6 ) > # Men > plot( pM, col=clx, xlab="Date of FU" ) > lines( as.numeric(rownames(pM)), pM[,2], lwd=3 ) > mtext( "60 year old male, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) > mtext( "Survival curve", side=3, line=1.5, adj=0 ) > mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) > mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) > axis( side=4 ) > axis( side=4, at=1:19/20, labels=FALSE ) > axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) > # Women > pF <- pState( nState( subset(simL,sex=="F"), + at=seq(0,11,0.2), + from=1995, + time.scale="Per" ), + perm=c(1,2,4,3) ) > plot( pF, col=clx, xlab="Date of FU" ) > lines( as.numeric(rownames(pF)), pF[,2], lwd=3 ) > mtext( "60 year old female, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) > mtext( "Survival curve", side=3, line=1.5, adj=0 ) > mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) > mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) > axis( side=4 ) > axis( side=4, at=1:19/20, labels=FALSE ) > axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) \end{Sinput} \end{Schunk} \insfig{pstatex}{1.0}{\textrm{\tt plot.pState} graphs where persons ever on insulin are given in orange and persons never on insulin in green, and the overall survival (dead over the line) as a black line.} If we instead wanted to show the results on the age-scale, we would use age as timescale when constructing the probabilities; otherwise the code is pretty much the same as before (Figure \ref{fig:pstatey}): \begin{Schunk} \begin{Sinput} > par( mfrow=c(1,2), las=1, mar=c(3,3,4,2), mgp=c(3,1,0)/1.6 ) > # Men > pM <- pState( nState( subset(simL,sex=="M"), + at=seq(0,11,0.2), + from=60, + time.scale="Age" ), + perm=c(1,2,4,3) ) > plot( pM, col=clx, xlab="Age" ) > lines( as.numeric(rownames(pM)), pM[,2], lwd=3 ) > mtext( "60 year old male, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) > mtext( "Survival curve", side=3, line=1.5, adj=0 ) > mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) > mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) > axis( side=4 ) > axis( side=4, at=1:19/20, labels=FALSE ) > axis( side=4, at=1:19/20, labels=FALSE, tcl=-0.4 ) > axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) > # Women > pF <- pState( nState( subset(simL,sex=="F"), + at=seq(0,11,0.2), + from=60, + time.scale="Age" ), + perm=c(1,2,4,3) ) > plot( pF, col=clx, xlab="Age" ) > lines( as.numeric(rownames(pF)), pF[,2], lwd=3 ) > mtext( "60 year old female, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) > mtext( "Survival curve", side=3, line=1.5, adj=0 ) > mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) > mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) > axis( side=4 ) > axis( side=4, at=1:9/10, labels=FALSE ) > axis( side=4, at=1:19/20, labels=FALSE, tcl=-0.4 ) > axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) \end{Sinput} \end{Schunk} Note the several statements with \texttt{axis(side=4,...}; they are necessary to get the fine tick-marks in the right hand side of the plots that you will need in order to read off the probabilities at 2006 (or 71 years). \insfig{pstatey}{1.0}{\textrm{\tt plot.pState} graphs where persons ever on insulin are given in orange and persons never on insulin in green, and the overall survival (dead over the line) as a black line.} \subsection{Comparing predictions from different models} We have actually fitted different models for the transitions, and we have simulated Lexis objects from all three approaches, so we can plot these predictions on top of each other: \begin{Schunk} \begin{Sinput} > PrM <- pState( nState( subset(simP,sex=="M"), + at=seq(0,11,0.2), + from=60, + time.scale="Age" ), + perm=c(1,2,4,3) ) > PrF <- pState( nState( subset(simP,sex=="F"), + at=seq(0,11,0.2), + from=60, + time.scale="Age" ), + perm=c(1,2,4,3) ) > CoxM <- pState( nState( subset(simC,sex=="M"), + at=seq(0,11,0.2), + from=60, + time.scale="Age" ), + perm=c(1,2,4,3) ) > CoxF <- pState( nState( subset(simC,sex=="F"), + at=seq(0,11,0.2), + from=60, + time.scale="Age" ), + perm=c(1,2,4,3) ) > par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) > plot( pM, border="black", col="transparent", lwd=3 ) > lines( PrM, border="blue" , col="transparent", lwd=3 ) > lines( CoxM, border="red" , col="transparent", lwd=3 ) > text( 60.5, 0.05, "M" ) > box( lwd=5, col="white" ) ; box( lwd=2, col="black" ) > plot( pF, border="black", col="transparent", lwd=3 ) > lines( PrF, border="blue" , col="transparent", lwd=3 ) > lines( CoxF, border="red" , col="transparent", lwd=3 ) > text( 60.5, 0.05, "F" ) > box( lwd=5, col="white" ) ; box( lwd=2, col="black" ) \end{Sinput} \end{Schunk} \insfig{comp-0}{1.0}{Comparison of the simulated state occupancy probabilities using separate Poisson models for the mortality rates with and without insulin (black) and using proportional hazards Poisson models (blue) and Cox-models with diabetes duration as timescale and age at diabetes diagnosis as covariate (red).} From figure \ref{fig:comp-0} it is clear that the two proportional hazards models (blue and red curves) produce pretty much the same estimates of the state occupancy probabilities over time, but also that they relative to the model with separately estimated transition intensities overestimates the probability of being alive without insulin and underestimates the probabilities of being dead without insulin. However both the overall survival, and the fraction of persons on insulin are quite well in agreement with the more elaborate model. Thus the proportional hazards models overestimate the relative mortality of the insulin treated diabetes patients relative to the non-insulin treated. Interestingly, we also see a bump in the estimated probabilities from the Cox-model based model, but this is entirely an artifact that comes from the estimation method for the baseline hazard of the Cox-model that lets the (cumulative) hazard have large jumps at event times where the risk set is small. So also here it shows up that an assumption of continuous underlying hazards leads to more credible estimates. \chapter{Simulation of transitions in multistate models} \section{Theory} Suppose that the rate functions for the transitions out of the current state to, say, 3 different states are $\lambda_1$, $\lambda_2$ and $\lambda_3$, and the corresponding cumulative rates are $\Lambda_1$, $\Lambda_2$ and $\Lambda_3$, and we want to simulate an exit time and an exit state (that is either 1, 2 or 3). This can be done in two slightly different ways: \begin{enumerate} \item First time, then state: \begin{enumerate} \item Compute the survival function, $S(t) = \exp\bigl(-\Lambda_1(t)-\Lambda_2(t)-\Lambda_3(t)\bigr)$ \item Simulate a random U(0,1) variate, $u$, say. \item The simulated exit time is then the solution $t_u$ to the equation $S(t_u) = u \quad \Leftrightarrow \quad \sum_j\Lambda_j(t_u) = -\log(u)$. \item A simulated transition at $t_u$ is then found by simulating a random draw from the multinomial distribution with probabilities $p_i=\lambda_i(t_u) / \sum_j\lambda_j(t_u)$. \end{enumerate} \item Separate cumulative incidences: \begin{enumerate} \item Simulate 3 independent U(0,1) random variates $u_1$, $u_2$ and $u_3$. \item Solve the equations $\Lambda_i(t_i)=-\log(u_i), i=1,2,3$ and get $(t_1,t_2,t_3)$. \item The simulated survival time is then $\min(t_1,t_2,t_3)$, and the simulated transition is to the state corresponding to this, that is $k \in \{1,2,3\}$, where $t_k=\min(t_1,t_2,t_3)$ \end{enumerate} \end{enumerate} The intuitive argument is that with three possible transition there are 3 independent processes running, but only the first transition is observed. The latter approach is used in the implementation in \texttt{simLexis}. The formal argument for the equality of the two approaches goes as follows: \begin{enumerate} \item Equality of the transition times: \begin{enumerate} \item In the first approach we simulate from a distribution with cumulative rate $\Lambda_1(t)+\Lambda_2(t)+\Lambda_3(t)$, hence from a distribution with survival function: \begin{align*} S(t) & = \exp\bigl(-(\Lambda_1(t)+\Lambda_2(t)+\Lambda_3(t))\bigr) \\ & = \exp\bigl(-\Lambda_1(t)\bigr)\times \exp\bigl(-\Lambda_2(t)\bigr)\times \exp\bigl(-\Lambda_3(t)\bigr) \end{align*} \item In the second approach we choose the smallest of three independent survival times, with survival functions $\exp(-\Lambda_i), i=1,2,3$. Now, the survival function for the minimum of three independent survival times is: \begin{align*} S_\text{min}(t) & = \pmat{\min(t_1,t_2,t_3)>t} \\ & = \pmat{t_1>t} \times \pmat{t_2>t} \times \pmat{t_3>t} \\ & = \exp\bigl(-\Lambda_1(t)\bigr)\times \exp\bigl(-\Lambda_2(t)\bigr)\times \exp\bigl(-\Lambda_3(t)\bigr) \end{align*} which is the same survival function as derived above. \end{enumerate} \item Type of transition: \begin{enumerate} \item In the first instance the probability of a transition to state $i$, conditional on the transition time being $t$, is as known from standard probability theory: $\lambda_i(t)/\bigl(\lambda_1(t)+\lambda_2(t)+\lambda_3(t)\bigr)$. \item In the second approach we choose the transition corresponding to the the smallest of the transition times. So when we condition on the event that a transition takes place at time $t$, we have to show that the conditional probability that the smallest of the three simulated transition times was actually the $i$th, is as above. But conditional on \emph{survival} till $t$, the probabilities that events of type $1,2,3$ takes place in the interval $(t,t+\dif t)$ are $\lambda_1(t)\dif t$, $\lambda_2(t)\dif t$ and $\lambda_1(t)\dif t$, respectively (assuming that the probability of more than one event in the interval of length $\dif t$ is 0). Hence the conditional probabilities \emph{given a transition time} in $(t,t+\dif t)$ is: \[ \frac{\lambda_i(t)\dif t}{\lambda_1(t)\dif t+\lambda_2(t)\dif t+\lambda_3(t)\dif t}= \frac{\lambda_i(t)}{\lambda_1(t)+\lambda_2(t)+\lambda_3(t)} \] --- exactly as above. \end{enumerate} \end{enumerate} \section{Components of \texttt{simLexis}} This section explains the actually existing code for \texttt{simLexis}, as it is in the current version of \texttt{Epi}. % The following code sources the originally formatted code in % simLexis.R in order to make it printable with all the formatting and % comments in it. However the sourcing does not work when compiling % the vignettes in R CMD build. So when checking the code we comment % this out by putting eval=FALSE, and moreover, because it is only % simLexis that is exported, we also need to bring the functions simX, % sim1, lint, get.next and chop.lex into the workspace. So depending % on whether we actually construct the pdf for the inst/doc folder or % test (upload) the package, one of the following to chunks are run % with eval=FALSE and the other with eval=TRUE % When compiling the published vignette \begin{Schunk} \begin{Sinput} > source( "../R/simLexis.R", keep.source=TRUE ) \end{Sinput} \end{Schunk} % When checking the package The function \texttt{simLexis} takes a \texttt{Lexis} object as input. This defines the initial state(s) and times of the start for a number of persons. Since the purpose is to simulate a history through the estimated multistate model, the input values of the outcome variables \texttt{lex.Xst} and \texttt{lex.dur} are ignored --- the aim is to simulate values for them. Note however that the attribute \texttt{time.since} must be present in the object. This is used for initializing timescales defined as time since entry into a particular state, it is a character vector of the same length as the \texttt{time.scales} attribute, with value equal to a state name if the corresponding time scale is defined as time since entry into that state. In this example the 4th timescale is time since entry into the \texttt{Ins} state, and hence: \begin{Schunk} \begin{Sinput} > cbind( + attr( ini, "time.scales" ), + attr( ini, "time.since" ) ) \end{Sinput} \begin{Soutput} [,1] [,2] [1,] "Per" "" [2,] "Age" "" [3,] "DMdur" "" [4,] "t.Ins" "Ins" \end{Soutput} \end{Schunk} \texttt{Lexis} objects will have this attribute set for time scales created using \texttt{cutLexis}. The other necessary argument is a transition object \texttt{Tr}, which is a list of lists. The elements of the lists should be \texttt{glm} objects derived by fitting Poisson models to a \texttt{Lexis} object representing follow-up data in a multistate model. It is assumed (but not checked) that timescales enter in the model via the timescales of the \texttt{Lexis} object. Formally, there are no assumptions about how \texttt{lex.dur} enters in the model. Optional arguments are \texttt{t.range}, \texttt{n.int} or \texttt{time.pts}, specifying the times after entry at which the cumulative rates will be computed (the maximum of which will be taken as the censoring time), and \texttt{N} a scalar or numerical vector of the number of persons with a given initial state each record of the \texttt{init} object should represent. The central part of the functions uses a \texttt{do.call} / \texttt{lapply} / \texttt{split} construction to do simulations for different initial states. This is the construction in the middle that calls \texttt{simX}. \texttt{simLexis} also calls \texttt{get.next} which is further detailed below. \begin{Schunk} \begin{Sinput} > simLexis \end{Sinput} \begin{Soutput} function (Tr, init, N = 1, lex.id, t.range = 20, n.int = 101, time.pts = seq(0, t.range, length.out = n.int)) { if (time.pts[1] != 0) stop("First time point must be 0, time.pts[1:3]= ", time.pts[1:3]) if (!missing(N)) { if (length(N) == 1) init <- init[rep(1:nrow(init), each = N), ] else init <- init[rep(1:nrow(init), N), ] } if (!missing(lex.id)) { if (length(lex.id) == nrow(init)) init$lex.id <- lex.id else init$lex.id <- 1:nrow(init) } else init$lex.id <- 1:nrow(init) if (is.null(tS <- attr(init, "time.scales"))) stop("No time.scales attribute for init") if (is.null(tF <- attr(init, "time.since"))) { attr(init, "time.since") <- tF <- rep("", tS) warning("'time.since' attribute set to blanks") } np <- length(time.pts) tr.st <- names(Tr) sf <- NULL nxt <- init[init$lex.Cst %in% tr.st, ] if (nrow(nxt) < nrow(init)) { tt <- table(init$lex.Cst) tt <- tt[tt > 0] nt <- length(tt) warning("\nSome initiators start in a absorbing state\n", "Initiator states represented are: ", paste(rbind(names(tt), rep(":", nt), paste(tt), rep(" ", nt)), collapse = ""), "\n", "Transient states are: ", paste(names(Tr), coll = " ")) if (nrow(nxt) == 0) stop("\nNo initiators in transient states!") } while (nrow(nxt) > 0) { nx <- do.call(rbind.data.frame, lapply(split(nxt, nxt$lex.Cst), simX, Tr, time.pts, tS)) sf <- rbind.data.frame(sf, nx) nxt <- get.next(nx, tr.st, tS, tF) } sf$lex.Xst <- factor(sf$lex.Xst, levels = levels(sf$lex.Cst)) sf$lex.Xst[is.na(sf$lex.Xst)] <- sf$lex.Cst[is.na(sf$lex.Xst)] nord <- match(c("lex.id", tS, "lex.dur", "lex.Cst", "lex.Xst"), names(sf)) noth <- setdiff(1:ncol(sf), nord) sf <- sf[order(sf$lex.id, sf[, tS[1]]), c(nord, noth)] rownames(sf) <- NULL attr(sf, "time.scales") <- tS attr(sf, "time.since") <- tF chop.lex(sf, tS, max(time.pts)) } \end{Soutput} \end{Schunk} \subsection{\texttt{simX}} \texttt{simX} is called by \texttt{simLexis} and simulates transition-times and -types for a set of patients assumed to be in the same state. It is called from \texttt{simLexis} with a data frame as argument, uses the state in \texttt{lex.Cst} to select the relevant component of \texttt{Tr} and compute predicted cumulative intensities for all states reachable from this state. Note that it is here the switch between \texttt{glm}, \texttt{coxph} and objects of class \texttt{function} is made. The dataset on which this prediction is done has \texttt{length(time.pts)} rows per person. \begin{Schunk} \begin{Sinput} > simX \end{Sinput} \begin{Soutput} function (nd, Tr, time.pts, tS) { np <- length(time.pts) nr <- nrow(nd) if (nr == 0) return(NULL) cst <- as.character(unique(nd$lex.Cst)) if (length(cst) > 1) stop("More than one lex.Cst present:\n", cst, "\n") prfrm <- nd[rep(1:nr, each = np), ] prfrm[, tS] <- prfrm[, tS] + rep(time.pts, nr) prfrm$lex.dur <- il <- min(diff(time.pts)) prfrp <- prfrm prfrp[, "lex.dur"] <- 1 prfrp[, tS] <- prfrp[, tS] + il/2 rt <- data.frame(lex.id = prfrm$lex.id) for (i in 1:length(Tr[[cst]])) { if (inherits(Tr[[cst]][[i]], "glm")) rt <- cbind(rt, predict(Tr[[cst]][[i]], type = "response", newdata = prfrp) * il) else if (inherits(Tr[[cst]][[i]], "coxph")) rt <- cbind(rt, predict(Tr[[cst]][[i]], type = "expected", newdata = prfrm)) else if (is.function(Tr[[cst]][[i]])) rt <- cbind(rt, Tr[[cst]][[i]](prfrm)) else stop("Invalid object supplied as transition, elements of the list must be either:\n", "- a glm(poisson) object fitted to a Lexis object\n", "- a coxph object fitted to a Lexis object\n", "- a function that takes a Lexis object as argument and returns\n", " average rates for each record in the same units as lex.dur.") } names(rt)[-1] <- names(Tr[[cst]]) xx <- match(c("lex.dur", "lex.Xst"), names(nd)) if (any(!is.na(xx))) nd <- nd[, -xx[!is.na(xx)]] merge(nd, do.call(rbind, lapply(split(rt, rt$lex.id), sim1, time.pts)), by = "lex.id") } \end{Soutput} \end{Schunk} As we see, \texttt{simX} calls \texttt{sim1} which simulates the transition for one person. \subsection{\texttt{sim1}} The predicted cumulative intensities are fed, person by person, to \texttt{sim1} --- again via a \texttt{do.call} / \texttt{lapply} / \texttt{split} construction --- and the resulting time and state is appended to the \texttt{nd} data frame. This way we have simulated \emph{one} transition (time and state) for each person: \begin{Schunk} \begin{Sinput} > sim1 \end{Sinput} \begin{Soutput} function (rt, time.pts) { ci <- apply(rbind(0, rt[, -1, drop = FALSE]), 2, cumsum)[1:nrow(rt), , drop = FALSE] tt <- uu <- -log(runif(ncol(ci))) for (i in 1:ncol(ci)) tt[i] <- lint(ci[, i], time.pts, uu[i]) data.frame(lex.id = rt[1, 1], lex.dur = min(tt, na.rm = TRUE), lex.Xst = factor(if (min(tt) < max(time.pts)) colnames(ci)[tt == min(tt)] else NA)) } \end{Soutput} \end{Schunk} The \texttt{sim1} function uses \texttt{lint} to do linear interpolation. \subsection{\texttt{lint}} We do not use \texttt{approx} to do the linear interpolation, because this function does not do the right thing if the cumulative incidences (\texttt{ci}) are constant across a number of times. Therefore we have a custom made linear interpolator that does the interpolation exploiting the fact the the \texttt{ci} is non-decreasing and \texttt{tt} is strictly monotonously increasing: \begin{Schunk} \begin{Sinput} > lint \end{Sinput} \begin{Soutput} function (ci, tt, u) { if (any(diff(ci) < 0) | any(diff(tt) < 0)) stop("Non-increasing arguments") c.u <- min(c(ci[ci > u], max(ci))) c.l <- max(c(ci[ci < u], min(ci))) t.u <- min(c(tt[ci > u], max(tt))) t.l <- max(c(tt[ci < u], min(tt))) ifelse(c.u == c.l, t.l, t.l + (u - c.l)/(c.u - c.l) * (t.u - t.l)) } \end{Soutput} \end{Schunk} \subsection{\texttt{get.next}} We must repeat the simulation operation on those that have a simulated entry to a transient state, and also make sure that any time scales defined as time since entry to one of these states be initialized to 0 before a call to \texttt{simX} is made for these persons. This accomplished by the function \texttt{get.next}: \begin{Schunk} \begin{Sinput} > get.next \end{Sinput} \begin{Soutput} function (sf, tr.st, tS, tF) { if (nrow(sf) == 0) return(sf) nxt <- sf[sf$lex.Xst %in% tr.st, ] if (nrow(nxt) == 0) return(nxt) nxt[, tS] <- nxt[, tS] + nxt$lex.dur wh <- tF for (i in 1:length(wh)) if (wh[i] != "") nxt[nxt$lex.Xst == wh[i], tS[i]] <- 0 nxt$lex.Cst <- nxt$lex.Xst return(nxt) } \end{Soutput} \end{Schunk} \subsection{\texttt{chop.lex}} The operation so far has censored individuals \texttt{max(time.pts)} after \emph{each} new entry to a transient state. In order to groom the output data we use \texttt{chop.lex} to censor all persons at the same designated time after \emph{initial} entry. \begin{Schunk} \begin{Sinput} > chop.lex \end{Sinput} \begin{Soutput} function (obj, tS, cens) { zz <- entry(obj, 1, by.id = TRUE) ww <- merge(obj, data.frame(lex.id = as.numeric(names(zz)), cens = zz + cens)) ww <- ww[ww[, tS[1]] < ww$cens, ] x.dur <- pmin(ww$lex.dur, ww[, "cens"] - ww[, tS[1]]) ww$lex.Xst[x.dur < ww$lex.dur] <- ww$lex.Cst[x.dur < ww$lex.dur] ww$lex.dur <- pmin(x.dur, ww$lex.dur) ww } \end{Soutput} \end{Schunk} \section{Probabilities from simulated \texttt{Lexis} objects} Once we have simulated a Lexis object we will of course want to use it for estimating probabilities, so basically we will want to enumerate the number of persons in each state at a pre-specified set of time points. \subsection{\texttt{nState}} Since we are dealing with multistate model with potentially multiple time scales, it is necessary to define the timescale (\texttt{time.scale}), the starting point on this timescale (\texttt{from}) and the points after this where we compute the number of occupants in each state, (\texttt{at}). \begin{Schunk} \begin{Sinput} > nState \end{Sinput} \begin{Soutput} function (obj, at, from, time.scale = 1) { tS <- check.time.scale(obj, time.scale) TT <- tmat(obj) absorb <- rownames(TT)[apply(!is.na(TT), 1, sum) == 0] transient <- setdiff(rownames(TT), absorb) tab.frm <- obj[rep(1:nrow(obj), each = length(at)), c(tS, "lex.dur", "lex.Cst", "lex.Xst")] tab.frm$when <- rep(at, nrow(obj)) + from tab.tr <- tab.frm[tab.frm[, tS] <= tab.frm$when & tab.frm[, tS] + tab.frm$lex.dur > tab.frm$when, ] tab.tr$State <- tab.tr$lex.Cst tab.ab <- tab.frm[tab.frm[, tS] + tab.frm$lex.dur <= tab.frm$when & tab.frm$lex.Xst %in% absorb, ] tab.ab$State <- tab.ab$lex.Xst with(rbind(tab.ab, tab.tr), table(when, State)) } \end{Soutput} \end{Schunk} \subsection{\texttt{pState}, \texttt{plot.pState} and \texttt{lines.pState}} In order to plot probabilities of state-occupancy it is useful to compute cumulative probabilities across states in any given order; this is done by the function \texttt{pState}, which returns a matrix of class \texttt{pState}: \begin{Schunk} \begin{Sinput} > pState \end{Sinput} \begin{Soutput} function (nSt, perm = 1:ncol(nSt)) { tt <- t(apply(nSt[, perm], 1, cumsum)) tt <- sweep(tt, 1, tt[, ncol(tt)], "/") class(tt) <- c("pState", "matrix") tt } \end{Soutput} \end{Schunk} There is also a \texttt{plot} and \texttt{lines} method for the resulting \texttt{pState} objects: \begin{Schunk} \begin{Sinput} > plot.pState \end{Sinput} \begin{Soutput} function (x, col = rainbow(ncol(x)), border = "transparent", xlab = "Time", ylim = 0:1, ylab = "Probability", ...) { matplot(as.numeric(rownames(x)), x, type = "n", ylim = ylim, yaxs = "i", xaxs = "i", xlab = xlab, ylab = ylab, ...) lines.pState(x, col = col, border = border, ...) } \end{Soutput} \begin{Sinput} > lines.pState \end{Sinput} \begin{Soutput} function (x, col = rainbow(ncol(x)), border = "transparent", ...) { nc <- ncol(x) col <- rep(col, nc)[1:nc] border <- rep(border, nc)[1:nc] pSt <- cbind(0, x) for (i in 2:ncol(pSt)) { polygon(c(as.numeric(rownames(pSt)), rev(as.numeric(rownames(pSt)))), c(pSt[, i], rev(pSt[, i - 1])), col = col[i - 1], border = border[i - 1], ...) } } \end{Soutput} \end{Schunk} \bibliographystyle{plain} \begin{thebibliography}{1} \bibitem{Carstensen.2011a} B~Carstensen and M~Plummer. \newblock Using {L}exis objects for multi-state models in {R}. \newblock {\em Journal of Statistical Software}, 38(6):1--18, 1 2011. \bibitem{Iacobelli.2013} S~Iacobelli and B~Carstensen. \newblock {Multiple time scales in multi-state models}. \newblock {\em Stat Med}, 32(30):5315--5327, Dec 2013. \bibitem{Plummer.2011} M~Plummer and B~Carstensen. \newblock Lexis: An {R} class for epidemiological studies with long-term follow-up. \newblock {\em Journal of Statistical Software}, 38(5):1--12, 1 2011. \end{thebibliography} \addcontentsline{toc}{chapter}{References} \end{document} Epi/vignettes/yl.tex0000644000176200001440000010621114003554036014146 0ustar liggesusers%\VignetteIndexEntry{Years of life lost (YLL)} \documentclass[a4paper,twoside,12pt]{report} \newcommand{\Title}{Years of Life Lost (YLL) to disease\\Diabetes in DK as example} \newcommand{\Tit}{YLL} \newcommand{\Version}{February 1.2} \newcommand{\Dates}{November 2017} \newcommand{\Where}{SDC} \newcommand{\Homepage}{\url{http://bendixcarstensen.com/Epi}} \newcommand{\Faculty}{\begin{tabular}{rl} Bendix Carstensen & Steno Diabetes Center, Gentofte, Denmark\\ & {\small \& Department of Biostatistics, University of Copenhagen} \\ & \texttt{b@bxc.dk}\\ & \url{http://BendixCarstensen.com} \\[1em] \end{tabular}} \input{topreport} \renewcommand{\rwpre}{./yll} \chapter{Theory and technicalities} This vignette for the \texttt{Epi} package describes the probabilistic and demographic background for and technical implementation of the \texttt{erl} and \texttt{yll} functions that computes the expected residual life time and years of life lost in an illness-death model. \section{Years of life lost (YLL)} \ldots to diabetes or any other disease for that matter. The general concept in calculation of ``years lost to\ldots'' is the comparison of the expected lifetime between two groups of persons; one with and one without disease (in this example DM). The expected lifetime is the area under the survival curve, so basically the exercise requires that two survival curves that are deemed relevant be available. The years of life lost is therefore just the area between the survival curves for those ``Well'', $S_W(t)$, and for those ``Diseased'', $S_D(t)$: \[ \YLL = \int_0^\infty S_W(t) - S_D(t) \dif t \] The time $t$ could of course be age, but it could also be ``time after age 50'' and the survival curves compared would then be survival curves \emph{conditional} on survival till age 50, and the YLL would be the years of life lost for a 50-year old person with diabetes. If we are referring to the expected lifetime we will more precisely use the label expected residual lifetime, ERL. \section{Constructing the survival curves} YLL can be computed in two different ways, depending on the way the survival curve and hence the expected lifetime of a person \emph{without} diabetes is computed: \begin{itemize} \item Assume that the ``Well'' persons are \emph{immune} to disease --- using only the non-DM mortality rates throughout for calculation of expected life time. \item Assume that the ``Well'' persons \emph{can} acquire the disease and thereby see an increased mortality, thus involving all three rates shown in figure \ref{fig:states}. \end{itemize} The former gives a higher YLL because the comparison is to persons assumed immune to DM (and yet with the same mortality as non-immune prior to diagnosis), the latter gives a more realistic picture of the comparison of group of persons with and without diabetes at a given age that can be interpreted in the real world. The differences can be illustrated by figure \ref{fig:states}; the immune approach corresponds to an assumption of $\lambda(t)=0$ in the calculation of the survival curve for a person in the ``Well'' state. Calculation of the survival of a diseased person already in the ``DM'' state is unaffected by assumptions about $\lambda$. \insfig{states}{0.7}{Illness-death model describing diabetes incidence and -mortality.} \subsection{Total mortality --- a shortcut?} A practical crude shortcut could be to compare the ERL in the diabetic population to the ERL for the \emph{entire} population (that is use the total mortality ignoring diabetes status). Note however that this approach also counts the mortality of persons that acquired the disease earlier, thus making the comparison population on average more ill than the population we aim at, namely those well at a given time, which only then become more gradually ill. How large these effects are can however be empirically explored, as we shall do later. \subsection{Disease duration} In the exposition above there is no explicit provision for the effect of disease duration, but if we were able to devise mortality rates for any combination of age and duration, this could be taken into account. There are however severe limitations in this as we in principle would want to have duration effects as long as the age-effects --- in principle for all $(a,d)$ where $d\leq A$, where $A$ is the age at which we condition. So even if we were only to compute ERL from age, say, 40 we would still need duration effects up to 60 years (namely to age 100). The incorporation of duration effects is in principle trivial from a computational point of view, but we would be forced to entertain models predicting duration effects way beyond what is actually observed disease duration in any practical case. \subsection{Computing integrals} The practical calculations of survival curves, ERL and YLL involves calculation of (cumulative) integrals of rates and functions of these as we shall see below. This is easy if we have a closed form expression of the function, so its value may be computed at any time point --- this will be the case if we model rates by smooth parametric functions. Computing the (cumulative) integral of a function is done as follows: \begin{itemize} \item Compute the value of the function (mortality rate for example) at the midpoints of a sequence of narrow equidistant intervals --- for example one- or three month intervals of age, say. \item Take the cumulative sum of these values multiplied by the interval length --- this will be a very close approximation to the cumulative integral evaluated at the end of each interval. \item If the intervals are really small (like 1/100 year), the distinction between the value at the middle and at the end of each interval becomes irrelevant. \end{itemize} Note that in the above it is assumed that the rates are given in units corresponding to the interval length --- or more precisely, as the cumulative rates over the interval. \section{Survival functions in the illness-death model} The survival functions for persons in the ``Well'' state can be computed under two fundamentally different scenarios, depending on whether persons in the ``Well'' state are assumed to be immune to the disease ($\lambda(a)=0$) or not. \subsection{Immune approach} In this case both survival functions for person in the two states are the usual simple transformation of the cumulative mortality rates: \[ S_W(a) = \exp\left(-\int_0^a\!\!\mu_W(u) \dif u \right), \qquad S_D(a) = \exp\left(-\int_0^a\!\!\mu_D(u) \dif u \right) \] \subsubsection{Conditional survival functions} If we want the \emph{conditional} survival functions given survival to age $A$, say, they are just: \[ S_W(a|A) = S_W(a)/S_W(A), \qquad S_D(a|A) = S_D(a)/S_D(A) \] \subsection{Non-immune approach} For a diseased person, the survival function in this states is the same as above, but the survival function for a person without disease (at age 0) is (see figure \ref{fig:states}): \[ S(a) = \ptxt{Well}\!(a) + \ptxt{DM}\!(a) \] In the appendix of the paper \cite{Carstensen.2008c} is an indication of how to compute the probability of being in any of the four states shown in figure \ref{fig:states}, which I shall repeat here: In terms of the rates, the probability of being in the ``Well'' box is simply the probability of escaping both death (at a rate of $\mu_W(a)$) and diabetes (at a rate of $\lambda(a)$): \[ \ptxt{Well}(a) = \exp\left(\!-\int_0^a\!\!\mu_W(u)+\lambda(u) \right) \dif u \] The probability of being alive with diabetes at age $a$, is computed given that diabetes occurred at age $s$ ($s data( DMepi ) \end{Sinput} \end{Schunk} The dataset \texttt{DMepi} contains diabetes events, deaths and person-years for persons without diabetes and deaths and person-years for persons with diabetes: \begin{Schunk} \begin{Sinput} > str( DMepi ) \end{Sinput} \begin{Soutput} 'data.frame': 4200 obs. of 8 variables: $ sex : Factor w/ 2 levels "M","F": 1 1 1 1 1 1 1 1 1 1 ... $ A : num 0 0 0 0 0 0 0 0 0 0 ... $ P : num 1996 1997 1998 1999 2000 ... $ D.DM: num 0 0 0 0 0 0 0 0 0 0 ... $ Y.DM: num 0.484 0.64 1.641 0.552 2.507 ... $ X : num 1 2 4 4 4 1 1 3 4 1 ... $ D.nD: num 28 19 20 11 21 16 21 15 16 16 ... $ Y.nD: num 35469 35085 34240 34056 34002 ... \end{Soutput} \begin{Sinput} > head( DMepi ) \end{Sinput} \begin{Soutput} sex A P D.DM Y.DM X D.nD Y.nD 2 M 0 1996 0 0.4839151 1 28 35468.92 3 M 0 1997 0 0.6399726 2 19 35085.18 4 M 0 1998 0 1.6406571 4 20 34240.14 5 M 0 1999 0 0.5523614 4 11 34055.52 6 M 0 2000 0 2.5065024 4 21 34002.22 7 M 0 2001 0 0.1184120 1 16 34177.39 \end{Soutput} \end{Schunk} For each combination of sex, age, period and date of birth in 1 year age groups, we have the person-years in the ``Well'' (\texttt{Y.nD}) and the ``DM'' (\texttt{Y.DM}) states, as well as the number of deaths from these (\texttt{D.nD}, \texttt{D.DM}) and the number of incident diabetes cases from the ``Well'' state (\texttt{X}). In order to compute the years of life lost to diabetes and how this has changed over time, we fit models for the mortality and incidence of both groups (and of course, separately for men and women). The models we use will be age-period-cohort models \cite{Carstensen.2007a} providing estimated mortality rates for ages 0--99 and dates 1.1.1996--1.1.2016. First we transform the age and period variables to reflect the mean age and period in each of the Lexis triangles. We also compute the total number of deaths and amount of risk time, as we are going to model the total mortality as well. Finally we restrict the dataset to ages over 30 only: \begin{Schunk} \begin{Sinput} > DMepi <- transform( subset( DMepi, A>30 ), + D.T = D.nD + D.DM, + Y.T = Y.nD + Y.DM ) > head(DMepi) \end{Sinput} \begin{Soutput} sex A P D.DM Y.DM X D.nD Y.nD D.T Y.T 684 M 31 1996 0 305.9671 29 51 44161.83 51 44467.80 685 M 31 1997 2 326.2074 31 54 45508.64 56 45834.85 686 M 31 1998 2 340.1759 34 46 44954.45 48 45294.63 687 M 31 1999 5 330.9918 24 39 41148.97 44 41479.96 688 M 31 2000 1 332.0876 41 26 39027.30 27 39359.39 689 M 31 2001 2 310.8467 35 33 37975.78 35 38286.63 \end{Soutput} \end{Schunk} With the correct age and period coding in the Lexis triangles, we fit models for the mortalities and incidences. Note that we for comparative purposes also fit a model for the \emph{total} mortality, ignoring the \begin{Schunk} \begin{Sinput} > # Knots used in all models > ( a.kn <- seq(40,95,,6) ) \end{Sinput} \begin{Soutput} [1] 40 51 62 73 84 95 \end{Soutput} \begin{Sinput} > ( p.kn <- seq(1997,2015,,4) ) \end{Sinput} \begin{Soutput} [1] 1997 2003 2009 2015 \end{Soutput} \begin{Sinput} > ( c.kn <- seq(1910,1976,,6) ) \end{Sinput} \begin{Soutput} [1] 1910.0 1923.2 1936.4 1949.6 1962.8 1976.0 \end{Soutput} \begin{Sinput} > # Check the number of events between knots > ae <- xtabs( cbind(D.nD,D.DM,X) ~ cut(A,c(30,a.kn,Inf)) + sex, data=DMepi ) > ftable( addmargins(ae,1), col.vars=3:2 ) \end{Sinput} \begin{Soutput} D.nD D.DM X sex M F M F M F cut(A, c(30, a.kn, Inf)) (30,40] 9135 4650 597 277 12080 9648 (40,51] 25535 15784 2947 1439 35445 23925 (51,62] 59698 40171 10838 5253 60539 40034 (62,73] 106519 81253 26197 14299 55908 44221 (73,84] 158365 156678 34510 28834 27985 30381 (84,95] 100880 179466 16194 25317 5272 8967 (95,Inf] 6095 21414 640 1928 90 288 Sum 466227 499416 91923 77347 197319 157464 \end{Soutput} \begin{Sinput} > pe <- xtabs( cbind(D.nD,D.DM,X) ~ cut(P,c(1990,p.kn,Inf)) + sex, data=DMepi ) > ftable( addmargins(pe,1), col.vars=3:2 ) \end{Sinput} \begin{Soutput} D.nD D.DM X sex M F M F M F cut(P, c(1990, p.kn, Inf)) (1990,1997] 51569 53567 6407 5990 13175 10960 (1997,2003] 144136 155695 22390 19922 49805 41277 (2003,2009] 131159 141782 26079 22249 60554 48066 (2009,2015] 119812 127714 31285 24704 63440 49457 (2015,Inf] 19551 20658 5762 4482 10345 7704 Sum 466227 499416 91923 77347 197319 157464 \end{Soutput} \begin{Sinput} > ce <- xtabs( cbind(D.nD,D.DM,X) ~ cut(P-A,c(-Inf,c.kn,Inf)) + sex, data=DMepi ) > ftable( addmargins(ce,1), col.vars=3:2 ) \end{Sinput} \begin{Soutput} D.nD D.DM X sex M F M F M F cut(P - A, c(-Inf, c.kn, Inf)) (-Inf,1.91e+03] 19679 49020 2004 4446 599 1416 (1.91e+03,1.92e+03] 129799 189192 19780 26870 10665 15275 (1.92e+03,1.94e+03] 158953 152454 35667 28471 37850 36659 (1.94e+03,1.95e+03] 99058 72432 25494 13074 71489 50631 (1.95e+03,1.96e+03] 44129 28315 7534 3731 51750 34255 (1.96e+03,1.98e+03] 13598 7484 1373 720 22942 17689 (1.98e+03, Inf] 1011 519 71 35 2024 1539 Sum 466227 499416 91923 77347 197319 157464 \end{Soutput} \begin{Sinput} > # Fit an APC-model for all transitions, seperately for men and women > mW.m <- glm( D.nD ~ -1 + Ns(A ,knots=a.kn,int=TRUE) + + Ns( P,knots=p.kn,ref=2005) + + Ns(P-A,knots=c.kn,ref=1950), + offset = log(Y.nD), + family = poisson, + data = subset( DMepi, sex=="M" ) ) > mD.m <- update( mW.m, D.DM ~ . , offset=log(Y.DM) ) > mT.m <- update( mW.m, D.T ~ . , offset=log(Y.T ) ) > lW.m <- update( mW.m, X ~ . ) > # Model for women > mW.f <- update( mW.m, data = subset( DMepi, sex=="F" ) ) > mD.f <- update( mD.m, data = subset( DMepi, sex=="F" ) ) > mT.f <- update( mT.m, data = subset( DMepi, sex=="F" ) ) > lW.f <- update( lW.m, data = subset( DMepi, sex=="F" ) ) \end{Sinput} \end{Schunk} \section{Residual life time and years lost to DM} We now collect the estimated years of life lost classified by method (immune assumption or not), sex, age and calendar time: \begin{Schunk} \begin{Sinput} > a.ref <- 30:90 > p.ref <- 1996:2016 > aYLL <- NArray( list( type = c("Imm","Tot","Sus"), + sex = levels( DMepi$sex ), + age = a.ref, + date = p.ref ) ) > str( aYLL ) \end{Sinput} \begin{Soutput} logi [1:3, 1:2, 1:61, 1:21] NA NA NA NA NA NA ... - attr(*, "dimnames")=List of 4 ..$ type: chr [1:3] "Imm" "Tot" "Sus" ..$ sex : chr [1:2] "M" "F" ..$ age : chr [1:61] "30" "31" "32" "33" ... ..$ date: chr [1:21] "1996" "1997" "1998" "1999" ... \end{Soutput} \begin{Sinput} > system.time( + for( ip in p.ref ) + { + nd <- data.frame( A = seq(30,90,0.2)+0.1, + P = ip, + Y.nD = 1, + Y.DM = 1, + Y.T = 1 ) + muW.m <- ci.pred( mW.m, nd )[,1] + muD.m <- ci.pred( mD.m, nd )[,1] + muT.m <- ci.pred( mT.m, nd )[,1] + lam.m <- ci.pred( lW.m, nd )[,1] + muW.f <- ci.pred( mW.f, nd )[,1] + muD.f <- ci.pred( mD.f, nd )[,1] + muT.f <- ci.pred( mT.f, nd )[,1] + lam.f <- ci.pred( lW.f, nd )[,1] + aYLL["Imm","M",,paste(ip)] <- yll( int=0.2, muW.m, muD.m, lam=NULL, + A=a.ref, age.in=30, note=FALSE )[-1] + aYLL["Imm","F",,paste(ip)] <- yll( int=0.2, muW.f, muD.f, lam=NULL, + A=a.ref, age.in=30, note=FALSE )[-1] + aYLL["Tot","M",,paste(ip)] <- yll( int=0.2, muT.m, muD.m, lam=NULL, + A=a.ref, age.in=30, note=FALSE )[-1] + aYLL["Tot","F",,paste(ip)] <- yll( int=0.2, muT.f, muD.f, lam=NULL, + A=a.ref, age.in=30, note=FALSE )[-1] + aYLL["Sus","M",,paste(ip)] <- yll( int=0.2, muW.m, muD.m, lam=lam.m, + A=a.ref, age.in=30, note=FALSE )[-1] + aYLL["Sus","F",,paste(ip)] <- yll( int=0.2, muW.f, muD.f, lam=lam.f, + A=a.ref, age.in=30, note=FALSE )[-1] + } ) \end{Sinput} \begin{Soutput} user system elapsed 16.741 8.250 14.896 \end{Soutput} \begin{Sinput} > round( ftable( aYLL[,,seq(1,61,10),], col.vars=c(3,2) ), 1 ) \end{Sinput} \begin{Soutput} age 30 40 50 60 70 80 90 sex M F M F M F M F M F M F M F type date Imm 1996 11.3 10.2 9.4 9.1 7.4 7.6 5.4 5.9 3.4 3.8 1.5 1.6 0.0 0.0 1997 11.1 9.9 9.2 8.9 7.3 7.4 5.3 5.7 3.3 3.7 1.4 1.5 0.0 0.0 1998 10.9 9.7 9.1 8.6 7.2 7.2 5.3 5.5 3.3 3.6 1.4 1.5 0.0 0.0 1999 10.7 9.4 9.0 8.4 7.1 7.0 5.2 5.3 3.3 3.5 1.4 1.5 0.0 0.0 2000 10.5 9.1 8.8 8.2 6.9 6.8 5.1 5.1 3.2 3.4 1.4 1.4 0.0 0.0 2001 10.3 8.9 8.6 7.9 6.8 6.6 5.0 5.0 3.1 3.2 1.3 1.4 0.0 0.0 2002 10.0 8.6 8.4 7.7 6.6 6.3 4.9 4.8 3.1 3.1 1.3 1.3 0.0 0.0 2003 9.7 8.3 8.2 7.4 6.4 6.1 4.7 4.6 3.0 3.0 1.3 1.3 0.0 0.0 2004 9.4 8.0 7.9 7.1 6.2 5.9 4.5 4.4 2.8 2.8 1.2 1.2 0.0 0.0 2005 9.0 7.6 7.6 6.9 6.0 5.6 4.4 4.1 2.7 2.6 1.1 1.1 0.0 0.0 2006 8.6 7.3 7.4 6.6 5.8 5.4 4.2 3.9 2.6 2.5 1.1 1.1 0.0 0.0 2007 8.3 7.0 7.1 6.3 5.5 5.2 4.0 3.8 2.5 2.4 1.0 1.0 0.0 0.0 2008 8.0 6.8 6.8 6.1 5.4 5.0 3.8 3.6 2.4 2.2 1.0 0.9 0.0 0.0 2009 7.7 6.6 6.6 6.0 5.2 4.9 3.7 3.5 2.3 2.1 0.9 0.9 0.0 0.0 2010 7.5 6.4 6.5 5.8 5.1 4.8 3.7 3.4 2.2 2.1 0.9 0.9 0.0 0.0 2011 7.4 6.3 6.4 5.8 5.1 4.7 3.6 3.4 2.2 2.0 0.9 0.8 0.0 0.0 2012 7.3 6.3 6.4 5.7 5.1 4.7 3.6 3.3 2.2 2.0 0.9 0.8 0.0 0.0 2013 7.3 6.2 6.4 5.7 5.1 4.7 3.6 3.3 2.2 2.0 0.9 0.8 0.0 0.0 2014 7.3 6.2 6.4 5.7 5.1 4.7 3.7 3.4 2.2 2.0 0.9 0.8 0.0 0.0 2015 7.3 6.2 6.4 5.7 5.2 4.8 3.7 3.4 2.3 2.0 0.9 0.8 0.0 0.0 2016 7.3 6.2 6.4 5.7 5.2 4.8 3.8 3.4 2.3 2.0 0.9 0.8 0.0 0.0 Tot 1996 10.7 9.8 8.8 8.7 6.9 7.2 5.0 5.5 3.1 3.5 1.3 1.4 0.0 0.0 1997 10.5 9.5 8.6 8.4 6.7 7.0 4.9 5.3 3.0 3.4 1.3 1.4 0.0 0.0 1998 10.3 9.2 8.5 8.2 6.6 6.8 4.8 5.1 3.0 3.3 1.3 1.4 0.0 0.0 1999 10.0 8.9 8.3 7.9 6.5 6.5 4.7 4.9 2.9 3.2 1.3 1.3 0.0 0.0 2000 9.8 8.7 8.1 7.7 6.3 6.3 4.6 4.7 2.9 3.1 1.2 1.3 0.0 0.0 2001 9.6 8.4 7.9 7.4 6.2 6.1 4.5 4.6 2.8 2.9 1.2 1.2 0.0 0.0 2002 9.3 8.1 7.7 7.2 6.0 5.9 4.3 4.4 2.7 2.8 1.2 1.2 0.0 0.0 2003 9.0 7.8 7.5 6.9 5.8 5.6 4.2 4.2 2.6 2.7 1.1 1.1 0.0 0.0 2004 8.6 7.5 7.2 6.6 5.6 5.4 4.0 4.0 2.5 2.5 1.1 1.1 0.0 0.0 2005 8.3 7.1 6.9 6.4 5.3 5.1 3.8 3.7 2.4 2.4 1.0 1.0 0.0 0.0 2006 7.9 6.8 6.6 6.1 5.1 4.9 3.6 3.6 2.2 2.2 0.9 0.9 0.0 0.0 2007 7.6 6.5 6.4 5.9 4.9 4.7 3.4 3.4 2.1 2.1 0.9 0.9 0.0 0.0 2008 7.3 6.3 6.1 5.6 4.7 4.5 3.3 3.2 2.0 2.0 0.8 0.8 0.0 0.0 2009 7.0 6.1 5.9 5.5 4.5 4.4 3.2 3.1 1.9 1.9 0.8 0.8 0.0 0.0 2010 6.8 5.9 5.8 5.4 4.4 4.3 3.1 3.0 1.8 1.8 0.8 0.7 0.0 0.0 2011 6.7 5.8 5.7 5.3 4.4 4.3 3.0 3.0 1.8 1.7 0.7 0.7 0.0 0.0 2012 6.6 5.8 5.6 5.2 4.3 4.2 3.0 2.9 1.8 1.7 0.7 0.7 0.0 0.0 2013 6.5 5.7 5.6 5.2 4.3 4.2 3.0 2.9 1.8 1.7 0.7 0.7 0.0 0.0 2014 6.5 5.7 5.6 5.2 4.4 4.2 3.0 2.9 1.8 1.7 0.7 0.7 0.0 0.0 2015 6.4 5.6 5.6 5.2 4.4 4.2 3.1 2.9 1.8 1.7 0.7 0.7 0.0 0.0 2016 6.4 5.6 5.6 5.2 4.4 4.3 3.1 3.0 1.8 1.7 0.8 0.7 0.0 0.0 Sus 1996 10.3 9.4 8.4 8.4 6.6 7.0 5.0 5.5 3.2 3.6 1.4 1.5 0.0 0.0 1997 10.1 9.2 8.3 8.2 6.5 6.8 4.9 5.3 3.1 3.5 1.4 1.5 0.0 0.0 1998 9.9 8.9 8.1 7.9 6.4 6.6 4.8 5.1 3.1 3.4 1.4 1.5 0.0 0.0 1999 9.7 8.6 8.0 7.7 6.3 6.4 4.7 4.9 3.1 3.3 1.4 1.4 0.0 0.0 2000 9.4 8.3 7.8 7.4 6.1 6.2 4.6 4.7 3.0 3.2 1.3 1.4 0.0 0.0 2001 9.2 8.1 7.6 7.2 6.0 5.9 4.5 4.5 2.9 3.0 1.3 1.3 0.0 0.0 2002 8.9 7.8 7.4 6.9 5.8 5.7 4.4 4.4 2.8 2.9 1.3 1.3 0.0 0.0 2003 8.6 7.5 7.2 6.7 5.6 5.5 4.2 4.2 2.7 2.8 1.2 1.2 0.0 0.0 2004 8.3 7.1 6.9 6.4 5.4 5.3 4.0 4.0 2.6 2.6 1.2 1.2 0.0 0.0 2005 7.9 6.8 6.6 6.1 5.2 5.0 3.8 3.8 2.5 2.5 1.1 1.1 0.0 0.0 2006 7.5 6.5 6.3 5.9 5.0 4.8 3.7 3.6 2.4 2.3 1.0 1.0 0.0 0.0 2007 7.2 6.3 6.1 5.6 4.7 4.6 3.5 3.4 2.3 2.2 1.0 1.0 0.0 0.0 2008 6.9 6.0 5.9 5.5 4.6 4.5 3.4 3.3 2.2 2.1 0.9 0.9 0.0 0.0 2009 6.7 5.8 5.7 5.3 4.4 4.3 3.3 3.2 2.1 2.0 0.9 0.9 0.0 0.0 2010 6.5 5.7 5.6 5.2 4.4 4.3 3.2 3.1 2.0 1.9 0.9 0.8 0.0 0.0 2011 6.4 5.6 5.5 5.1 4.3 4.2 3.2 3.1 2.0 1.9 0.9 0.8 0.0 0.0 2012 6.4 5.6 5.5 5.1 4.4 4.2 3.2 3.1 2.0 1.9 0.9 0.8 0.0 0.0 2013 6.4 5.6 5.5 5.1 4.4 4.3 3.2 3.1 2.0 1.9 0.9 0.8 0.0 0.0 2014 6.4 5.6 5.5 5.2 4.5 4.3 3.3 3.1 2.1 1.9 0.9 0.8 0.0 0.0 2015 6.4 5.6 5.6 5.2 4.5 4.4 3.3 3.1 2.1 1.9 0.9 0.8 0.0 0.0 2016 6.4 5.6 5.6 5.2 4.6 4.4 3.4 3.2 2.1 1.9 0.9 0.8 0.0 0.0 \end{Soutput} \end{Schunk} We now have the relevant points for the graph showing YLL to diabetes for men and women by age, and calendar year, both under the immunity and susceptibility models for the calculation of YLL. \begin{Schunk} \begin{Sinput} > plyll <- function(wh){ + par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, bty="n", las=1 ) + + matplot( a.ref, aYLL[wh,"M",,], + type="l", lty=1, col="blue", lwd=1:2, + ylim=c(0,12), xlab="Age", + ylab="Years lost to DM", yaxs="i" ) + abline(v=50,h=1:10,col=gray(0.7)) + text( 90, 11, "Men", col="blue", adj=1 ) + text( 40, aYLL[wh,"M","40","1996"], "1996", adj=c(0,0), col="blue" ) + text( 43, aYLL[wh,"M","44","2016"], "2016", adj=c(1,1), col="blue" ) + + matplot( a.ref, aYLL[wh,"F",,], + type="l", lty=1, col="red", lwd=1:2, + ylim=c(0,12), xlab="Age", + ylab="Years lost to DM", yaxs="i" ) + abline(v=50,h=1:10,col=gray(0.7)) + text( 90, 11, "Women", col="red", adj=1 ) + text( 40, aYLL[wh,"F","40","1996"], "1996", adj=c(0,0), col="red" ) + text( 43, aYLL[wh,"F","44","2016"], "2016", adj=c(1,1), col="red" ) + } > plyll("Imm") \end{Sinput} \end{Schunk} \begin{Schunk} \begin{Sinput} > plyll("Tot") \end{Sinput} \end{Schunk} \begin{Schunk} \begin{Sinput} > plyll("Sus") \end{Sinput} \end{Schunk} \begin{figure}[h] \centering \includegraphics[width=\textwidth]{yll-imm} \caption{Years of life lost to DM: the difference in expected residual life time at different ages between persons with and without diabetes, assuming the persons without diabetes at a given age remain free from diabetes (immunity assumption --- not reasonable). The lines refer to date of evaluation; the top lines refer to 1.1.1996 the bottom ones to 1.1.2016. Blue curves are men, red women.} \label{fig:imm} \end{figure} \begin{figure}[h] \centering \includegraphics[width=\textwidth]{yll-sus} \caption{Years of life lost to DM: the difference in expected residual life time at different ages between persons with and without diabetes, allowing the persons without diabetes at a given to contract diabetes and thus be subject to higher mortality. The lines refer to date of evaluation; the top lines refer to 1.1.1996 the bottom ones to 1.1.2016. Blue curves are men, red women.} \label{fig:sus} \end{figure} \begin{figure}[h] \centering \includegraphics[width=\textwidth]{yll-tot} \caption{Years of life lost to DM: the difference in expected residual life time at different ages between persons with and without diabetes. Allowance for susceptibility is approximated by using the total population mortality instead of non-DM mortality. The lines refer to date of evaluation; the top lines refer to 1.1.1996 the bottom ones to 1.1.2016. Blue curves are men, red women.} \label{fig:tot} \end{figure} From figure \ref{fig:sus} we see that for men aged 50 the years lost to diabetes has decreased from a bit over 8 to a bit less than 6 years, and for women from 8.5 to 5 years; so a greater improvement for women. \chapter{Practical implementation} We have devised functions that wraps these formulae up for practical use. \section{Function definitions} % The following code sources the originally formatted code in erl.R in % order to make it printable with all the formatting and comments in % it. However the sourcing does not work when compiling the vignettes % in R CMD build. So when checking the code we comment this out by % putting eval=FALSE. So depending on whether we actually construct % the pdf for the inst/doc folder or test (upload) the package, one of % the following two chunks are run with eval=FALSE and the other with % eval=TRUE. \begin{Schunk} \begin{Sinput} > source( "../R/erl.R", keep.source=TRUE ) \end{Sinput} \end{Schunk} % When checking the package When using the functions it is assumed that the functions $\mu_W$, $\mu_D$ and $\lambda$ are given as vectors corresponding to equidistantly (usually tightly) spaced ages from 0 to $K$ where K is the age where everyone can safely be assumed dead. \texttt{surv1} is a simple function that computes the survival function from a vector of mortality rates, and optionally the conditional survival given being alive at prespecified ages: \begin{Schunk} \begin{Sinput} > surv1 \end{Sinput} \begin{Soutput} function (int, mu, age.in = 0, A = NULL) { if (any(is.na(mu))) { mu[is.na(mu)] <- 0 warning("NAs in agument 'mu' set to 0") } age <- 0:length(mu) * int + age.in Mu <- c(0, cumsum(mu) * int) Sv <- exp(-Mu) surv <- data.frame(age = age, surv = Sv) if (cond <- !is.null(A)) { j <- 0 cage <- NULL for (ia in A) { j <- j + 1 cA <- which(diff(age > ia) == 1) surv <- cbind(surv, pmin(1, surv$surv/(surv$surv[cA]))) cage[j] <- surv$age[cA] } } names(surv)[-1] <- paste("A", c(age.in, if (cond) cage else NULL), sep = "") rownames(surv) <- NULL return(surv) } \end{Soutput} \end{Schunk} \texttt{erl1} basically just expands the result of \texttt{surv1} with a column of expected residual life times: \begin{Schunk} \begin{Sinput} > erl1 \end{Sinput} \begin{Soutput} function (int, mu, age.in = 0) { age <- 0:length(mu) * int + age.in musmuc <- function(x) rev(cumsum(rev(x))) surv <- surv1(int = int, mu = mu, age.in = age.in)[, 2] cbind(age = age, surv = surv, erl = c(musmuc((surv[-1] - diff(surv)/2))/surv[-length(surv)], 0) * int) } \end{Soutput} \end{Schunk} We also define a function, \texttt{surv2}, that computes the survival function for a non-diseased person that may become diseased with rate \texttt{lam} and after that die at a rate of \texttt{muD} (corresponding to the formulae above). This is the sane way of handling years of life lost to a particular illness: \begin{Schunk} \begin{Sinput} > surv2 \end{Sinput} \begin{Soutput} function (int, muW, muD, lam, age.in = 0, A = NULL) { if (length(muW) != length(muD) | length(muD) != length(lam)) stop("Vectors with rates must have same length:\n", "length(muW)=", length(muW), ", length(muD)=", length(muD), ", length(lam)=", length(lam)) if (!is.null(lam)) { if (any(is.na(lam))) { lam[is.na(lam)] <- 0 warning("NAs in agument 'lam' set to 0") } } if (any(is.na(muD))) { muD[is.na(muD)] <- 0 warning("NAs in agument 'muD' set to 0") } if (any(is.na(muW))) { muW[is.na(muW)] <- 0 warning("NAs in agument 'muW' set to 0") } wsurv2 <- function(int, muW, muD, lam, age.in = 0, A = 0) { age <- 0:length(muW) * int + age.in MuW <- cumsum(c(0, muW) * (age > A)) * int MuD <- cumsum(c(0, muD) * (age > A)) * int Lam <- cumsum(c(0, lam) * (age > A)) * int pW <- exp(-(Lam + MuW)) Dis <- c(0, lam) * (age > A) * exp(-(Lam + MuW)) * int pDM <- Dis * 0 for (ia in 1:length(age)) pDM[ia] <- sum(Dis[1:ia] * exp(-(MuD[ia] - MuD[1:ia]))) surv <- data.frame(age = age, surv = pDM + pW) return(surv) } surv <- wsurv2(int, muW, muD, lam, age.in = age.in, A = 0) if (!is.null(A)) { for (j in 1:length(A)) { surv <- cbind(surv, wsurv2(int, muW, muD, lam, age.in = age.in, A = A[j])[, 2]) } } Al <- A for (i in 1:length(A)) Al[i] <- max(surv$age[surv$age <= A[i]]) colnames(surv)[-1] <- paste("A", c(age.in, Al), sep = "") return(surv) } \end{Soutput} \end{Schunk} Finally we devised a function using these to compute the expected residual lifetime at select ages: \begin{Schunk} \begin{Sinput} > erl \end{Sinput} \begin{Soutput} function (int, muW, muD, lam = NULL, age.in = 0, A = NULL, immune = is.null(lam), yll = TRUE, note = TRUE) { trsum <- function(x) { x[c(diff(x) == 0, TRUE)] <- NA sum((x[-length(x)] + x[-1])/2, na.rm = TRUE) } if (!immune & is.null(lam)) stop("'lam' is required when immune=FALSE\n") if (!is.null(lam)) { if (any(is.na(lam))) { lam[is.na(lam)] <- 0 warning("NAs in agument 'lam' set to 0") } } if (any(is.na(muD))) { muD[is.na(muD)] <- 0 warning("NAs in agument 'muD' set to 0") } if (any(is.na(muW))) { muW[is.na(muW)] <- 0 warning("NAs in agument 'muW' set to 0") } sD <- surv1(int = int, muD, age.in = age.in, A = A) if (immune) sW <- surv1(int = int, muW, age.in = age.in, A = A) else sW <- surv2(int = int, muW, muD, lam, age.in = age.in, A = A) erl <- cbind(apply(sW[, -1], 2, trsum), apply(sD[, -1], 2, trsum)) * int colnames(erl) <- c("Well", "Dis") rownames(erl) <- colnames(sW)[-1] if (yll) erl <- cbind(erl, YLL = erl[, "Well"] - erl[, "Dis"]) if (immune) { attr(erl, "NOTE") <- "Calculations assume that Well persons cannot get Ill (quite silly!)." if (note) cat("NOTE:", attr(erl, "NOTE"), "\n") } return(erl) } \end{Soutput} \end{Schunk} \ldots and a wrapper for this if we only want the years of life lost returned: \begin{Schunk} \begin{Sinput} > yll \end{Sinput} \begin{Soutput} function (int, muW, muD, lam = NULL, age.in = 0, A = NULL, immune = is.null(lam), note = TRUE) erl(int = int, muW = muW, muD = muD, lam = lam, age.in = age.in, A = A, immune = immune, yll = TRUE, note = note)[, "YLL"] \end{Soutput} \end{Schunk} \bibliographystyle{plain} \begin{thebibliography}{1} \bibitem{Carstensen.2007a} B~Carstensen. \newblock Age-{P}eriod-{C}ohort models for the {L}exis diagram. \newblock {\em Statistics in Medicine}, 26(15):3018--3045, 2007. \bibitem{Carstensen.2008c} B~Carstensen, JK~Kristensen, P~Ottosen, and K~Borch-Johnsen. \newblock The {D}anish {N}ational {D}iabetes {R}egister: {T}rends in incidence, prevalence and mortality. \newblock {\em Diabetologia}, 51:2187--2196, 2008. \end{thebibliography} \addcontentsline{toc}{chapter}{References} \end{document} Epi/vignettes/crisk.rnw0000644000176200001440000005506714003730034014651 0ustar liggesusers%\VignetteIndexEntry{Parametric competing risks with simulation based confidence intervals} \SweaveOpts{results=verbatim,keep.source=TRUE,include=FALSE,eps=FALSE} \documentclass[a4paper,dvipsnames,twoside,12pt]{report} % ---------------------------------------------------------------------- % General information for the title page and the page headings \newcommand{\Title}{Parametric competing risks with simulation based confidence intervals} \newcommand{\Tit}{ParCmpRSim} \newcommand{\Version}{Version 3} \newcommand{\Dates}{January 2021} \newcommand{\Where}{SDCC} \newcommand{\Homepage}{\url{http://bendixcarstensen.com/}} \newcommand{\Faculty}{\begin{tabular}{rl} Bendix Carstensen & Steno Diabetes Center Copenhagen, Gentofte, Denmark\\ & {\small \& Department of Biostatistics, University of Copenhagen} \\ & \href{mailto:b@bxc.dk}{\tt b@bxc.dk} \\ & \url{http://BendixCarstensen.com} \\[1em] \end{tabular}} \input{topreport} \renewcommand{\rwpre}{./crisk} <>= options( width=90, SweaveHooks=list( fig=function() par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") ) ) @ % \chapter{Competing risks in practice} The concept of competing risks is one where persons in a given state, 'alive', say, er subject to a number of different causes of deaths, 'cause1', 'cause2' etc. Causes of death are required to be exhaustive and mutually exclusive. In situations where the causes are not causes of death but other events, it is implicit that we only consider the first occurrence of an event from the state 'alive', and ignore what occurs after. The likelihood for observations from a competing risk scenario is a function of the cause-specific transition rates, and is \emph{product} of the likelihoods that would emerge if we considered each cause the only one. Thus analysis is in principle straight forward; just estimate a model for each of the cause-specific rates. These will together form a complete model for the competing risks problem. If the cause-specific rates are all we want to assess then we will be done. But most often we would like to have estimates of the cumulative risks, that is the probability of dying from a specific cause before a given time as function of time. Each of these are functions of \emph{all} rates. Specifically, if the cause-specific rates are $\lambda_c(t)$, then: \[ R_c(t) = \int_0^t \lambda_c(s) \exp\left(-\int_0^s \sum_j \lambda_j(u) \dif u \right) \dif s \] Even if we from the modeling of the $\lambda$s have standard errors of $\log(\lambda_c)$ the standard errors of $R_c$s will be analytically intractable from these. The only viable way to get confidence intervals for the cumulative risks, $R_c$, is by calculation of the rates $\lambda(t)$ by sampling from the posterior distribution of the parameters in the models for $\log(\lambda(s))$, and computing the integrals numerically for each simulated sample. The simulation approach also allows calculation of confidence intervals for sums of the cumulative risks, $R_1(t)+R_2(t)$, for example, which will be needed if we want to show stacked cumulative risks. Finally, it will also allow calculation of standard errors of sojourn times in each of the states 'alive' and 'cause1', 'cause2'. While the latter two may not be of direct interest, then \texttt{differences} between such sojourn times between different groups can be interpreted as years of life lost to each cause between groups. \section{Example data} As an illustrative data example we use the (fake) diabetes register data; we set up the Lexis object, cut the follow-up time at dates of OAD, resp Ins: <<>>= library(Epi) library(popEpi) data(DMlate) Ldm <- Lexis(entry = list( per = dodm, age = dodm-dobth, tfd = 0 ), exit = list( per = dox ), exit.status = factor( !is.na(dodth), labels = c("DM","Dead") ), data = DMlate ) summary(Ldm, t = T) Mdm <- mcutLexis( Ldm, wh = c('dooad','doins'), new.states = c('OAD','Ins'), precursor = 'DM', seq.states = FALSE, ties = TRUE ) summary( Mdm ) @ We initially split the FU before drug inception in intervals of 1/12 year, creating a \texttt{Lexis} object for a competing risks situation with three possible event types: <<>>= Sdm <- splitMulti(factorize(subset(Mdm, lex.Cst == "DM")), tfd = seq(0, 20, 1/12)) @ % We can illustrate the follow-up in the full data set and in the restricted <>= boxes(Mdm, boxpos = list(x = c(15, 50, 15, 85, 85), y = c(85, 50, 15, 85, 15)), scale.R = 100, show.BE = TRUE) @ % \insfig{boxes5}{1.0}{The transitions in the multistate model, where follow-up is extended also after beginning of first drug exposure. Rates in brackets are per 100 PY.}% <>= boxes( Relevel(Sdm, c(1, 4, 2, 3)), boxpos = list(x = c(15, 85, 80, 15), y = c(85, 85, 20, 15)), scale.R = 100, show.BE = TRUE ) @ % \insfig{boxes4}{1.0}{The transitions in the competing risks model, where follow-up is stopped at drug exposure. By that token only the \texttt{DM} state has person-years; a characteristic of a competing risks situation.} \section{Models for rates} Now that we have set up a dataset with three competing events, we can model the cause-specific rates separately by time from diagnosis as the only underlying time scale. Note that we only need to specify the \texttt{to=} argument because there is only one possible \texttt{from} for each \texttt{to} (incidentally the same for all \texttt{to} states, namely \texttt{DM}): <<>>= mD <- gam.Lexis(Sdm, ~ s(tfd, k = 5), to = 'Dead') mO <- gam.Lexis(Sdm, ~ s(tfd, k = 5), to = 'OAD' ) mI <- gam.Lexis(Sdm, ~ s(tfd, k = 5), to = 'Ins' ) @ % With these models fitted we can compute the rates, cumulative rates and the cumulative risks an sojourn times in states using the usual formulae. First we compute the rates in intervals of length 1/100 years. Note that these models only have time since diagnosis as covariates, so they are the counterpart of Nelson-Aalen estimates, albeit in a biologically more meaningful guise. The points where we compute the predicted rates are midpoints of intervals of length 1/100 year. These points are unrelated to the follow-up intervals in which we split the data---they were 1 month intervals, here we use 1/100 year (about 3.7 days): <<>>= int <- 1/100 nd <- data.frame( tfd = seq(int,10,int)-int/2 ) # not the same as the split, # and totally unrelated to it rownames(nd) <- nd$tfd str(nd) @ % With this we can show the rates as a function of the time since diagnosis: <>= matshade(nd$tfd, cbind(ci.pred(mD, nd), ci.pred(mI, nd), ci.pred(mO, nd))*1000, ylim = c(0.02,500), yaxt = "n", ylab = "Rates per 1000 PY", xlab = "Time since DM diagnosis (years)", col = c("black","red","blue"), log = "y", lwd = 3, plot = TRUE) axis(side = 2, at = ll<-outer(c(1,2,5),-2:3,function(x,y) x*10^y), labels = formatC(ll,digits = 4), las = 1) axis(side = 2, at = ll<-outer(c(1.5,2:9),-2:3,function(x,y) x*10^y), labels = NA, tcl = -0.3) text(0, 0.5*0.6^c(1,2,0), c("Dead","Ins","OAD"), col = c("black","red","blue"), adj = 0) @ % \insfig{rates}{0.8}{Estimated rates from the \textrm{\tt DM} state, estimates are from \textrm{\tt gam} models fitted to data split in 1 month intervals (1/12 year, that is). Rates of \textrm{\tt OAD} is in the vicinity of 0.1/year, and mortality about half of this. Rates of insulin start among persons on no other drug are beginning high decreasing to about 4 year and then have a peak at 8 years.} Note that the graph in figure \ref{fig:rates} is not normally shown in analyses of competing risks; the competing cause-specific rates are hardly ever shown. I suspect that this is frequently because they are often modeled by a Cox model and so are buried in the model. \section{Cumulative rates and risks} For the calculation of the cumulative rates and state probabilities, we need just the rates without CIs: <<>>= # rates at midpoints lD <- ci.pred( mD, nd )[,1] lI <- ci.pred( mI, nd )[,1] lO <- ci.pred( mO, nd )[,1] # cumulative rates and survival fuction at right border of the intervals LD <- cumsum(lD) * int LI <- cumsum(lI) * int LO <- cumsum(lO) * int Sv <- exp( -LD - LI - LO ) # but when integrating to get the cumulative risks we use the average # of the survival function at the two endpoints (adding 1 as the first) mp <- function(x) x - diff(c(1, x)) / 2 rD <- cumsum(lD * mp(Sv)) * int rI <- cumsum(lI * mp(Sv)) * int rO <- cumsum(lO * mp(Sv)) * int @ % Now we have the cumulative risks for the three causes and the survival, computed at the end of each of the intervals, at any time point the sum of the 3 cumulative risks and the survival should be 1: <<>>= summary(rD + rI +rO + Sv) oo <- options(digits = 20) cbind(summary(Sv + rD + rI + rO)) options(oo) @ % We can then plot the 3 cumulative risk functions together: <>= zz <- mat2pol(cbind(rD,rI,rO,Sv), x = nd$tfd, xlim = c(0,10), xaxs = "i", yaxs = "i", las = 1, xlab = "Time since DM diagnosis (years)", ylab = "Probability", col = c("black","red","blue","forestgreen") ) mm <- t(apply(zz,1,mid<-function(x) x[-1]-diff(x)/2)) text( 9, mm[900,], c("Dead","Ins","OAD","DM"), col = "white" ) box(col = "white",lwd = 3) @ % $ \insfig{stack}{1.0}{Probabilities of being in the 4 different states as a function of time since diagnosis. Note that \texttt{OAD} means that OAD was initiated first, and similarly for \texttt{Ins}. We are not concerned about what occur after these events. \texttt{Dead} means dead without being on any drug.} \chapter{Confidence intervals} We want confidence intervals for each of the 4 cumulative risks, but we may also be interested in confidence intervals for \emph{sums} of any subset of the cumulative risks, corresponding to the borders between the colours in figure \ref{fig:stack}. If we only had two competing risks (and hence three states) the latter would not be an issue, because the sum of any two cumulative risks will be 1 minus the cumulative risk of the remainder, so we could get away with the confidence intervals for the single cumulative risks. This is the reason we have chosen an example with 3 competing risks and not just 2; we then have 4 probabilities to sum in different order. A short look at the formulae for cumulative risks will reveal that analytic approximation to the standard error of these probabilities (or some transform of them) is not really a viable way to go. Particularly if we also want confidence intervals of sums of the state probabilities as those shown in stacked plots. So in practice, if we want confidence intervals not only for the state probabilities, but also for any sum of subsets of them we would want a large number of simulated copies of the cumulative risks, each copy of the same structure as the one we just extracted from the model. Moreover, we might also want confidence intervals for sojourn times (i.e. time spent) in each state up to a given time, which would come almost for free from the simulation approach. This means that we must devise a method to make a prediction not from the estimated model, but where we instead of the model parameters use a sample from the posterior distribution of the estimated parameters. Here the posterior distribution of the parameters is taken to be the multivariate normal distribution with mean equal to the vector of parameter estimates and variance-covariance matrix equal to the estimated variance-covariance matrix of the parameters. Precisely this approach is implemented in \texttt{ci.lin} via the \texttt{sample} argument; we can get a predicted value from a given prediction data frame just as from \texttt{ci.pred} resp. \texttt{ci.exp}; here is an indication of different ways of getting predicted values of the cause-specific rates: <<>>= head(cbind(ci.pred(mI,nd), ci.exp(mI,nd) )) head(cbind(ci.pred(mI,nd), exp(ci.lin(mI,nd)[,c(1,5:6)]))) @ % Here is an illustration of the prediction with model based confidence intervals for the rates, alongside predictions based on samples from the posterior distribution of the parameters in the model: <<>>= str(ci.lin(mI, nd, sample = 4)) head(cbind(ci.pred(mI,nd), exp(ci.lin(mI, nd, sample = 4)))) @ % The simulation is taking place at the parameter level and the transformation to survival and cumulative risks is simply a function applied to every simulated set of rates. \section{Joint models for several transitions} Note that we are implicitly assuming that the transitions are being modeled separately. If some transitions are modeled jointly---for example assuming that the rates of \texttt{OAD} and \texttt{Ins} are proportional as functions of time since entry, using one model---we are in trouble, because we then need one sample from the posterior generating two predictions, one for each of the transitions modeled together. Moreover the model will have to be a model fitted to a \texttt{stack.Lexis} object, so a little more complicated to work with. A simple way to program would be to reset the seed to the same value before simulating with different values of \texttt{nd}, this is what is intended to be implemented, but is not yet. This is mainly the complication of having different prediction frames for different risks in this case. Finally, it is not a very urgent need, since the situation where you want common parameters for different rates out of a common state is quite rare. \section{Simulation based confidence intervals} These ideas have been implemented in the function \texttt{ci.Crisk} (\texttt{c}onfidence \texttt{i}ntervals for \texttt{C}umulative \texttt{risk}s) in the \texttt{Epi} package: <>= setwd("/home/bendix/stat/R/examples") source('ci.Crisk.R', echo=TRUE, max=10000) @ We can now run the function using the model objects for the three competing events, using a common prediction data frame, \texttt{nd} for the rates: <<>>= system.time( res <- ci.Crisk(list(OAD = mO, Ins = mI, Dead = mD), nd = data.frame(tfd = (1:1000-0.5)/100), nB = 1000, perm = 4:1)) str(res) @ % As we see, the returned object (\texttt{res}) is a list of length 3, each element a 3-way arrays. The three components of \texttt{res} represent \begin{itemize} \item \texttt{Crisk} \texttt{C}umulative \texttt{risk}s for each state \item \texttt{Srisk} \texttt{S}tacked cumulative \texttt{risk}s across states \item \texttt{Stime} \texttt{S}ojourn \texttt{time} for each state, truncated at each point of the time dimension, hence there is no 0 in the time dimension \end{itemize} The first dimension of each is time as interval \emph{number}, starting with 0, and corresponding to endpoints of intervals of length \texttt{int}. The second dimension is states (or combinations thereof). The last dimension of the arrays is the type of statistic; \texttt{50\%} the median of the samples, and the bootstrap intervals as indicated. The argument \texttt{perm} governs in which order the state probabilities are stacked in the \texttt{Srisk} element of the returned list, the default is the states in the order given in the list of models in the first argument to \texttt{ci.Crisk} followed by the survival. If we want the bootstrap samples to make other calculations we can ask the function to return the bootstrap samples of the rates by using the argument \texttt{sim.res='rates'} (defaults to \texttt{'none'}): <<>>= system.time( rsm <- ci.Crisk(list(OAD = mO, Ins = mI, Dead = mD), nd = data.frame(tfd = (1:1000-0.5)/100), nB = 2000, sim.res = 'rates')) str(rsm) @ % This is bootstrap samples of the rates evaluated at the 1000 midpoints of intervals. Alternatively we can get the bootstrap samples of the cumulative risks by setting \texttt{sim.res='crisk'}: <<>>= system.time( csm <- ci.Crisk(list(OAD = mO, Ins = mI, Dead = mD), nd = data.frame(tfd = (1:1000-0.5)/100), nB = 2000, sim.res = 'crisk')) str(csm) @ % This is the cumulative risks evaluated at the 1001 endpoints of the 1000 intervals, and also includes the survival probability in the first slot of the \nth{1} dimension of \texttt{rsm}. In both cases, the first slot of the \nth{3} dimension, \texttt{sim}, is the rates, resp. cumulative risks from the model. \section{Simulated confidence intervals for rates} In figure \ref{fig:rates} we showed the rates with confidence intervals from the model. But in \texttt{rsm} we have 2000 (parametric) bootstrap samples of the occurrence rates, so we can derive the bootstrap medians and the bootstrap c.i.---remember that the first slice of the \nth{3} dimension is the model estimates that should not enter the calculations. We use the function \texttt{mnqt} to compute the model estimate and the mean, median and quantiles of the simulated values. <<>>= Brates <- aperm(apply(rsm, 1:2, Epi:::mnqt), c(2,3,1)) str(Brates) @ % Then we can plot the bootstrap estimates on top of the estimates based on the normal approximation to distribution of the parameters. They are not surprisingly in close agreement since they are both based on an assumption of normality of the parameters on the log-rate scale: <>= matshade(nd$tfd, cbind(ci.pred(mD, nd), ci.pred(mI, nd), ci.pred(mO, nd))*1000, ylim = c(0.1,500), yaxt = "n", ylab = "Rates per 1000 PY", xlab = "Time since DM diagnosis (years)", col = c("black","red","blue"), log = "y", lwd = 3, plot = TRUE) matlines(nd$tfd, cbind(Brates[,"Dead",], Brates[,"Ins" ,], Brates[,"OAD" ,])*1000, col = c("white","black","black"), lty = 3, lwd=c(3,1,1)) axis(side = 2, at = ll<-outer(c(1,2,5),-2:3,function(x,y) x*10^y), labels = formatC(ll,digits = 4), las = 1) axis(side = 2, at = ll<-outer(c(1.5,2:9),-2:3,function(x,y) x*10^y), labels = NA, tcl = -0.3) text(0, 0.5*0.6^c(1,2,0), c("Dead","Ins","OAD"), col = c("black","red","blue"), adj = 0) @ % \insfig{rates-ci}{0.8}{Estimated rates from the \textrm{\tt DM} state, estimates are from \textrm{\tt gam} models fitted to data split in 1 month intervals (1/12 year, that is). The white dotted curves are the bootstrap medians, black dotted curves are the bootstrap 95\% c.i.s.} \section{Confidence intervals for cumulative risks} In the \texttt{Crisk} component of \texttt{res} we have the cumulative risks as functions of of time, with bootstrap confidence intervals, so we can immediately plot the three cumulative risks: <>= matshade(c(0,nd$tfd+1/200), cbind(res$Crisk[,"Dead",], res$Crisk[,"Ins" ,], res$Crisk[,"OAD" ,]), plot = TRUE, xlim = c(0,10), xaxs = "i", yaxs = "i", las = 1, xlab = "Time since DM diagnosis (years)", ylab = "Cumulative probability", col = c("black","red","blue")) text(8, 0.3 + c(1,0,2)/25, c("Dead","Ins","OAD"), col = c("black","red","blue"), adj = 0) @ % $ \insfig{crates}{0.9}{Cumulative risks for the three types of events, with 95\% bootstrap-based confidence intervals as shades.} \section{Confidence intervals for stacked cumulative risks} Unlike the single cumulative risks where we have a confidence interval for each cumulative risk, when we want to show the stacked probabilities we must deliver the confidence intervals for the relevant sums, they are in the \texttt{Srisk} component of \texttt{res}. <<>>= str(res$Crisk) str(res$Srisk) @ But we start out by plotting the stacked probabilities using \texttt{mat2pol} (\texttt{mat}rix to \texttt{pol}ygon), the input required is the single components from the \texttt{Crisk} component. Then we can add the confidence intervals <>= zz <- mat2pol(res$Crisk[,c("Dead","Ins","OAD","Surv"),1], x = as.numeric(dimnames(res$Crisk)[[1]])/100, xlim = c(0,10), xaxs = "i", yaxs = "i", las = 1, xlab = "Time since DM diagnosis (years)", ylab = "Probability", col = c("black","red","blue","forestgreen") ) mm <- t(apply(zz, 1, mid<-function(x) x[-1] - diff(x) / 2)) text( 9, mm[900,], c("Dead","Ins","OAD","DM"), col = "white" ) matshade(as.numeric(dimnames(res$Srisk)[[1]])/100, cbind(res$Srisk[,1,], res$Srisk[,2,], res$Srisk[,3,]), col = 'transparent', col.shade = "white", alpha = 0.3) @ % $ \insfig{stack-ci}{1.0}{Probabilities of being in the 4 different states as a function of time since diagnosis. Note that \texttt{OAD} means that OAD was initiated first, and similarly for \texttt{Ins}. We are not concerned about what occurs \emph{after} these events. \texttt{Dead} means dead without being on any drug.\newline The white shadings around the borders between coloured areas represent the 95\% confidence intervals for the (sum of) probabilities.} \section{Sojourn times} From the \texttt{Stime} component of the \texttt{res} we can derive the estimated time spent in each state during the first, say, 5 or 10 years: <<>>= str(res$Stime) @ % We extract the 5 and 10 years components: <<>>= s510 <- res$Stime[1:2*500,,] dimnames(s510)[[1]] <- c(" 5 yr","10 yr") round(ftable(s510, row.vars=1:2), 2) @ % So we see that the expected life lived without pharmaceutical treatment during the first 10 years after DM diagnosis is 4.31 years with a 95\% CI of (4.21;4.42), and during the first 5 years 2.77 (2.72;2.82). The quantity \texttt{OAD} is the years lived without medication that has been terminated by OAD inception, and similarly for \texttt{Ins} and \texttt{Dead}. \end{document} Epi/vignettes/flup.R0000644000176200001440000004611314003562712014075 0ustar liggesusers### R code from vignette source 'flup' ### Encoding: UTF-8 ################################################### ### code chunk number 1: flup.rnw:22-25 ################################################### options( width=90, SweaveHooks=list( fig=function() par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") ) ) ################################################### ### code chunk number 2: flup.rnw:137-139 ################################################### library(Epi) print( sessionInfo(), l=F ) ################################################### ### code chunk number 3: flup.rnw:148-157 ################################################### data( DMlate ) head( DMlate ) dmL <- Lexis( entry = list( per=dodm, age=dodm-dobth, tfD=0 ), exit = list( per=dox ), exit.status = factor( !is.na(dodth), labels=c("DM","Dead") ), data = DMlate ) timeScales(dmL) ################################################### ### code chunk number 4: flup.rnw:180-182 ################################################### str( dmL ) head( dmL )[,1:10] ################################################### ### code chunk number 5: flup.rnw:198-199 ################################################### summary.Lexis( dmL, timeScales=TRUE ) ################################################### ### code chunk number 6: dmL1 ################################################### plot( dmL ) ################################################### ### code chunk number 7: dmL2 ################################################### par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) plot( dmL, 1:2, lwd=1, col=c("blue","red")[dmL$sex], grid=TRUE, lty.grid=1, col.grid=gray(0.7), xlim=1960+c(0,60), xaxs="i", ylim= 40+c(0,60), yaxs="i", las=1 ) points( dmL, 1:2, pch=c(NA,3)[dmL$lex.Xst], col="lightgray", lwd=3, cex=0.3 ) points( dmL, 1:2, pch=c(NA,3)[dmL$lex.Xst], col=c("blue","red")[dmL$sex], lwd=1, cex=0.3 ) box(bty='o') ################################################### ### code chunk number 8: flup.rnw:255-258 ################################################### dmS1 <- splitLexis( dmL, "age", breaks=seq(0,100,5) ) summary( dmL ) summary( dmS1 ) ################################################### ### code chunk number 9: flup.rnw:268-271 ################################################### wh.id <- c(9,27,52,484) subset( dmL , lex.id %in% wh.id )[,1:10] subset( dmS1, lex.id %in% wh.id )[,1:10] ################################################### ### code chunk number 10: flup.rnw:277-279 ################################################### dmS2 <- splitLexis( dmS1, "tfD", breaks=c(0,1,2,5,10,20,30,40) ) subset( dmS2, lex.id %in% wh.id )[,1:10] ################################################### ### code chunk number 11: flup.rnw:284-290 ################################################### library( popEpi ) dmM <- splitMulti( dmL, age = seq(0,100,5), tfD = c(0,1,2,5,10,20,30,40), drop = FALSE ) summary( dmS2 ) summary( dmM ) ################################################### ### code chunk number 12: flup.rnw:301-304 ################################################### identical( dmS2, dmM ) class( dmS2 ) class( dmM ) ################################################### ### code chunk number 13: flup.rnw:334-344 ################################################### whc <- c(names(dmL)[1:7],"dodm","doins") # WHich Columns do we want to see? subset( dmL, lex.id %in% wh.id )[,whc] dmC <- cutLexis( data = dmL, cut = dmL$doins, timescale = "per", new.state = "Ins", new.scale = "tfI", precursor.states = "DM" ) whc <- c(names(dmL)[1:8],"doins") # WHich Columns do we want to see? subset( dmC, lex.id %in% wh.id )[,whc] ################################################### ### code chunk number 14: flup.rnw:362-369 ################################################### dmS2C <- cutLexis( data = dmS2, cut = dmS2$doins, timescale = "per", new.state = "Ins", new.scale = "tfI", precursor.states = "DM" ) subset( dmS2C, lex.id %in% wh.id )[,whc] ################################################### ### code chunk number 15: flup.rnw:393-394 ################################################### summary( dmS2C, timeScales=TRUE ) ################################################### ### code chunk number 16: box1 ################################################### boxes( dmC, boxpos=TRUE, scale.R=1000, show.BE=TRUE ) ################################################### ### code chunk number 17: flup.rnw:437-445 ################################################### timeBand( dmS2C, "age", "middle" )[1:10] # For nice printing and column labelling we use the data.frame() function: data.frame( dmS2C[,c("per","age","tfD","lex.dur")], mid.age=timeBand( dmS2C, "age", "middle" ), mid.t=timeBand( dmS2C, "tfD", "middle" ), left.t=timeBand( dmS2C, "tfD", "left" ), right.t=timeBand( dmS2C, "tfD", "right" ), fact.t=timeBand( dmS2C, "tfD", "factor" ) )[1:15,] ################################################### ### code chunk number 18: flup.rnw:481-482 ################################################### summary( (dmS2$age-dmS2$tfD) - (dmS2$dodm-dmS2$dobth) ) ################################################### ### code chunk number 19: flup.rnw:487-489 ################################################### summary( timeBand( dmS2, "age", "middle" ) - timeBand( dmS2, "tfD", "middle" ) - (dmS2$dodm-dmS2$dobth) ) ################################################### ### code chunk number 20: flup.rnw:594-596 ################################################### dmCs <- splitMulti( dmC, age = seq(0,110,1/4) ) summary( dmCs, t=T ) ################################################### ### code chunk number 21: flup.rnw:618-623 ################################################### ( a.kn <- with( subset( dmCs, lex.Xst=="Dead" ), quantile( age+lex.dur, (1:5-0.5)/5 ) ) ) ( i.kn <- c( 0, with( subset( dmCs, lex.Xst=="Dead" & lex.Cst=="Ins" ), quantile( tfI+lex.dur, (1:4)/5 ) ) ) ) ################################################### ### code chunk number 22: flup.rnw:639-644 ################################################### ma <- glm( (lex.Xst=="Dead") ~ Ns(age,knots=a.kn), family = poisson, offset = log(lex.dur), data = dmCs ) summary( ma ) ################################################### ### code chunk number 23: flup.rnw:663-666 ################################################### Ma <- glm( cbind(lex.Xst=="Dead",lex.dur) ~ Ns(age,knots=a.kn), family = poisreg, data = dmCs ) summary( Ma ) ################################################### ### code chunk number 24: flup.rnw:674-676 ################################################### Xa <- glm.Lexis( dmCs, from="DM", to="Dead", formula = ~ Ns(age,knots=a.kn) ) ################################################### ### code chunk number 25: flup.rnw:679-680 ################################################### attr( Xa, "Lexis" ) ################################################### ### code chunk number 26: flup.rnw:689-690 ################################################### xa <- glm.Lexis( dmCs, formula = ~ Ns(age,knots=a.kn) ) ################################################### ### code chunk number 27: flup.rnw:693-694 ################################################### c( deviance(ma), deviance(Ma), deviance(Xa), deviance(xa) ) ################################################### ### code chunk number 28: pr-a ################################################### nd <- data.frame( age=40:85, lex.dur=1000 ) pr.0 <- ci.pred( ma, newdata = nd ) # mortality per 100 PY pr.a <- ci.pred( Ma, newdata = nd )*1000 # mortality per 100 PY summary(pr.0/pr.a) matshade( nd$age, pr.a, plot=TRUE, type="l", lty=1, log="y", xlab="Age (years)", ylab="DM mortality per 1000 PY") ################################################### ### code chunk number 29: flup.rnw:741-745 ################################################### pm <- glm( cbind(lex.Xst=="Dead",lex.dur) ~ Ns(age,knots=a.kn) + lex.Cst + sex, family=poisreg, data = dmCs ) round( ci.exp( pm ), 3 ) ################################################### ### code chunk number 30: flup.rnw:759-763 ################################################### pm <- glm( cbind(lex.Xst=="Dead",lex.dur) ~ Ns(age,knots=a.kn) + Ns(tfI,knots=i.kn) + lex.Cst + sex, family=poisreg, data = tsNA20(dmCs) ) ################################################### ### code chunk number 31: flup.rnw:769-775 ################################################### Pm <- glm.Lexis( tsNA20(dmCs), form = ~ Ns(age,knots=a.kn) + Ns(tfI,knots=i.kn) + lex.Cst + sex ) c( deviance(Pm), deviance(pm) ) identical( model.matrix(Pm), model.matrix(pm) ) ################################################### ### code chunk number 32: flup.rnw:781-782 ################################################### round( ci.exp( Pm, subset="ex" ), 3 ) ################################################### ### code chunk number 33: ins-time ################################################### ndI <- data.frame( expand.grid( tfI=c(NA,seq(0,15,0.1)), ai=seq(40,80,10) ), sex="M", lex.Cst="Ins" ) ndI <- transform( ndI, age=ai+tfI ) head( ndI ) ndA <- data.frame( age= seq(40,100,0.1), tfI=0, lex.Cst="DM", sex="M" ) pri <- ci.pred( Pm, ndI ) * 1000 pra <- ci.pred( Pm, ndA ) * 1000 matshade( ndI$age, pri, plot=TRUE, las=1, xlab="Age (years)", ylab="DM mortality per 1000 PY", log="y", lty=1, col="blue" ) matshade( ndA$age, pra ) ################################################### ### code chunk number 34: flup.rnw:819-823 ################################################### library( survival ) cm <- coxph( Surv(age,age+lex.dur,lex.Xst=="Dead") ~ Ns(tfI,knots=i.kn) + lex.Cst + sex, data = tsNA20(dmCs) ) ################################################### ### code chunk number 35: flup.rnw:827-830 ################################################### Cm <- coxph.Lexis( tsNA20(dmCs), form= age ~ Ns(tfI,knots=i.kn) + lex.Cst + sex ) cbind( ci.exp( cm ), ci.exp( Cm ) ) ################################################### ### code chunk number 36: flup.rnw:839-842 ################################################### round( cbind( ci.exp( Pm ), rbind( matrix(NA,5,3), ci.exp( cm )[-6,] ) ), 3 ) ################################################### ### code chunk number 37: Ieff ################################################### nd <- data.frame( tfI=seq(0,15,,151), lex.Cst="Ins", sex="M" ) nr <- data.frame( tfI= 2 , lex.Cst="Ins", sex="M" ) ppr <- ci.exp( pm, list(nd,nr), xvars="age" ) cpr <- ci.exp( cm, list(nd,nr) ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( nd$tfI, cbind(ppr,cpr), plot=T, lty=c(1,2), log="y", xlab="Time since insulin (years)", ylab="Rate ratio") abline( h=1, lty=3 ) ################################################### ### code chunk number 38: IeffR ################################################### nd <- data.frame( tfI=seq(0,15,,151), lex.Cst="Ins", sex="M" ) nr <- data.frame( tfI= 0 , lex.Cst="DM" , sex="M" ) ppr <- ci.exp( pm, list(nd,nr), xvars="age" ) cpr <- ci.exp( cm, list(nd,nr) ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( nd$tfI, cbind(ppr,cpr), xlab="Time since insulin (years)", ylab="Rate ratio relative to non-Insulin", lty=c(1,2), log="y", plot=T ) ################################################### ### code chunk number 39: flup.rnw:948-953 ################################################### imx <- glm.Lexis( tsNA20(dmCs), formula = ~ Ns(age ,knots=a.kn) + Ns( tfI,knots=i.kn) + Ns(age-tfI,knots=a.kn) + lex.Cst + sex ) ################################################### ### code chunk number 40: flup.rnw:963-973 ################################################### Im <- glm.Lexis( tsNA20(dmCs), formula = ~ Ns(age ,knots=a.kn) + Ns( tfI,knots=i.kn) + Ns((age-tfI)*(lex.Cst=="Ins"),knots=a.kn) + lex.Cst + sex ) im <- glm.Lexis( tsNA20(dmCs), formula = ~ Ns(age ,knots=a.kn) + Ns( tfI,knots=i.kn) + lex.Cst:Ns(age-tfI,knots=a.kn) + lex.Cst + sex ) ################################################### ### code chunk number 41: flup.rnw:988-989 ################################################### anova( imx, Im, im, test='Chisq') ################################################### ### code chunk number 42: dur-int ################################################### pxi <- ci.pred( imx, ndI ) pxa <- ci.pred( imx, ndA ) pIi <- ci.pred( Im , ndI ) pIa <- ci.pred( Im , ndA ) pii <- ci.pred( im , ndI ) pia <- ci.pred( im , ndA ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( ndI$age, cbind( pxi, pIi, pii)*1000, plot=T, log="y", xlab="Age", ylab="Mortality per 1000 PY", lty=1, lwd=2, col=c("blue","forestgreen","red"), alpha=0.1 ) matshade( ndA$age, cbind( pxa, pIa, pia)*1000, lty=1, lwd=2, col=c("blue","forestgreen","red"), alpha=0.1 ) ################################################### ### code chunk number 43: dur-int-RR ################################################### ndR <- transform( ndI, tfI=0, lex.Cst="DM" ) cbind( head(ndI), head(ndR) ) Rxi <- ci.exp( imx, list(ndI,ndR) ) Rii <- ci.exp( im , list(ndI,ndR) ) RIi <- ci.exp( Im , list(ndI,ndR) ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( ndI$age, cbind( Rxi, RIi, Rii), plot=T, log="y", xlab="Age (years)", ylab="Rate ratio vs, non-Insulin", lty=1, lwd=2, col=c("blue","forestgreen","red"), alpha=0.1 ) abline( h=1 ) abline( h=ci.exp(imx,subset="lex.Cst")[,1], lty="25", col="blue" ) ################################################### ### code chunk number 44: splint ################################################### gm <- glm.Lexis( tsNA20(dmCs), formula = ~ Ns(age,knots=a.kn) + Ns(tfI,knots=i.kn) + lex.Cst:Ns(age,knots=a.kn):Ns(tfI,knots=i.kn) + lex.Cst + sex ) pgi <- ci.pred( gm, ndI ) pga <- ci.pred( gm, ndA ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( ndI$age, cbind( pgi, pii )*1000, plot=T, lty=c("solid","21"), lend="butt", lwd=2, log="y", xlab="Age (years)", ylab="Mortality rates per 1000 PY", alpha=c(0.2,0.1), col=c("black","red") ) matshade( ndA$age, cbind( pga, pia )*1000, lty=c("solid","21"), lend="butt", lwd=2, alpha=c(0.2,0.1), col=c("black","red") ) ################################################### ### code chunk number 45: RR-int ################################################### ndR <- transform( ndI, lex.Cst="DM", tfI=0 ) iRR <- ci.exp( im, ctr.mat=list(ndI,ndR) ) gRR <- ci.exp( gm, ctr.mat=list(ndI,ndR) ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( ndI$age, cbind(gRR,iRR), lty=1, log="y", plot=TRUE, xlab="Age (years)", ylab="Rate ratio: Ins vs. non-Ins", col=c("black","red") ) abline( h=1 ) ################################################### ### code chunk number 46: flup.rnw:1112-1125 ################################################### dmd <- glm.Lexis( dmCs, from="DM", to="Dead", formula = ~ Ns(age,knots=a.kn) + sex ) ind <- glm.Lexis( dmCs, from="Ins", to="Dead", formula = ~ Ns(age,knots=a.kn) + Ns(tfI,knots=i.kn) + Ns(age-tfI,knots=a.kn) + sex ) ini <- ci.pred( ind, ndI ) dmi <- ci.pred( dmd, ndI ) dma <- ci.pred( dmd, ndA ) ################################################### ### code chunk number 47: sep-mort ################################################### par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") matshade( ndI$age, ini*1000, plot=TRUE, log="y", xlab="Age (years)", ylab="Mortality rates per 1000 PY", lwd=2, col="red" ) matshade( ndA$age, dma*1000, lwd=2, col="black" ) ################################################### ### code chunk number 48: sep-HR ################################################### par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") matshade( ndI$age, ci.ratio(ini,dmi), plot=TRUE, log="y", xlab="Age (years)", ylab="RR insulin vs. no insulin", lwd=2, col="red" ) abline( h=1 ) ################################################### ### code chunk number 49: flup.rnw:1171-1179 ################################################### dmCs <- cutLexis( data = dmS2, cut = dmS2$doins, timescale = "per", new.state = "Ins", new.scale = "tfI", precursor.states = "DM", split.states = TRUE ) summary( dmCs ) ################################################### ### code chunk number 50: box4 ################################################### boxes( dmCs, boxpos=list(x=c(15,15,85,85), y=c(85,15,85,15)), scale.R=1000, show.BE=TRUE ) ################################################### ### code chunk number 51: flup.rnw:1209-1217 ################################################### dmM <- mcutLexis( dmL, timescale = "per", wh = c("doins","dooad"), new.states = c("Ins","OAD"), new.scales = c("tfI","tfO"), precursor.states = "DM", ties.resolve = TRUE ) summary( dmM, t=T ) ################################################### ### code chunk number 52: flup.rnw:1221-1226 ################################################### wh <- c(subset(dmM,lex.Cst=="Ins-OAD")$lex.id[1:2], subset(dmM,lex.Cst=="OAD-Ins")$lex.id[1:2]) options( width=110 ) print( subset( dmM, lex.id %in% wh )[,c('lex.id',names(dmM[1:8]),c("doins","dooad"))], digits=6, row.names=FALSE ) ################################################### ### code chunk number 53: mbox ################################################### boxes( dmM, boxpos=list(x=c(15,80,40,40,85,85), y=c(50,50,90,10,90,10)), scale.R=1000, show.BE=TRUE ) ################################################### ### code chunk number 54: mboxr ################################################### summary( dmMr <- Relevel( dmM, list('OAD+Ins'=5:6), first=FALSE) ) boxes( dmMr, boxpos=list(x=c(15,50,15,85,85), y=c(85,50,15,85,15)), scale.R=1000, show.BE=TRUE ) Epi/vignettes/yll.tex0000644000176200001440000010604614003563063014330 0ustar liggesusers%\VignetteIndexEntry{Years of life lost (YLL)} \documentclass[a4paper,twoside,12pt]{report} \newcommand{\Title}{Years of Life Lost (YLL) to disease\\Diabetes in DK as example} \newcommand{\Tit}{YLL} \newcommand{\Version}{February 1.2} \newcommand{\Dates}{November 2017} \newcommand{\Where}{SDC} \newcommand{\Homepage}{\url{http://bendixcarstensen.com/Epi}} \newcommand{\Faculty}{\begin{tabular}{rl} Bendix Carstensen & Steno Diabetes Center, Gentofte, Denmark\\ & {\small \& Department of Biostatistics, University of Copenhagen} \\ & \texttt{b@bxc.dk}\\ & \url{http://BendixCarstensen.com} \\[1em] \end{tabular}} \input{topreport} \renewcommand{\rwpre}{./yll} \chapter{Theory and technicalities} This vignette for the \texttt{Epi} package describes the probabilistic and demographic background for and technical implementation of the \texttt{erl} and \texttt{yll} functions that computes the expected residual life time and years of life lost in an illness-death model. \section{Years of life lost (YLL)} \ldots to diabetes or any other disease for that matter. The general concept in calculation of ``years lost to\ldots'' is the comparison of the expected lifetime between two groups of persons; one with and one without disease (in this example DM). The expected lifetime is the area under the survival curve, so basically the exercise requires that two survival curves that are deemed relevant be available. The years of life lost is therefore just the area between the survival curves for those ``Well'', $S_W(t)$, and for those ``Diseased'', $S_D(t)$: \[ \YLL = \int_0^\infty S_W(t) - S_D(t) \dif t \] The time $t$ could of course be age, but it could also be ``time after age 50'' and the survival curves compared would then be survival curves \emph{conditional} on survival till age 50, and the YLL would be the years of life lost for a 50-year old person with diabetes. If we are referring to the expected lifetime we will more precisely use the label expected residual lifetime, ERL. \section{Constructing the survival curves} YLL can be computed in two different ways, depending on the way the survival curve and hence the expected lifetime of a person \emph{without} diabetes is computed: \begin{itemize} \item Assume that the ``Well'' persons are \emph{immune} to disease --- using only the non-DM mortality rates throughout for calculation of expected life time. \item Assume that the ``Well'' persons \emph{can} acquire the disease and thereby see an increased mortality, thus involving all three rates shown in figure \ref{fig:states}. \end{itemize} The former gives a higher YLL because the comparison is to persons assumed immune to DM (and yet with the same mortality as non-immune prior to diagnosis), the latter gives a more realistic picture of the comparison of group of persons with and without diabetes at a given age that can be interpreted in the real world. The differences can be illustrated by figure \ref{fig:states}; the immune approach corresponds to an assumption of $\lambda(t)=0$ in the calculation of the survival curve for a person in the ``Well'' state. Calculation of the survival of a diseased person already in the ``DM'' state is unaffected by assumptions about $\lambda$. \insfig{states}{0.7}{Illness-death model describing diabetes incidence and -mortality.} \subsection{Total mortality --- a shortcut?} A practical crude shortcut could be to compare the ERL in the diabetic population to the ERL for the \emph{entire} population (that is use the total mortality ignoring diabetes status). Note however that this approach also counts the mortality of persons that acquired the disease earlier, thus making the comparison population on average more ill than the population we aim at, namely those well at a given time, which only then become more gradually ill. How large these effects are can however be empirically explored, as we shall do later. \subsection{Disease duration} In the exposition above there is no explicit provision for the effect of disease duration, but if we were able to devise mortality rates for any combination of age and duration, this could be taken into account. There are however severe limitations in this as we in principle would want to have duration effects as long as the age-effects --- in principle for all $(a,d)$ where $d\leq A$, where $A$ is the age at which we condition. So even if we were only to compute ERL from age, say, 40 we would still need duration effects up to 60 years (namely to age 100). The incorporation of duration effects is in principle trivial from a computational point of view, but we would be forced to entertain models predicting duration effects way beyond what is actually observed disease duration in any practical case. \subsection{Computing integrals} The practical calculations of survival curves, ERL and YLL involves calculation of (cumulative) integrals of rates and functions of these as we shall see below. This is easy if we have a closed form expression of the function, so its value may be computed at any time point --- this will be the case if we model rates by smooth parametric functions. Computing the (cumulative) integral of a function is done as follows: \begin{itemize} \item Compute the value of the function (mortality rate for example) at the midpoints of a sequence of narrow equidistant intervals --- for example one- or three month intervals of age, say. \item Take the cumulative sum of these values multiplied by the interval length --- this will be a very close approximation to the cumulative integral evaluated at the end of each interval. \item If the intervals are really small (like 1/100 year), the distinction between the value at the middle and at the end of each interval becomes irrelevant. \end{itemize} Note that in the above it is assumed that the rates are given in units corresponding to the interval length --- or more precisely, as the cumulative rates over the interval. \section{Survival functions in the illness-death model} The survival functions for persons in the ``Well'' state can be computed under two fundamentally different scenarios, depending on whether persons in the ``Well'' state are assumed to be immune to the disease ($\lambda(a)=0$) or not. \subsection{Immune approach} In this case both survival functions for person in the two states are the usual simple transformation of the cumulative mortality rates: \[ S_W(a) = \exp\left(-\int_0^a\!\!\mu_W(u) \dif u \right), \qquad S_D(a) = \exp\left(-\int_0^a\!\!\mu_D(u) \dif u \right) \] \subsubsection{Conditional survival functions} If we want the \emph{conditional} survival functions given survival to age $A$, say, they are just: \[ S_W(a|A) = S_W(a)/S_W(A), \qquad S_D(a|A) = S_D(a)/S_D(A) \] \subsection{Non-immune approach} For a diseased person, the survival function in this states is the same as above, but the survival function for a person without disease (at age 0) is (see figure \ref{fig:states}): \[ S(a) = \ptxt{Well}\!(a) + \ptxt{DM}\!(a) \] In the appendix of the paper \cite{Carstensen.2008c} is an indication of how to compute the probability of being in any of the four states shown in figure \ref{fig:states}, which I shall repeat here: In terms of the rates, the probability of being in the ``Well'' box is simply the probability of escaping both death (at a rate of $\mu_W(a)$) and diabetes (at a rate of $\lambda(a)$): \[ \ptxt{Well}(a) = \exp\left(\!-\int_0^a\!\!\mu_W(u)+\lambda(u) \right) \dif u \] The probability of being alive with diabetes at age $a$, is computed given that diabetes occurred at age $s$ ($s data( DMepi ) \end{Sinput} \end{Schunk} The dataset \texttt{DMepi} contains diabetes events, deaths and person-years for persons without diabetes and deaths and person-years for persons with diabetes: \begin{Schunk} \begin{Sinput} > str( DMepi ) \end{Sinput} \begin{Soutput} 'data.frame': 4200 obs. of 8 variables: $ sex : Factor w/ 2 levels "M","F": 1 1 1 1 1 1 1 1 1 1 ... $ A : num 0 0 0 0 0 0 0 0 0 0 ... $ P : num 1996 1997 1998 1999 2000 ... $ D.DM: num 0 0 0 0 0 0 0 0 0 0 ... $ Y.DM: num 0.484 0.64 1.641 0.552 2.507 ... $ X : num 1 2 4 4 4 1 1 3 4 1 ... $ D.nD: num 28 19 20 11 21 16 21 15 16 16 ... $ Y.nD: num 35469 35085 34240 34056 34002 ... \end{Soutput} \begin{Sinput} > head( DMepi ) \end{Sinput} \begin{Soutput} sex A P D.DM Y.DM X D.nD Y.nD 2 M 0 1996 0 0.4839151 1 28 35468.92 3 M 0 1997 0 0.6399726 2 19 35085.18 4 M 0 1998 0 1.6406571 4 20 34240.14 5 M 0 1999 0 0.5523614 4 11 34055.52 6 M 0 2000 0 2.5065024 4 21 34002.22 7 M 0 2001 0 0.1184120 1 16 34177.39 \end{Soutput} \end{Schunk} For each combination of sex, age, period and date of birth in 1 year age groups, we have the person-years in the ``Well'' (\texttt{Y.nD}) and the ``DM'' (\texttt{Y.DM}) states, as well as the number of deaths from these (\texttt{D.nD}, \texttt{D.DM}) and the number of incident diabetes cases from the ``Well'' state (\texttt{X}). In order to compute the years of life lost to diabetes and how this has changed over time, we fit models for the mortality and incidence of both groups (and of course, separately for men and women). The models we use will be age-period-cohort models \cite{Carstensen.2007a} providing estimated mortality rates for ages 0--99 and dates 1.1.1996--1.1.2016. First we transform the age and period variables to reflect the mean age and period in each of the Lexis triangles. We also compute the total number of deaths and amount of risk time, as we are going to model the total mortality as well. Finally we restrict the dataset to ages over 30 only: \begin{Schunk} \begin{Sinput} > DMepi <- transform( subset( DMepi, A>30 ), + D.T = D.nD + D.DM, + Y.T = Y.nD + Y.DM ) > head(DMepi) \end{Sinput} \begin{Soutput} sex A P D.DM Y.DM X D.nD Y.nD D.T Y.T 684 M 31 1996 0 305.9671 29 51 44161.83 51 44467.80 685 M 31 1997 2 326.2074 31 54 45508.64 56 45834.85 686 M 31 1998 2 340.1759 34 46 44954.45 48 45294.63 687 M 31 1999 5 330.9918 24 39 41148.97 44 41479.96 688 M 31 2000 1 332.0876 41 26 39027.30 27 39359.39 689 M 31 2001 2 310.8467 35 33 37975.78 35 38286.63 \end{Soutput} \end{Schunk} With the correct age and period coding in the Lexis triangles, we fit models for the mortalities and incidences. Note that we for comparative purposes also fit a model for the \emph{total} mortality, ignoring the \begin{Schunk} \begin{Sinput} > # Knots used in all models > ( a.kn <- seq(40,95,,6) ) \end{Sinput} \begin{Soutput} [1] 40 51 62 73 84 95 \end{Soutput} \begin{Sinput} > ( p.kn <- seq(1997,2015,,4) ) \end{Sinput} \begin{Soutput} [1] 1997 2003 2009 2015 \end{Soutput} \begin{Sinput} > ( c.kn <- seq(1910,1976,,6) ) \end{Sinput} \begin{Soutput} [1] 1910.0 1923.2 1936.4 1949.6 1962.8 1976.0 \end{Soutput} \begin{Sinput} > # Check the number of events between knots > ae <- xtabs( cbind(D.nD,D.DM,X) ~ cut(A,c(30,a.kn,Inf)) + sex, data=DMepi ) > ftable( addmargins(ae,1), col.vars=3:2 ) \end{Sinput} \begin{Soutput} D.nD D.DM X sex M F M F M F cut(A, c(30, a.kn, Inf)) (30,40] 9135 4650 597 277 12080 9648 (40,51] 25535 15784 2947 1439 35445 23925 (51,62] 59698 40171 10838 5253 60539 40034 (62,73] 106519 81253 26197 14299 55908 44221 (73,84] 158365 156678 34510 28834 27985 30381 (84,95] 100880 179466 16194 25317 5272 8967 (95,Inf] 6095 21414 640 1928 90 288 Sum 466227 499416 91923 77347 197319 157464 \end{Soutput} \begin{Sinput} > pe <- xtabs( cbind(D.nD,D.DM,X) ~ cut(P,c(1990,p.kn,Inf)) + sex, data=DMepi ) > ftable( addmargins(pe,1), col.vars=3:2 ) \end{Sinput} \begin{Soutput} D.nD D.DM X sex M F M F M F cut(P, c(1990, p.kn, Inf)) (1990,1997] 51569 53567 6407 5990 13175 10960 (1997,2003] 144136 155695 22390 19922 49805 41277 (2003,2009] 131159 141782 26079 22249 60554 48066 (2009,2015] 119812 127714 31285 24704 63440 49457 (2015,Inf] 19551 20658 5762 4482 10345 7704 Sum 466227 499416 91923 77347 197319 157464 \end{Soutput} \begin{Sinput} > ce <- xtabs( cbind(D.nD,D.DM,X) ~ cut(P-A,c(-Inf,c.kn,Inf)) + sex, data=DMepi ) > ftable( addmargins(ce,1), col.vars=3:2 ) \end{Sinput} \begin{Soutput} D.nD D.DM X sex M F M F M F cut(P - A, c(-Inf, c.kn, Inf)) (-Inf,1.91e+03] 19679 49020 2004 4446 599 1416 (1.91e+03,1.92e+03] 129799 189192 19780 26870 10665 15275 (1.92e+03,1.94e+03] 158953 152454 35667 28471 37850 36659 (1.94e+03,1.95e+03] 99058 72432 25494 13074 71489 50631 (1.95e+03,1.96e+03] 44129 28315 7534 3731 51750 34255 (1.96e+03,1.98e+03] 13598 7484 1373 720 22942 17689 (1.98e+03, Inf] 1011 519 71 35 2024 1539 Sum 466227 499416 91923 77347 197319 157464 \end{Soutput} \begin{Sinput} > # Fit an APC-model for all transitions, seperately for men and women > mW.m <- glm( D.nD ~ -1 + Ns(A ,knots=a.kn,int=TRUE) + + Ns( P,knots=p.kn,ref=2005) + + Ns(P-A,knots=c.kn,ref=1950), + offset = log(Y.nD), + family = poisson, + data = subset( DMepi, sex=="M" ) ) > mD.m <- update( mW.m, D.DM ~ . , offset=log(Y.DM) ) > mT.m <- update( mW.m, D.T ~ . , offset=log(Y.T ) ) > lW.m <- update( mW.m, X ~ . ) > # Model for women > mW.f <- update( mW.m, data = subset( DMepi, sex=="F" ) ) > mD.f <- update( mD.m, data = subset( DMepi, sex=="F" ) ) > mT.f <- update( mT.m, data = subset( DMepi, sex=="F" ) ) > lW.f <- update( lW.m, data = subset( DMepi, sex=="F" ) ) \end{Sinput} \end{Schunk} \section{Residual life time and years lost to DM} We now collect the estimated years of life lost classified by method (immune assumption or not), sex, age and calendar time: \begin{Schunk} \begin{Sinput} > a.ref <- 30:90 > p.ref <- 1996:2016 > aYLL <- NArray( list( type = c("Imm","Tot","Sus"), + sex = levels( DMepi$sex ), + age = a.ref, + date = p.ref ) ) > str( aYLL ) \end{Sinput} \begin{Soutput} logi [1:3, 1:2, 1:61, 1:21] NA NA NA NA NA NA ... - attr(*, "dimnames")=List of 4 ..$ type: chr [1:3] "Imm" "Tot" "Sus" ..$ sex : chr [1:2] "M" "F" ..$ age : chr [1:61] "30" "31" "32" "33" ... ..$ date: chr [1:21] "1996" "1997" "1998" "1999" ... \end{Soutput} \begin{Sinput} > system.time( + for( ip in p.ref ) + { + nd <- data.frame( A = seq(30,90,0.2)+0.1, + P = ip, + Y.nD = 1, + Y.DM = 1, + Y.T = 1 ) + muW.m <- ci.pred( mW.m, nd )[,1] + muD.m <- ci.pred( mD.m, nd )[,1] + muT.m <- ci.pred( mT.m, nd )[,1] + lam.m <- ci.pred( lW.m, nd )[,1] + muW.f <- ci.pred( mW.f, nd )[,1] + muD.f <- ci.pred( mD.f, nd )[,1] + muT.f <- ci.pred( mT.f, nd )[,1] + lam.f <- ci.pred( lW.f, nd )[,1] + aYLL["Imm","M",,paste(ip)] <- yll( int=0.2, muW.m, muD.m, lam=NULL, + A=a.ref, age.in=30, note=FALSE )[-1] + aYLL["Imm","F",,paste(ip)] <- yll( int=0.2, muW.f, muD.f, lam=NULL, + A=a.ref, age.in=30, note=FALSE )[-1] + aYLL["Tot","M",,paste(ip)] <- yll( int=0.2, muT.m, muD.m, lam=NULL, + A=a.ref, age.in=30, note=FALSE )[-1] + aYLL["Tot","F",,paste(ip)] <- yll( int=0.2, muT.f, muD.f, lam=NULL, + A=a.ref, age.in=30, note=FALSE )[-1] + aYLL["Sus","M",,paste(ip)] <- yll( int=0.2, muW.m, muD.m, lam=lam.m, + A=a.ref, age.in=30, note=FALSE )[-1] + aYLL["Sus","F",,paste(ip)] <- yll( int=0.2, muW.f, muD.f, lam=lam.f, + A=a.ref, age.in=30, note=FALSE )[-1] + } ) \end{Sinput} \begin{Soutput} user system elapsed 17.679 8.252 15.803 \end{Soutput} \begin{Sinput} > round( ftable( aYLL[,,seq(1,61,10),], col.vars=c(3,2) ), 1 ) \end{Sinput} \begin{Soutput} age 30 40 50 60 70 80 90 sex M F M F M F M F M F M F M F type date Imm 1996 11.3 10.2 9.4 9.1 7.4 7.6 5.4 5.9 3.4 3.8 1.5 1.6 0.0 0.0 1997 11.1 9.9 9.2 8.9 7.3 7.4 5.3 5.7 3.3 3.7 1.4 1.5 0.0 0.0 1998 10.9 9.7 9.1 8.6 7.2 7.2 5.3 5.5 3.3 3.6 1.4 1.5 0.0 0.0 1999 10.7 9.4 9.0 8.4 7.1 7.0 5.2 5.3 3.3 3.5 1.4 1.5 0.0 0.0 2000 10.5 9.1 8.8 8.2 6.9 6.8 5.1 5.1 3.2 3.4 1.4 1.4 0.0 0.0 2001 10.3 8.9 8.6 7.9 6.8 6.6 5.0 5.0 3.1 3.2 1.3 1.4 0.0 0.0 2002 10.0 8.6 8.4 7.7 6.6 6.3 4.9 4.8 3.1 3.1 1.3 1.3 0.0 0.0 2003 9.7 8.3 8.2 7.4 6.4 6.1 4.7 4.6 3.0 3.0 1.3 1.3 0.0 0.0 2004 9.4 8.0 7.9 7.1 6.2 5.9 4.5 4.4 2.8 2.8 1.2 1.2 0.0 0.0 2005 9.0 7.6 7.6 6.9 6.0 5.6 4.4 4.1 2.7 2.6 1.1 1.1 0.0 0.0 2006 8.6 7.3 7.4 6.6 5.8 5.4 4.2 3.9 2.6 2.5 1.1 1.1 0.0 0.0 2007 8.3 7.0 7.1 6.3 5.5 5.2 4.0 3.8 2.5 2.4 1.0 1.0 0.0 0.0 2008 8.0 6.8 6.8 6.1 5.4 5.0 3.8 3.6 2.4 2.2 1.0 0.9 0.0 0.0 2009 7.7 6.6 6.6 6.0 5.2 4.9 3.7 3.5 2.3 2.1 0.9 0.9 0.0 0.0 2010 7.5 6.4 6.5 5.8 5.1 4.8 3.7 3.4 2.2 2.1 0.9 0.9 0.0 0.0 2011 7.4 6.3 6.4 5.8 5.1 4.7 3.6 3.4 2.2 2.0 0.9 0.8 0.0 0.0 2012 7.3 6.3 6.4 5.7 5.1 4.7 3.6 3.3 2.2 2.0 0.9 0.8 0.0 0.0 2013 7.3 6.2 6.4 5.7 5.1 4.7 3.6 3.3 2.2 2.0 0.9 0.8 0.0 0.0 2014 7.3 6.2 6.4 5.7 5.1 4.7 3.7 3.4 2.2 2.0 0.9 0.8 0.0 0.0 2015 7.3 6.2 6.4 5.7 5.2 4.8 3.7 3.4 2.3 2.0 0.9 0.8 0.0 0.0 2016 7.3 6.2 6.4 5.7 5.2 4.8 3.8 3.4 2.3 2.0 0.9 0.8 0.0 0.0 Tot 1996 10.7 9.8 8.8 8.7 6.9 7.2 5.0 5.5 3.1 3.5 1.3 1.4 0.0 0.0 1997 10.5 9.5 8.6 8.4 6.7 7.0 4.9 5.3 3.0 3.4 1.3 1.4 0.0 0.0 1998 10.3 9.2 8.5 8.2 6.6 6.8 4.8 5.1 3.0 3.3 1.3 1.4 0.0 0.0 1999 10.0 8.9 8.3 7.9 6.5 6.5 4.7 4.9 2.9 3.2 1.3 1.3 0.0 0.0 2000 9.8 8.7 8.1 7.7 6.3 6.3 4.6 4.7 2.9 3.1 1.2 1.3 0.0 0.0 2001 9.6 8.4 7.9 7.4 6.2 6.1 4.5 4.6 2.8 2.9 1.2 1.2 0.0 0.0 2002 9.3 8.1 7.7 7.2 6.0 5.9 4.3 4.4 2.7 2.8 1.2 1.2 0.0 0.0 2003 9.0 7.8 7.5 6.9 5.8 5.6 4.2 4.2 2.6 2.7 1.1 1.1 0.0 0.0 2004 8.6 7.5 7.2 6.6 5.6 5.4 4.0 4.0 2.5 2.5 1.1 1.1 0.0 0.0 2005 8.3 7.1 6.9 6.4 5.3 5.1 3.8 3.7 2.4 2.4 1.0 1.0 0.0 0.0 2006 7.9 6.8 6.6 6.1 5.1 4.9 3.6 3.6 2.2 2.2 0.9 0.9 0.0 0.0 2007 7.6 6.5 6.4 5.9 4.9 4.7 3.4 3.4 2.1 2.1 0.9 0.9 0.0 0.0 2008 7.3 6.3 6.1 5.6 4.7 4.5 3.3 3.2 2.0 2.0 0.8 0.8 0.0 0.0 2009 7.0 6.1 5.9 5.5 4.5 4.4 3.2 3.1 1.9 1.9 0.8 0.8 0.0 0.0 2010 6.8 5.9 5.8 5.4 4.4 4.3 3.1 3.0 1.8 1.8 0.8 0.7 0.0 0.0 2011 6.7 5.8 5.7 5.3 4.4 4.3 3.0 3.0 1.8 1.7 0.7 0.7 0.0 0.0 2012 6.6 5.8 5.6 5.2 4.3 4.2 3.0 2.9 1.8 1.7 0.7 0.7 0.0 0.0 2013 6.5 5.7 5.6 5.2 4.3 4.2 3.0 2.9 1.8 1.7 0.7 0.7 0.0 0.0 2014 6.5 5.7 5.6 5.2 4.4 4.2 3.0 2.9 1.8 1.7 0.7 0.7 0.0 0.0 2015 6.4 5.6 5.6 5.2 4.4 4.2 3.1 2.9 1.8 1.7 0.7 0.7 0.0 0.0 2016 6.4 5.6 5.6 5.2 4.4 4.3 3.1 3.0 1.8 1.7 0.8 0.7 0.0 0.0 Sus 1996 10.3 9.4 8.4 8.4 6.6 7.0 5.0 5.5 3.2 3.6 1.4 1.5 0.0 0.0 1997 10.1 9.2 8.3 8.2 6.5 6.8 4.9 5.3 3.1 3.5 1.4 1.5 0.0 0.0 1998 9.9 8.9 8.1 7.9 6.4 6.6 4.8 5.1 3.1 3.4 1.4 1.5 0.0 0.0 1999 9.7 8.6 8.0 7.7 6.3 6.4 4.7 4.9 3.1 3.3 1.4 1.4 0.0 0.0 2000 9.4 8.3 7.8 7.4 6.1 6.2 4.6 4.7 3.0 3.2 1.3 1.4 0.0 0.0 2001 9.2 8.1 7.6 7.2 6.0 5.9 4.5 4.5 2.9 3.0 1.3 1.3 0.0 0.0 2002 8.9 7.8 7.4 6.9 5.8 5.7 4.4 4.4 2.8 2.9 1.3 1.3 0.0 0.0 2003 8.6 7.5 7.2 6.7 5.6 5.5 4.2 4.2 2.7 2.8 1.2 1.2 0.0 0.0 2004 8.3 7.1 6.9 6.4 5.4 5.3 4.0 4.0 2.6 2.6 1.2 1.2 0.0 0.0 2005 7.9 6.8 6.6 6.1 5.2 5.0 3.8 3.8 2.5 2.5 1.1 1.1 0.0 0.0 2006 7.5 6.5 6.3 5.9 5.0 4.8 3.7 3.6 2.4 2.3 1.0 1.0 0.0 0.0 2007 7.2 6.3 6.1 5.6 4.7 4.6 3.5 3.4 2.3 2.2 1.0 1.0 0.0 0.0 2008 6.9 6.0 5.9 5.5 4.6 4.5 3.4 3.3 2.2 2.1 0.9 0.9 0.0 0.0 2009 6.7 5.8 5.7 5.3 4.4 4.3 3.3 3.2 2.1 2.0 0.9 0.9 0.0 0.0 2010 6.5 5.7 5.6 5.2 4.4 4.3 3.2 3.1 2.0 1.9 0.9 0.8 0.0 0.0 2011 6.4 5.6 5.5 5.1 4.3 4.2 3.2 3.1 2.0 1.9 0.9 0.8 0.0 0.0 2012 6.4 5.6 5.5 5.1 4.4 4.2 3.2 3.1 2.0 1.9 0.9 0.8 0.0 0.0 2013 6.4 5.6 5.5 5.1 4.4 4.3 3.2 3.1 2.0 1.9 0.9 0.8 0.0 0.0 2014 6.4 5.6 5.5 5.2 4.5 4.3 3.3 3.1 2.1 1.9 0.9 0.8 0.0 0.0 2015 6.4 5.6 5.6 5.2 4.5 4.4 3.3 3.1 2.1 1.9 0.9 0.8 0.0 0.0 2016 6.4 5.6 5.6 5.2 4.6 4.4 3.4 3.2 2.1 1.9 0.9 0.8 0.0 0.0 \end{Soutput} \end{Schunk} We now have the relevant points for the graph showing YLL to diabetes for men and women by age, and calendar year, both under the immunity and susceptibility models for the calculation of YLL. \begin{Schunk} \begin{Sinput} > plyll <- function(wh){ + par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, bty="n", las=1 ) + + matplot( a.ref, aYLL[wh,"M",,], + type="l", lty=1, col="blue", lwd=1:2, + ylim=c(0,12), xlab="Age", + ylab="Years lost to DM", yaxs="i" ) + abline(v=50,h=1:10,col=gray(0.7)) + text( 90, 11, "Men", col="blue", adj=1 ) + text( 40, aYLL[wh,"M","40","1996"], "1996", adj=c(0,0), col="blue" ) + text( 43, aYLL[wh,"M","44","2016"], "2016", adj=c(1,1), col="blue" ) + + matplot( a.ref, aYLL[wh,"F",,], + type="l", lty=1, col="red", lwd=1:2, + ylim=c(0,12), xlab="Age", + ylab="Years lost to DM", yaxs="i" ) + abline(v=50,h=1:10,col=gray(0.7)) + text( 90, 11, "Women", col="red", adj=1 ) + text( 40, aYLL[wh,"F","40","1996"], "1996", adj=c(0,0), col="red" ) + text( 43, aYLL[wh,"F","44","2016"], "2016", adj=c(1,1), col="red" ) + } > plyll("Imm") \end{Sinput} \end{Schunk} \begin{Schunk} \begin{Sinput} > plyll("Tot") \end{Sinput} \end{Schunk} \begin{Schunk} \begin{Sinput} > plyll("Sus") \end{Sinput} \end{Schunk} \begin{figure}[h] \centering \includegraphics[width=\textwidth]{yll-imm} \caption{Years of life lost to DM: the difference in expected residual life time at different ages between persons with and without diabetes, assuming the persons without diabetes at a given age remain free from diabetes (immunity assumption --- not reasonable). The lines refer to date of evaluation; the top lines refer to 1.1.1996 the bottom ones to 1.1.2016. Blue curves are men, red women.} \label{fig:imm} \end{figure} \begin{figure}[h] \centering \includegraphics[width=\textwidth]{yll-sus} \caption{Years of life lost to DM: the difference in expected residual life time at different ages between persons with and without diabetes, allowing the persons without diabetes at a given to contract diabetes and thus be subject to higher mortality. The lines refer to date of evaluation; the top lines refer to 1.1.1996 the bottom ones to 1.1.2016. Blue curves are men, red women.} \label{fig:sus} \end{figure} \begin{figure}[h] \centering \includegraphics[width=\textwidth]{yll-tot} \caption{Years of life lost to DM: the difference in expected residual life time at different ages between persons with and without diabetes. Allowance for susceptibility is approximated by using the total population mortality instead of non-DM mortality. The lines refer to date of evaluation; the top lines refer to 1.1.1996 the bottom ones to 1.1.2016. Blue curves are men, red women.} \label{fig:tot} \end{figure} From figure \ref{fig:sus} we see that for men aged 50 the years lost to diabetes has decreased from a bit over 8 to a bit less than 6 years, and for women from 8.5 to 5 years; so a greater improvement for women. \chapter{Practical implementation} We have devised functions that wraps these formulae up for practical use. \section{Function definitions} % The following code sources the originally formatted code in erl.R in % order to make it printable with all the formatting and comments in % it. However the sourcing does not work when compiling the vignettes % in R CMD build. So when checking the code we comment this out by % putting eval=FALSE. So depending on whether we actually construct % the pdf for the inst/doc folder or test (upload) the package, one of % the following two chunks are run with eval=FALSE and the other with % eval=TRUE. % When checking the package When using the functions it is assumed that the functions $\mu_W$, $\mu_D$ and $\lambda$ are given as vectors corresponding to equidistantly (usually tightly) spaced ages from 0 to $K$ where K is the age where everyone can safely be assumed dead. \texttt{surv1} is a simple function that computes the survival function from a vector of mortality rates, and optionally the conditional survival given being alive at prespecified ages: \begin{Schunk} \begin{Sinput} > surv1 \end{Sinput} \begin{Soutput} function (int, mu, age.in = 0, A = NULL) { if (any(is.na(mu))) { mu[is.na(mu)] <- 0 warning("NAs in agument 'mu' set to 0") } age <- 0:length(mu) * int + age.in Mu <- c(0, cumsum(mu) * int) Sv <- exp(-Mu) surv <- data.frame(age = age, surv = Sv) if (cond <- !is.null(A)) { j <- 0 cage <- NULL for (ia in A) { j <- j + 1 cA <- which(diff(age > ia) == 1) surv <- cbind(surv, pmin(1, surv$surv/(surv$surv[cA]))) cage[j] <- surv$age[cA] } } names(surv)[-1] <- paste("A", c(age.in, if (cond) cage else NULL), sep = "") rownames(surv) <- NULL return(surv) } \end{Soutput} \end{Schunk} \texttt{erl1} basically just expands the result of \texttt{surv1} with a column of expected residual life times: \begin{Schunk} \begin{Sinput} > erl1 \end{Sinput} \begin{Soutput} function (int, mu, age.in = 0) { age <- 0:length(mu) * int + age.in musmuc <- function(x) rev(cumsum(rev(x))) surv <- surv1(int = int, mu = mu, age.in = age.in)[, 2] cbind(age = age, surv = surv, erl = c(musmuc((surv[-1] - diff(surv)/2))/surv[-length(surv)], 0) * int) } \end{Soutput} \end{Schunk} We also define a function, \texttt{surv2}, that computes the survival function for a non-diseased person that may become diseased with rate \texttt{lam} and after that die at a rate of \texttt{muD} (corresponding to the formulae above). This is the sane way of handling years of life lost to a particular illness: \begin{Schunk} \begin{Sinput} > surv2 \end{Sinput} \begin{Soutput} function (int, muW, muD, lam, age.in = 0, A = NULL) { if (length(muW) != length(muD) | length(muD) != length(lam)) stop("Vectors with rates must have same length:\n", "length(muW)=", length(muW), ", length(muD)=", length(muD), ", length(lam)=", length(lam)) if (!is.null(lam)) { if (any(is.na(lam))) { lam[is.na(lam)] <- 0 warning("NAs in agument 'lam' set to 0") } } if (any(is.na(muD))) { muD[is.na(muD)] <- 0 warning("NAs in agument 'muD' set to 0") } if (any(is.na(muW))) { muW[is.na(muW)] <- 0 warning("NAs in agument 'muW' set to 0") } wsurv2 <- function(int, muW, muD, lam, age.in = 0, A = 0) { age <- 0:length(muW) * int + age.in MuW <- cumsum(c(0, muW) * (age > A)) * int MuD <- cumsum(c(0, muD) * (age > A)) * int Lam <- cumsum(c(0, lam) * (age > A)) * int pW <- exp(-(Lam + MuW)) Dis <- c(0, lam) * (age > A) * exp(-(Lam + MuW)) * int pDM <- Dis * 0 for (ia in 1:length(age)) pDM[ia] <- sum(Dis[1:ia] * exp(-(MuD[ia] - MuD[1:ia]))) surv <- data.frame(age = age, surv = pDM + pW) return(surv) } surv <- wsurv2(int, muW, muD, lam, age.in = age.in, A = 0) if (!is.null(A)) { for (j in 1:length(A)) { surv <- cbind(surv, wsurv2(int, muW, muD, lam, age.in = age.in, A = A[j])[, 2]) } } Al <- A for (i in 1:length(A)) Al[i] <- max(surv$age[surv$age <= A[i]]) colnames(surv)[-1] <- paste("A", c(age.in, Al), sep = "") return(surv) } \end{Soutput} \end{Schunk} Finally we devised a function using these to compute the expected residual lifetime at select ages: \begin{Schunk} \begin{Sinput} > erl \end{Sinput} \begin{Soutput} function (int, muW, muD, lam = NULL, age.in = 0, A = NULL, immune = is.null(lam), yll = TRUE, note = TRUE) { trsum <- function(x) { x[c(diff(x) == 0, TRUE)] <- NA sum((x[-length(x)] + x[-1])/2, na.rm = TRUE) } if (!immune & is.null(lam)) stop("'lam' is required when immune=FALSE\n") if (!is.null(lam)) { if (any(is.na(lam))) { lam[is.na(lam)] <- 0 warning("NAs in agument 'lam' set to 0") } } if (any(is.na(muD))) { muD[is.na(muD)] <- 0 warning("NAs in agument 'muD' set to 0") } if (any(is.na(muW))) { muW[is.na(muW)] <- 0 warning("NAs in agument 'muW' set to 0") } sD <- surv1(int = int, muD, age.in = age.in, A = A) if (immune) sW <- surv1(int = int, muW, age.in = age.in, A = A) else sW <- surv2(int = int, muW, muD, lam, age.in = age.in, A = A) erl <- cbind(apply(sW[, -1], 2, trsum), apply(sD[, -1], 2, trsum)) * int colnames(erl) <- c("Well", "Dis") rownames(erl) <- colnames(sW)[-1] if (yll) erl <- cbind(erl, YLL = erl[, "Well"] - erl[, "Dis"]) if (immune) { attr(erl, "NOTE") <- "Calculations assume that Well persons cannot get Ill (quite silly!)." if (note) cat("NOTE:", attr(erl, "NOTE"), "\n") } return(erl) } \end{Soutput} \end{Schunk} \ldots and a wrapper for this if we only want the years of life lost returned: \begin{Schunk} \begin{Sinput} > yll \end{Sinput} \begin{Soutput} function (int, muW, muD, lam = NULL, age.in = 0, A = NULL, immune = is.null(lam), note = TRUE) erl(int = int, muW = muW, muD = muD, lam = lam, age.in = age.in, A = A, immune = immune, yll = TRUE, note = note)[, "YLL"] \end{Soutput} \end{Schunk} \bibliographystyle{plain} \begin{thebibliography}{1} \bibitem{Carstensen.2007a} B~Carstensen. \newblock Age-{P}eriod-{C}ohort models for the {L}exis diagram. \newblock {\em Statistics in Medicine}, 26(15):3018--3045, 2007. \bibitem{Carstensen.2008c} B~Carstensen, JK~Kristensen, P~Ottosen, and K~Borch-Johnsen. \newblock The {D}anish {N}ational {D}iabetes {R}egister: {T}rends in incidence, prevalence and mortality. \newblock {\em Diabetologia}, 51:2187--2196, 2008. \end{thebibliography} \addcontentsline{toc}{chapter}{References} \end{document} Epi/vignettes/toparticle.tex0000644000176200001440000000715613240230017015670 0ustar liggesusers %---------------------------------------------------------------------- %\usepackage[inline]{showlabels} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[english]{babel} \usepackage[font=it,labelfont=normalfont]{caption} \usepackage[colorlinks,urlcolor=blue,linkcolor=red,citecolor=Maroon]{hyperref} % \usepackage[ae,hyper]{Rd} \usepackage[dvipsnames]{xcolor} \usepackage[super]{nth} % \usepackage[retainorgcmds]{IEEEtrantools} \usepackage{makeidx,Sweave,floatflt,amsmath,amsfonts,amsbsy,enumitem,verbatim,dcolumn,needspace} \usepackage{booktabs,longtable,rotating,graphicx,verbatim,fancyhdr,datetime,afterpage,setspace} \usepackage{ifthen,calc,eso-pic,everyshi,pdfpages} \usepackage[abspath]{currfile} % \usepackage{mslapa} \definecolor{blaa}{RGB}{99,99,255} \DeclareGraphicsExtensions{.png,.pdf,.jpg} % Make the Sweave output nicer \DefineVerbatimEnvironment{Sinput}{Verbatim}{fontsize=\footnotesize,fontshape=sl,formatcom=\color{Blue}} \DefineVerbatimEnvironment{Soutput}{Verbatim}{fontsize=\footnotesize,formatcom=\color{Maroon},xleftmargin=0em} \DefineVerbatimEnvironment{Scode}{Verbatim}{fontsize=\footnotesize} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}% {\renewcommand{\baselinestretch}{0.85} \vspace{\topsep}}% {\renewcommand{\baselinestretch}{1.00} \vspace{\topsep}} %---------------------------------------------------------------------- % The usual usefuls \input{useful.tex} \setcounter{secnumdepth}{2} \setcounter{tocdepth}{2} %---------------------------------------------------------------------- % How to insert a figure \newcommand{\rwpre}{./graph/gr} \newcommand{\insfig}[3]{ \begin{figure}[h] \centering \includegraphics[width=#2\textwidth]{\rwpre-#1} \caption{#3} \label{fig:#1} % \afterpage{\clearpage} \end{figure}} %---------------------------------------------------------------------- % Set up layout of pages \oddsidemargin 1mm \evensidemargin 1mm \topmargin -5mm \headheight 8mm \headsep 8mm \textheight 230mm \textwidth 165mm %\footheight 5mm \footskip 15mm \renewcommand{\topfraction}{0.9} \renewcommand{\bottomfraction}{0.9} \renewcommand{\textfraction}{0.1} \renewcommand{\floatpagefraction}{0.9} \renewcommand{\headrulewidth}{0.1pt} \setcounter{secnumdepth}{4} \setcounter{tocdepth}{4} %---------------------------------------------------------------------- % Here is the document starting with the titlepage \begin{document} %---------------------------------------------------------------------- % The title page \setcounter{page}{1} \pagenumbering{roman} \pagestyle{plain} \thispagestyle{empty} %\vspace*{0.1\textheight} \flushright {\Huge \bfseries \Title }\ \\[-1.5ex] \noindent\textcolor{blaa}{\rule[-1ex]{\textwidth}{5pt}}\\[2.5ex] \large \Where \\ \Homepage \\ \Dates \\ \Version \\[1em] \normalsize Compiled \today,\ \currenttime\\ from: \texttt{\currfileabspath}\\[1em] \normalsize \vfill \Faculty % End of titlepage \newpage \raggedright \parindent 1em \parskip 0ex % \section*{Preface} % Here is space for the preface % \input{preface} %---------------------------------------------------------------------- % Table of contents \tableofcontents \newpage % \listoftables % \listoffigures % \cleardoublepage %---------------------------------------------------------------------- % General page style \pagenumbering{arabic} \setcounter{page}{1} \pagestyle{fancy} \renewcommand{\sectionmark}[1]{\markright{%\thesection\ \textsl{#1}}{}} \fancyhead[EL]{\bf \thepage} \fancyhead[ER]{\sl \Tit} \fancyhead[OR]{\bf \thepage} \fancyhead[OL]{\rm \rightmark} \fancyfoot{} Epi/vignettes/simLexis.R0000644000176200001440000004201314003562715014722 0ustar liggesusers### R code from vignette source 'simLexis' ### Encoding: UTF-8 ################################################### ### code chunk number 1: simLexis.rnw:23-26 ################################################### options( width=90, SweaveHooks=list( fig=function() par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") ) ) ################################################### ### code chunk number 2: start ################################################### options( width=90 ) library( Epi ) print( sessionInfo(), l=F ) ################################################### ### code chunk number 3: Lexis ################################################### data(DMlate) dml <- Lexis( entry = list(Per=dodm, Age=dodm-dobth, DMdur=0 ), exit = list(Per=dox), exit.status = factor(!is.na(dodth),labels=c("DM","Dead")), data = DMlate ) ################################################### ### code chunk number 4: cut ################################################### dmi <- cutLexis( dml, cut = dml$doins, pre = "DM", new.state = "Ins", new.scale = "t.Ins", split.states = TRUE ) summary( dmi, timeScales=T ) ################################################### ### code chunk number 5: boxes ################################################### boxes( dmi, boxpos = list(x=c(20,20,80,80), y=c(80,20,80,20)), scale.R = 1000, show.BE = TRUE ) ################################################### ### code chunk number 6: split ################################################### Si <- splitLexis( dmi, seq(0,20,1/4), "DMdur" ) summary( Si ) print( subset( Si, lex.id==97 )[,1:10], digits=6 ) ################################################### ### code chunk number 7: knots ################################################### nk <- 5 ( ai.kn <- with( subset(Si,lex.Xst=="Ins" & lex.Cst!=lex.Xst ), quantile( Age+lex.dur , probs=(1:nk-0.5)/nk ) ) ) ( ad.kn <- with( subset(Si,lex.Xst=="Dead"), quantile( Age+lex.dur , probs=(1:nk-0.5)/nk ) ) ) ( di.kn <- with( subset(Si,lex.Xst=="Ins" & lex.Cst!=lex.Xst ), c(0,quantile( DMdur+lex.dur, probs=(1:(nk-1))/nk ) )) ) ( dd.kn <- with( subset(Si,lex.Xst=="Dead"), c(0,quantile( DMdur+lex.dur, probs=(1:(nk-1))/nk ) )) ) ( ti.kn <- with( subset(Si,lex.Xst=="Dead(Ins)"), c(0,quantile( t.Ins+lex.dur, probs=(1:(nk-1))/nk ) )) ) ################################################### ### code chunk number 8: Poisson ################################################### library( splines ) DM.Ins <- glm( (lex.Xst=="Ins") ~ Ns( Age , knots=ai.kn ) + Ns( DMdur, knots=di.kn ) + I(Per-2000) + sex, family=poisson, offset=log(lex.dur), data = subset(Si,lex.Cst=="DM") ) ci.exp( DM.Ins ) class( DM.Ins ) ################################################### ### code chunk number 9: simLexis.rnw:282-288 ################################################### DM.Ins <- glm.Lexis( Si, from = "DM", to = "Ins", formula = ~ Ns( Age , knots=ai.kn ) + Ns( DMdur, knots=di.kn ) + I(Per-2000) + sex ) ci.exp( DM.Ins ) class( DM.Ins ) ################################################### ### code chunk number 10: simLexis.rnw:293-302 ################################################### DM.Dead <- glm.Lexis( Si, from = "DM", to = "Dead", formula = ~ Ns( Age , knots=ad.kn ) + Ns( DMdur, knots=dd.kn ) + I(Per-2000) + sex ) Ins.Dead <- glm.Lexis( Si, from = "Ins", formula = ~ Ns( Age , knots=ad.kn ) + Ns( DMdur, knots=dd.kn ) + Ns( t.Ins, knots=ti.kn ) + I(Per-2000) + sex ) ################################################### ### code chunk number 11: prop-haz ################################################### All.Dead <- glm.Lexis( Si, to = c("Dead(Ins)","Dead"), formula = ~ Ns( Age , knots=ad.kn ) + Ns( DMdur, knots=dd.kn ) + lex.Cst + I(Per-2000) + sex ) round( ci.exp( All.Dead ), 3 ) ################################################### ### code chunk number 12: get-dev ################################################### what <- c("null.deviance","df.null","deviance","df.residual") ( rD <- unlist( DM.Dead[what] ) ) ( rI <- unlist( Ins.Dead[what] ) ) ( rA <- unlist( All.Dead[what] ) ) round( c( dd <- rA-(rI+rD), "pVal"=1-pchisq(dd[3],dd[4]+1) ), 3 ) ################################################### ### code chunk number 13: pr-array ################################################### pr.rates <- NArray( list( DMdur = seq(0,12,0.1), DMage = 4:7*10, r.Ins = c(NA,0,2,5), model = c("DM/Ins","All"), what = c("rate","lo","hi") ) ) str( pr.rates ) ################################################### ### code chunk number 14: mknd ################################################### nd <- data.frame( DMdur = as.numeric( dimnames(pr.rates)[[1]] ), lex.Cst = factor( 1, levels=1:4, labels=levels(Si$lex.Cst) ), sex = factor( 1, levels=1:2, labels=c("M","F")) ) ################################################### ### code chunk number 15: make-pred ################################################### for( ia in dimnames(pr.rates)[[2]] ) { dnew <- transform( nd, Age = as.numeric(ia)+DMdur, Per = 1998+DMdur ) pr.rates[,ia,1,"DM/Ins",] <- ci.pred( DM.Dead, newdata = dnew ) pr.rates[,ia,1,"All" ,] <- ci.pred( All.Dead, newdata = dnew ) for( ii in dimnames(pr.rates)[[3]][-1] ) { dnew = transform( dnew, lex.Cst = factor( 2, levels=1:4, labels=levels(Si$lex.Cst) ), t.Ins = ifelse( (DMdur-as.numeric(ii)) >= 0, DMdur-as.numeric(ii), NA ) ) pr.rates[,ia, ii ,"DM/Ins",] <- ci.pred( Ins.Dead, newdata = dnew ) pr.rates[,ia, ii ,"All" ,] <- ci.pred( All.Dead, newdata = dnew ) } } ################################################### ### code chunk number 16: mort-int ################################################### par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1 ) plot( NA, xlim=c(40,82), ylim=c(5,300), bty="n", log="y", xlab="Age", ylab="Mortality rate per 1000 PY" ) abline( v=seq(40,80,5), h=outer(1:9,10^(0:2),"*"), col=gray(0.8) ) for( aa in 4:7*10 ) for( ii in 1:4 ) matshade( aa+as.numeric(dimnames(pr.rates)[[1]]), cbind( pr.rates[,paste(aa),ii,"DM/Ins",], pr.rates[,paste(aa),ii,"All" ,] )*1000, type="l", lty=1, lwd=2, col=c("red","limegreen") ) ################################################### ### code chunk number 17: Tr ################################################### Tr <- list( "DM" = list( "Ins" = DM.Ins, "Dead" = DM.Dead ), "Ins" = list( "Dead(Ins)" = Ins.Dead ) ) ################################################### ### code chunk number 18: make-ini ################################################### str( ini <- Si[NULL,1:9] ) ################################################### ### code chunk number 19: ini-fill ################################################### ini[1:2,"lex.id"] <- 1:2 ini[1:2,"lex.Cst"] <- "DM" ini[1:2,"Per"] <- 1995 ini[1:2,"Age"] <- 60 ini[1:2,"DMdur"] <- 5 ini[1:2,"sex"] <- c("M","F") ini ################################################### ### code chunk number 20: simL ################################################### set.seed( 52381764 ) Nsim <- 5000 system.time( simL <- simLexis( Tr, ini, t.range = 12, N = Nsim ) ) ################################################### ### code chunk number 21: sum-simL ################################################### summary( simL, by="sex" ) ################################################### ### code chunk number 22: Tr.p-simP ################################################### Tr.p <- list( "DM" = list( "Ins" = DM.Ins, "Dead" = All.Dead ), "Ins" = list( "Dead(Ins)" = All.Dead ) ) system.time( simP <- simLexis( Tr.p, ini, t.range = 12, N = Nsim ) ) summary( simP, by="sex" ) ################################################### ### code chunk number 23: Cox-dur ################################################### library( survival ) Cox.Dead <- coxph( Surv( DMdur, DMdur+lex.dur, lex.Xst %in% c("Dead(Ins)","Dead")) ~ Ns( Age-DMdur, knots=ad.kn ) + I(lex.Cst=="Ins") + I(Per-2000) + sex, data = Si ) round( ci.exp( Cox.Dead ), 3 ) ################################################### ### code chunk number 24: TR.c ################################################### Tr.c <- list( "DM" = list( "Ins" = Tr$DM$Ins, "Dead" = Cox.Dead ), "Ins" = list( "Dead(Ins)" = Cox.Dead ) ) system.time( simC <- simLexis( Tr.c, ini, t.range = 12, N = Nsim ) ) summary( simC, by="sex" ) ################################################### ### code chunk number 25: nState ################################################### system.time( nSt <- nState( subset(simL,sex=="M"), at=seq(0,11,0.2), from=1995, time.scale="Per" ) ) nSt[1:10,] ################################################### ### code chunk number 26: pstate0 ################################################### pM <- pState( nSt, perm=c(1,2,4,3) ) head( pM ) par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) plot( pM ) plot( pM, border="black", col="transparent", lwd=3 ) text( rep(as.numeric(rownames(pM)[nrow(pM)-1]),ncol(pM)), pM[nrow(pM),]-diff(c(0,pM[nrow(pM),]))/5, colnames( pM ), adj=1 ) box( col="white", lwd=3 ) box() ################################################### ### code chunk number 27: pstatex ################################################### clr <- c("limegreen","orange") # expand with a lighter version of the two chosen colors clx <- c( clr, rgb( t( col2rgb( clr[2:1] )*2 + rep(255,3) ) / 3, max=255 ) ) par( mfrow=c(1,2), las=1, mar=c(3,3,4,2), mgp=c(3,1,0)/1.6 ) # Men plot( pM, col=clx, xlab="Date of FU" ) lines( as.numeric(rownames(pM)), pM[,2], lwd=3 ) mtext( "60 year old male, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) mtext( "Survival curve", side=3, line=1.5, adj=0 ) mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) axis( side=4 ) axis( side=4, at=1:19/20, labels=FALSE ) axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) # Women pF <- pState( nState( subset(simL,sex=="F"), at=seq(0,11,0.2), from=1995, time.scale="Per" ), perm=c(1,2,4,3) ) plot( pF, col=clx, xlab="Date of FU" ) lines( as.numeric(rownames(pF)), pF[,2], lwd=3 ) mtext( "60 year old female, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) mtext( "Survival curve", side=3, line=1.5, adj=0 ) mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) axis( side=4 ) axis( side=4, at=1:19/20, labels=FALSE ) axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) ################################################### ### code chunk number 28: pstatey ################################################### par( mfrow=c(1,2), las=1, mar=c(3,3,4,2), mgp=c(3,1,0)/1.6 ) # Men pM <- pState( nState( subset(simL,sex=="M"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) plot( pM, col=clx, xlab="Age" ) lines( as.numeric(rownames(pM)), pM[,2], lwd=3 ) mtext( "60 year old male, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) mtext( "Survival curve", side=3, line=1.5, adj=0 ) mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) axis( side=4 ) axis( side=4, at=1:19/20, labels=FALSE ) axis( side=4, at=1:19/20, labels=FALSE, tcl=-0.4 ) axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) # Women pF <- pState( nState( subset(simL,sex=="F"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) plot( pF, col=clx, xlab="Age" ) lines( as.numeric(rownames(pF)), pF[,2], lwd=3 ) mtext( "60 year old female, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) mtext( "Survival curve", side=3, line=1.5, adj=0 ) mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) axis( side=4 ) axis( side=4, at=1:9/10, labels=FALSE ) axis( side=4, at=1:19/20, labels=FALSE, tcl=-0.4 ) axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) ################################################### ### code chunk number 29: comp-0 ################################################### PrM <- pState( nState( subset(simP,sex=="M"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) PrF <- pState( nState( subset(simP,sex=="F"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) CoxM <- pState( nState( subset(simC,sex=="M"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) CoxF <- pState( nState( subset(simC,sex=="F"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) plot( pM, border="black", col="transparent", lwd=3 ) lines( PrM, border="blue" , col="transparent", lwd=3 ) lines( CoxM, border="red" , col="transparent", lwd=3 ) text( 60.5, 0.05, "M" ) box( lwd=5, col="white" ) ; box( lwd=2, col="black" ) plot( pF, border="black", col="transparent", lwd=3 ) lines( PrF, border="blue" , col="transparent", lwd=3 ) lines( CoxF, border="red" , col="transparent", lwd=3 ) text( 60.5, 0.05, "F" ) box( lwd=5, col="white" ) ; box( lwd=2, col="black" ) ################################################### ### code chunk number 30: CHANGE1 (eval = FALSE) ################################################### ## source( "../R/simLexis.R", keep.source=TRUE ) ################################################### ### code chunk number 31: CHANGE2 ################################################### simX <- Epi:::simX sim1 <- Epi:::sim1 lint <- Epi:::lint get.next <- Epi:::get.next chop.lex <- Epi:::chop.lex ################################################### ### code chunk number 32: simLexis.rnw:972-975 ################################################### cbind( attr( ini, "time.scales" ), attr( ini, "time.since" ) ) ################################################### ### code chunk number 33: simLexis.rnw:1000-1001 ################################################### simLexis ################################################### ### code chunk number 34: simLexis.rnw:1018-1019 ################################################### simX ################################################### ### code chunk number 35: simLexis.rnw:1031-1032 ################################################### sim1 ################################################### ### code chunk number 36: simLexis.rnw:1044-1045 ################################################### lint ################################################### ### code chunk number 37: simLexis.rnw:1055-1056 ################################################### get.next ################################################### ### code chunk number 38: simLexis.rnw:1065-1066 ################################################### chop.lex ################################################### ### code chunk number 39: simLexis.rnw:1083-1084 ################################################### nState ################################################### ### code chunk number 40: simLexis.rnw:1093-1094 ################################################### pState ################################################### ### code chunk number 41: simLexis.rnw:1098-1100 ################################################### plot.pState lines.pState Epi/vignettes/crisk.R0000644000176200001440000002347414003562515014250 0ustar liggesusers### R code from vignette source 'crisk' ### Encoding: UTF-8 ################################################### ### code chunk number 1: crisk.rnw:24-27 ################################################### options( width=90, SweaveHooks=list( fig=function() par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") ) ) ################################################### ### code chunk number 2: crisk.rnw:83-100 ################################################### library(Epi) library(popEpi) data(DMlate) Ldm <- Lexis(entry = list( per = dodm, age = dodm-dobth, tfd = 0 ), exit = list( per = dox ), exit.status = factor( !is.na(dodth), labels = c("DM","Dead") ), data = DMlate ) summary(Ldm, t = T) Mdm <- mcutLexis( Ldm, wh = c('dooad','doins'), new.states = c('OAD','Ins'), precursor = 'DM', seq.states = FALSE, ties = TRUE ) summary( Mdm ) ################################################### ### code chunk number 3: crisk.rnw:105-107 ################################################### Sdm <- splitMulti(factorize(subset(Mdm, lex.Cst == "DM")), tfd = seq(0, 20, 1/12)) ################################################### ### code chunk number 4: boxes5 ################################################### boxes(Mdm, boxpos = list(x = c(15, 50, 15, 85, 85), y = c(85, 50, 15, 85, 15)), scale.R = 100, show.BE = TRUE) ################################################### ### code chunk number 5: boxes4 ################################################### boxes( Relevel(Sdm, c(1, 4, 2, 3)), boxpos = list(x = c(15, 85, 80, 15), y = c(85, 85, 20, 15)), scale.R = 100, show.BE = TRUE ) ################################################### ### code chunk number 6: crisk.rnw:139-142 ################################################### mD <- gam.Lexis(Sdm, ~ s(tfd, k = 5), to = 'Dead') mO <- gam.Lexis(Sdm, ~ s(tfd, k = 5), to = 'OAD' ) mI <- gam.Lexis(Sdm, ~ s(tfd, k = 5), to = 'Ins' ) ################################################### ### code chunk number 7: crisk.rnw:155-160 ################################################### int <- 1/100 nd <- data.frame( tfd = seq(int,10,int)-int/2 ) # not the same as the split, # and totally unrelated to it rownames(nd) <- nd$tfd str(nd) ################################################### ### code chunk number 8: rates ################################################### matshade(nd$tfd, cbind(ci.pred(mD, nd), ci.pred(mI, nd), ci.pred(mO, nd))*1000, ylim = c(0.02,500), yaxt = "n", ylab = "Rates per 1000 PY", xlab = "Time since DM diagnosis (years)", col = c("black","red","blue"), log = "y", lwd = 3, plot = TRUE) axis(side = 2, at = ll<-outer(c(1,2,5),-2:3,function(x,y) x*10^y), labels = formatC(ll,digits = 4), las = 1) axis(side = 2, at = ll<-outer(c(1.5,2:9),-2:3,function(x,y) x*10^y), labels = NA, tcl = -0.3) text(0, 0.5*0.6^c(1,2,0), c("Dead","Ins","OAD"), col = c("black","red","blue"), adj = 0) ################################################### ### code chunk number 9: crisk.rnw:194-209 ################################################### # rates at midpoints lD <- ci.pred( mD, nd )[,1] lI <- ci.pred( mI, nd )[,1] lO <- ci.pred( mO, nd )[,1] # cumulative rates and survival fuction at right border of the intervals LD <- cumsum(lD) * int LI <- cumsum(lI) * int LO <- cumsum(lO) * int Sv <- exp( -LD - LI - LO ) # but when integrating to get the cumulative risks we use the average # of the survival function at the two endpoints (adding 1 as the first) mp <- function(x) x - diff(c(1, x)) / 2 rD <- cumsum(lD * mp(Sv)) * int rI <- cumsum(lI * mp(Sv)) * int rO <- cumsum(lO * mp(Sv)) * int ################################################### ### code chunk number 10: crisk.rnw:214-218 ################################################### summary(rD + rI +rO + Sv) oo <- options(digits = 20) cbind(summary(Sv + rD + rI + rO)) options(oo) ################################################### ### code chunk number 11: stack ################################################### zz <- mat2pol(cbind(rD,rI,rO,Sv), x = nd$tfd, xlim = c(0,10), xaxs = "i", yaxs = "i", las = 1, xlab = "Time since DM diagnosis (years)", ylab = "Probability", col = c("black","red","blue","forestgreen") ) mm <- t(apply(zz,1,mid<-function(x) x[-1]-diff(x)/2)) text( 9, mm[900,], c("Dead","Ins","OAD","DM"), col = "white" ) box(col = "white",lwd = 3) ################################################### ### code chunk number 12: crisk.rnw:278-280 ################################################### head(cbind(ci.pred(mI,nd), ci.exp(mI,nd) )) head(cbind(ci.pred(mI,nd), exp(ci.lin(mI,nd)[,c(1,5:6)]))) ################################################### ### code chunk number 13: crisk.rnw:285-287 ################################################### str(ci.lin(mI, nd, sample = 4)) head(cbind(ci.pred(mI,nd), exp(ci.lin(mI, nd, sample = 4)))) ################################################### ### code chunk number 14: crisk.rnw:319-321 (eval = FALSE) ################################################### ## setwd("/home/bendix/stat/R/examples") ## source('ci.Crisk.R', echo=TRUE, max=10000) ################################################### ### code chunk number 15: crisk.rnw:326-334 ################################################### system.time( res <- ci.Crisk(list(OAD = mO, Ins = mI, Dead = mD), nd = data.frame(tfd = (1:1000-0.5)/100), nB = 1000, perm = 4:1)) str(res) ################################################### ### code chunk number 16: crisk.rnw:364-372 ################################################### system.time( rsm <- ci.Crisk(list(OAD = mO, Ins = mI, Dead = mD), nd = data.frame(tfd = (1:1000-0.5)/100), nB = 2000, sim.res = 'rates')) str(rsm) ################################################### ### code chunk number 17: crisk.rnw:379-387 ################################################### system.time( csm <- ci.Crisk(list(OAD = mO, Ins = mI, Dead = mD), nd = data.frame(tfd = (1:1000-0.5)/100), nB = 2000, sim.res = 'crisk')) str(csm) ################################################### ### code chunk number 18: crisk.rnw:406-408 ################################################### Brates <- aperm(apply(rsm, 1:2, Epi:::mnqt), c(2,3,1)) str(Brates) ################################################### ### code chunk number 19: rates-ci ################################################### matshade(nd$tfd, cbind(ci.pred(mD, nd), ci.pred(mI, nd), ci.pred(mO, nd))*1000, ylim = c(0.1,500), yaxt = "n", ylab = "Rates per 1000 PY", xlab = "Time since DM diagnosis (years)", col = c("black","red","blue"), log = "y", lwd = 3, plot = TRUE) matlines(nd$tfd, cbind(Brates[,"Dead",], Brates[,"Ins" ,], Brates[,"OAD" ,])*1000, col = c("white","black","black"), lty = 3, lwd=c(3,1,1)) axis(side = 2, at = ll<-outer(c(1,2,5),-2:3,function(x,y) x*10^y), labels = formatC(ll,digits = 4), las = 1) axis(side = 2, at = ll<-outer(c(1.5,2:9),-2:3,function(x,y) x*10^y), labels = NA, tcl = -0.3) text(0, 0.5*0.6^c(1,2,0), c("Dead","Ins","OAD"), col = c("black","red","blue"), adj = 0) ################################################### ### code chunk number 20: crates ################################################### matshade(c(0,nd$tfd+1/200), cbind(res$Crisk[,"Dead",], res$Crisk[,"Ins" ,], res$Crisk[,"OAD" ,]), plot = TRUE, xlim = c(0,10), xaxs = "i", yaxs = "i", las = 1, xlab = "Time since DM diagnosis (years)", ylab = "Cumulative probability", col = c("black","red","blue")) text(8, 0.3 + c(1,0,2)/25, c("Dead","Ins","OAD"), col = c("black","red","blue"), adj = 0) ################################################### ### code chunk number 21: crisk.rnw:467-469 ################################################### str(res$Crisk) str(res$Srisk) ################################################### ### code chunk number 22: stack-ci ################################################### zz <- mat2pol(res$Crisk[,c("Dead","Ins","OAD","Surv"),1], x = as.numeric(dimnames(res$Crisk)[[1]])/100, xlim = c(0,10), xaxs = "i", yaxs = "i", las = 1, xlab = "Time since DM diagnosis (years)", ylab = "Probability", col = c("black","red","blue","forestgreen") ) mm <- t(apply(zz, 1, mid<-function(x) x[-1] - diff(x) / 2)) text( 9, mm[900,], c("Dead","Ins","OAD","DM"), col = "white" ) matshade(as.numeric(dimnames(res$Srisk)[[1]])/100, cbind(res$Srisk[,1,], res$Srisk[,2,], res$Srisk[,3,]), col = 'transparent', col.shade = "white", alpha = 0.3) ################################################### ### code chunk number 23: crisk.rnw:503-504 ################################################### str(res$Stime) ################################################### ### code chunk number 24: crisk.rnw:507-510 ################################################### s510 <- res$Stime[1:2*500,,] dimnames(s510)[[1]] <- c(" 5 yr","10 yr") round(ftable(s510, row.vars=1:2), 2) Epi/vignettes/yll.R0000644000176200001440000001611014003563041013715 0ustar liggesusers### R code from vignette source 'yll' ### Encoding: UTF-8 ################################################### ### code chunk number 1: yll.rnw:21-24 ################################################### options( width=90, SweaveHooks=list( fig=function() par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") ) ) ################################################### ### code chunk number 2: states ################################################### library( Epi ) TM <- matrix(NA,4,4) rownames(TM) <- colnames(TM) <- c("Well","DM","Dead","Dead(DM)") TM[1,2:3] <- TM[2,4] <- 1 zz <- boxes( TM, boxpos=list(x=c(20,80,20,80),y=c(80,80,20,20)), wm=1.5, hm=4 ) ################################################### ### code chunk number 3: states ################################################### zz$Arrowtext <- c( expression(lambda), expression(mu[W]), expression(mu[D][M]) ) boxes( zz ) ################################################### ### code chunk number 4: yll.rnw:265-266 ################################################### data( DMepi ) ################################################### ### code chunk number 5: yll.rnw:271-273 ################################################### str( DMepi ) head( DMepi ) ################################################### ### code chunk number 6: yll.rnw:293-297 ################################################### DMepi <- transform( subset( DMepi, A>30 ), D.T = D.nD + D.DM, Y.T = Y.nD + Y.DM ) head(DMepi) ################################################### ### code chunk number 7: yll.rnw:303-329 ################################################### # Knots used in all models ( a.kn <- seq(40,95,,6) ) ( p.kn <- seq(1997,2015,,4) ) ( c.kn <- seq(1910,1976,,6) ) # Check the number of events between knots ae <- xtabs( cbind(D.nD,D.DM,X) ~ cut(A,c(30,a.kn,Inf)) + sex, data=DMepi ) ftable( addmargins(ae,1), col.vars=3:2 ) pe <- xtabs( cbind(D.nD,D.DM,X) ~ cut(P,c(1990,p.kn,Inf)) + sex, data=DMepi ) ftable( addmargins(pe,1), col.vars=3:2 ) ce <- xtabs( cbind(D.nD,D.DM,X) ~ cut(P-A,c(-Inf,c.kn,Inf)) + sex, data=DMepi ) ftable( addmargins(ce,1), col.vars=3:2 ) # Fit an APC-model for all transitions, seperately for men and women mW.m <- glm( D.nD ~ -1 + Ns(A ,knots=a.kn,int=TRUE) + Ns( P,knots=p.kn,ref=2005) + Ns(P-A,knots=c.kn,ref=1950), offset = log(Y.nD), family = poisson, data = subset( DMepi, sex=="M" ) ) mD.m <- update( mW.m, D.DM ~ . , offset=log(Y.DM) ) mT.m <- update( mW.m, D.T ~ . , offset=log(Y.T ) ) lW.m <- update( mW.m, X ~ . ) # Model for women mW.f <- update( mW.m, data = subset( DMepi, sex=="F" ) ) mD.f <- update( mD.m, data = subset( DMepi, sex=="F" ) ) mT.f <- update( mT.m, data = subset( DMepi, sex=="F" ) ) lW.f <- update( lW.m, data = subset( DMepi, sex=="F" ) ) ################################################### ### code chunk number 8: yll.rnw:336-373 ################################################### a.ref <- 30:90 p.ref <- 1996:2016 aYLL <- NArray( list( type = c("Imm","Tot","Sus"), sex = levels( DMepi$sex ), age = a.ref, date = p.ref ) ) str( aYLL ) system.time( for( ip in p.ref ) { nd <- data.frame( A = seq(30,90,0.2)+0.1, P = ip, Y.nD = 1, Y.DM = 1, Y.T = 1 ) muW.m <- ci.pred( mW.m, nd )[,1] muD.m <- ci.pred( mD.m, nd )[,1] muT.m <- ci.pred( mT.m, nd )[,1] lam.m <- ci.pred( lW.m, nd )[,1] muW.f <- ci.pred( mW.f, nd )[,1] muD.f <- ci.pred( mD.f, nd )[,1] muT.f <- ci.pred( mT.f, nd )[,1] lam.f <- ci.pred( lW.f, nd )[,1] aYLL["Imm","M",,paste(ip)] <- yll( int=0.2, muW.m, muD.m, lam=NULL, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Imm","F",,paste(ip)] <- yll( int=0.2, muW.f, muD.f, lam=NULL, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Tot","M",,paste(ip)] <- yll( int=0.2, muT.m, muD.m, lam=NULL, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Tot","F",,paste(ip)] <- yll( int=0.2, muT.f, muD.f, lam=NULL, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Sus","M",,paste(ip)] <- yll( int=0.2, muW.m, muD.m, lam=lam.m, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Sus","F",,paste(ip)] <- yll( int=0.2, muW.f, muD.f, lam=lam.f, A=a.ref, age.in=30, note=FALSE )[-1] } ) round( ftable( aYLL[,,seq(1,61,10),], col.vars=c(3,2) ), 1 ) ################################################### ### code chunk number 9: imm ################################################### plyll <- function(wh){ par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, bty="n", las=1 ) matplot( a.ref, aYLL[wh,"M",,], type="l", lty=1, col="blue", lwd=1:2, ylim=c(0,12), xlab="Age", ylab="Years lost to DM", yaxs="i" ) abline(v=50,h=1:10,col=gray(0.7)) text( 90, 11, "Men", col="blue", adj=1 ) text( 40, aYLL[wh,"M","40","1996"], "1996", adj=c(0,0), col="blue" ) text( 43, aYLL[wh,"M","44","2016"], "2016", adj=c(1,1), col="blue" ) matplot( a.ref, aYLL[wh,"F",,], type="l", lty=1, col="red", lwd=1:2, ylim=c(0,12), xlab="Age", ylab="Years lost to DM", yaxs="i" ) abline(v=50,h=1:10,col=gray(0.7)) text( 90, 11, "Women", col="red", adj=1 ) text( 40, aYLL[wh,"F","40","1996"], "1996", adj=c(0,0), col="red" ) text( 43, aYLL[wh,"F","44","2016"], "2016", adj=c(1,1), col="red" ) } plyll("Imm") ################################################### ### code chunk number 10: tot ################################################### plyll("Tot") ################################################### ### code chunk number 11: sus ################################################### plyll("Sus") ################################################### ### code chunk number 12: CHANGE1 (eval = FALSE) ################################################### ## source( "../R/erl.R", keep.source=TRUE ) ################################################### ### code chunk number 13: CHANGE2 ################################################### surv1 <- Epi::surv1 surv2 <- Epi::surv2 erl1 <- Epi::erl1 erl <- Epi::erl yll <- Epi::yll ################################################### ### code chunk number 14: yll.rnw:484-485 ################################################### surv1 ################################################### ### code chunk number 15: yll.rnw:489-490 ################################################### erl1 ################################################### ### code chunk number 16: yll.rnw:497-498 ################################################### surv2 ################################################### ### code chunk number 17: yll.rnw:502-503 ################################################### erl ################################################### ### code chunk number 18: yll.rnw:507-508 ################################################### yll Epi/vignettes/simLexis.tex0000644000176200001440000021405214003563037015323 0ustar liggesusers%\VignetteIndexEntry{Simulation of multistate models with multiple timescales: simLexis} \documentclass[a4paper,dvipsnames,twoside,12pt]{report} \newcommand{\Title}{Simulation of\\ multistate models with\\ multiple timescales:\\ \texttt{simLexis} in the \texttt{Epi} package} \newcommand{\Tit}{Multistate models with multiple timescales} \newcommand{\Version}{Version 2.5} \newcommand{\Dates}{\today} \newcommand{\Where}{SDCC} \newcommand{\Homepage}{\url{http://BendixCarstensen.com/Epi/simLexis.pdf}} \newcommand{\Faculty}{\begin{tabular}{rl} Bendix Carstensen & Steno Diabetes Center Copenhagen, Gentofte, Denmark\\ & {\small \& Department of Biostatistics, University of Copenhagen} \\ & \texttt{b@bxc.dk}\\ & \url{http://BendixCarstensen.com} \\[1em] \end{tabular}} \input{topreport} \renewcommand{\rwpre}{./simLexis} \chapter{Using \texttt{simLexis}} \section{Introduction} This vignette explains the machinery behind simulation of life histories through multistate models implemented in \texttt{simLexis}. In \texttt{simLexis} transition rates are allowed to depend on multiple time scales, including timescales defined as time since entry to a particular state (duration). This therefore also covers the case where time \emph{at} entry into a state is an explanatory variable for the rates, since time at entry is merely time minus duration. Thus, the set-up here goes beyond Markov- and semi-Markov-models, and brings simulation based estimation of state-occupancy probabilities into the realm of realistic multistate models. The basic idea is to simulate a new \texttt{Lexis} object \cite{Plummer.2011,Carstensen.2011a} as defined in the \texttt{Epi} package for \R, based on 1) a multistate model defined by its states and the transition rates between them and 2) an initial population of individuals. Thus the output will be a \texttt{Lexis} object describing the transitions of a predefined set of persons through a multistate model. Therefore, if persons are defined to be identical at start, then calculation of the probability of being in a particular state at a given time boils down to a simple enumeration of the fraction of the persons in the particular state at the given time. Bar of course the (binomial) simulation error, but this can be brought down by simulation a sufficiently large number of persons. An observed \texttt{Lexis} object with follow-up of persons through a number of states will normally be the basis for estimation of transition rates between states, and thus will contain all information about covariates determining the occurrence rates, in particular the \emph{timescales} \cite{Iacobelli.2013}. Hence, the natural input to simulation from an estimated multistate model will typically be an object of the same structure as the originally observed. Since transitions and times are what is simulated, any values of \texttt{lex.Xst} and \texttt{lex.dur} in the input object will of course be ignored. This first chapter of this vignette shows by an example how to use the function \texttt{simLexis} and display the results. The second chapter discusses in more detail how the simulation machinery is implemented and is not needed for the practical use of \texttt{simLexis}. \section{\texttt{simLexis} in practice} This section is largely a commented walk-trough of the example from the help-page of \texttt{simLexis}, with a larger number of simulated persons in order to minimize the pure simulation variation. When we want to simulate transition times through a multistate model where transition rates may depend on time since entry to the current or a previous state, it is essential that we have a machinery to keep track of the transition time on \emph{all} time scales, as well as a mechanism that can initiate a new time scale to 0 when a transition occurs to a state where we shall use time since entry as determinant of exit rates from that state. This is provided by \texttt{simLexis}. \subsection{Input for the simulation} Input for simulation of a single trajectory through a multistate model requires a representation of the \emph{current status} of a person; the starting conditions. The object that we supply to the simulation function must contain information about all covariates and all timescales upon which transitions depend, and in particular which one(s) of the timescales that are defined as time since entry into a particular state. Hence, starting conditions should be represented as a \texttt{Lexis} object (where \texttt{lex.dur} and \texttt{lex.Xst} are ignored, since there is no follow-up yet), where the time scale information is in the attributes \texttt{time.scales} and \texttt{time.since} respectively. Note that \texttt{time.scales} attribute is a vector of names of variables in the \texttt{Lexis} object, so all of these variables should be present even if they are not used in the models for the transitions, and they should be set to 0; if they are not in the initial dataset, \texttt{simLexis} will crash, if they are \texttt{NA}, the \texttt{simLexis} will produce an object with 0 rows. Thus there are two main arguments to a function to simulate from a multistate model: \begin{enumerate} \item A \texttt{Lexis} object representing the initial states and covariates of the population to be simulated. This has to have the same structure as the original \texttt{Lexis} object representing the multistate model from which transition rates in the model were estimated. As noted above, the values for \texttt{lex.Xst} and \texttt{lex.dur} are not required (since these are the quantities that will be simulated). \item A transition object, representing the transition intensities between states, which should be a list of lists of intensity representations. As an intensity representation we mean a function that for a given \texttt{Lexis} object can be used to produce estimates of the transition intensities at a set of supplied time points. The names of the elements of the transition object (which are lists) will be names of the \emph{transient} states, that is the states \emph{from} which a transition can occur. The names of the elements of each of these lists are the names of states \emph{to} which transitions can occur (which may be either transient or absorbing states). Hence, if the transition object is called \texttt{Tr} then \verb+TR$A$B+ (or \verb+Tr[["A"]][["B"]]+) will represent the transition intensity from state \texttt{A} to the state \texttt{B}. The entries in the transition object can be either \texttt{glm} objects (either with \texttt{poisson} or \texttt{poisreg} family), representing Poisson models for the transitions, \texttt{coxph} objects representing an intensity model along one time scale, or simply a function that takes a \texttt{Lexis} object as input and returns an estimated intensity for each row. \end{enumerate} In addition to these two input items, there will be a couple of tuning parameters. The output of the function will simply be a \texttt{Lexis} object with simulated transitions between states. This will be the basis for deriving sensible statistics from the \texttt{Lexis} object --- see next section. \section{Setting up a \texttt{Lexis} object} As an example we will use the \texttt{DMlate} dataset from the \texttt{Epi} package; it is a dataset simulated to resemble a random sample of 10,000 patients from the Danish National Diabetes Register. We start by loading the \texttt{Epi} package: \begin{Schunk} \begin{Sinput} > options( width=90 ) > library( Epi ) > print( sessionInfo(), l=F ) \end{Sinput} \begin{Soutput} R version 3.6.3 (2020-02-29) Platform: x86_64-pc-linux-gnu (64-bit) Running under: Ubuntu 14.04.6 LTS Matrix products: default BLAS: /usr/lib/openblas-base/libopenblas.so.0 LAPACK: /usr/lib/lapack/liblapack.so.3.0 attached base packages: [1] utils datasets graphics grDevices stats methods base other attached packages: [1] Epi_2.43 loaded via a namespace (and not attached): [1] Rcpp_1.0.3 magrittr_1.5 splines_3.6.3 MASS_7.3-53 [5] tidyselect_0.2.5 lattice_0.20-41 R6_2.4.1 rlang_0.4.4 [9] plyr_1.8.5 dplyr_0.8.4 cmprsk_2.2-7 tools_3.6.3 [13] parallel_3.6.3 grid_3.6.3 data.table_1.12.0 nlme_3.1-149 [17] mgcv_1.8-33 survival_3.2-7 assertthat_0.2.1 tibble_2.1.3 [21] etm_1.0.4 numDeriv_2016.8-1 crayon_1.3.4 Matrix_1.2-18 [25] purrr_0.3.0 glue_1.3.1 compiler_3.6.3 pillar_1.4.3 [29] zoo_1.8-4 pkgconfig_2.0.3 \end{Soutput} \end{Schunk} First we load the diabetes data and set up a simple illness-death model: \begin{Schunk} \begin{Sinput} > data(DMlate) > dml <- Lexis( entry = list(Per=dodm, Age=dodm-dobth, DMdur=0 ), + exit = list(Per=dox), + exit.status = factor(!is.na(dodth),labels=c("DM","Dead")), + data = DMlate ) \end{Sinput} \begin{Soutput} NOTE: entry.status has been set to "DM" for all. NOTE: Dropping 4 rows with duration of follow up < tol \end{Soutput} \end{Schunk} This is just data for a simple survival model with states \texttt{DM} and \texttt{Dead}. Now we cut the follow-up at insulin start, which for the majority of patients (T2D) is a clinical indicator of deterioration of disease regulation. We therefore also introduce a new timescale, and split the non-precursor states, so that we can address the question of ever having been on insulin: \begin{Schunk} \begin{Sinput} > dmi <- cutLexis( dml, cut = dml$doins, + pre = "DM", + new.state = "Ins", + new.scale = "t.Ins", + split.states = TRUE ) > summary( dmi, timeScales=T ) \end{Sinput} \begin{Soutput} Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 6157 1694 2048 0 9899 3742 45885.49 9899 Ins 0 1340 0 451 1791 451 8387.77 1791 Sum 6157 3034 2048 451 11690 4193 54273.27 9996 Timescales: Per Age DMdur t.Ins "" "" "" "Ins" \end{Soutput} \end{Schunk} Note that we show the time scales in the \texttt{Lexis} object, and that it is indicated that the time scale \texttt{t.Ins} is defined as time since entry into stat state \texttt{Ins.} We can show how many person-years we have and show the number of transitions and transition rates (per 1000), using the \texttt{boxes.Lexis} function to display the states and the number of transitions between them: \begin{Schunk} \begin{Sinput} > boxes( dmi, boxpos = list(x=c(20,20,80,80), + y=c(80,20,80,20)), + scale.R = 1000, show.BE = TRUE ) \end{Sinput} \end{Schunk} \insfig{boxes}{0.8}{Data overview for the \textrm{\tt dmi} dataset. Numbers in the boxes are person-years and the number of persons who begin, resp. end their follow-up in each state, and numbers on the arrows are no. of transitions and rates (transition intensities) per 1000 PY.} \section{Analysis of rates} In the \texttt{Lexis} object (which is just a data frame) each person is represented by one record for each transient state occupied, thus in this case either 1 or 2 records; those who have a recorded time both without and with insulin have two records. In order to be able to fit Poisson models with occurrence rates varying by the different time-scales, we split the follow-up in 3-month intervals for modeling: \begin{Schunk} \begin{Sinput} > Si <- splitLexis( dmi, seq(0,20,1/4), "DMdur" ) > summary( Si ) \end{Sinput} \begin{Soutput} Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 184986 1694 2048 0 188728 3742 45885.49 9899 Ins 0 34707 0 451 35158 451 8387.77 1791 Sum 184986 36401 2048 451 223886 4193 54273.27 9996 \end{Soutput} \begin{Sinput} > print( subset( Si, lex.id==97 )[,1:10], digits=6 ) \end{Sinput} \begin{Soutput} lex.id Per Age DMdur t.Ins lex.dur lex.Cst lex.Xst sex dobth 2142 97 1997.55 58.9268 0.00000 NA 0.2500000 DM DM F 1938.62 2143 97 1997.80 59.1768 0.25000 NA 0.2500000 DM DM F 1938.62 2144 97 1998.05 59.4268 0.50000 NA 0.2500000 DM DM F 1938.62 2145 97 1998.30 59.6768 0.75000 NA 0.2500000 DM DM F 1938.62 2146 97 1998.55 59.9268 1.00000 NA 0.2500000 DM DM F 1938.62 2147 97 1998.80 60.1768 1.25000 NA 0.2500000 DM DM F 1938.62 2148 97 1999.05 60.4268 1.50000 NA 0.2500000 DM DM F 1938.62 2149 97 1999.30 60.6768 1.75000 NA 0.2500000 DM DM F 1938.62 2150 97 1999.55 60.9268 2.00000 NA 0.1793292 DM Ins F 1938.62 2151 97 1999.72 61.1061 2.17933 0.0000000 0.0706708 Ins Ins F 1938.62 2152 97 1999.80 61.1768 2.25000 0.0706708 0.2500000 Ins Ins F 1938.62 2153 97 2000.05 61.4268 2.50000 0.3206708 0.2500000 Ins Ins F 1938.62 2154 97 2000.30 61.6768 2.75000 0.5706708 0.2500000 Ins Ins F 1938.62 2155 97 2000.55 61.9268 3.00000 0.8206708 0.0116359 Ins Dead(Ins) F 1938.62 \end{Soutput} \end{Schunk} Note that when we split the follow-up, each person's follow up now consists of many records, each with the \emph{current} values of the timescales at the start of the interval represented by the record. In the modeling we shall assume that the rates are constant within each 6-month interval, but the \emph{size} of these rates we model as smooth functions of the time scales (that is the values at the beginning of each interval). The approach often used in epidemiology where one parameter is attached to each interval of time (or age) is not feasible when more than one time scale is used, because intervals are not classified the same way on all timescales. We shall use natural splines (restricted cubic splines) for the analysis of rates, and hence we must allocate knots for the splines. This is done for each of the time-scales, and separately for the transition out of states \texttt{DM} and \texttt{Ins}. For age, we place the knots so that the number of events is the same between each pair of knots, but only half of this beyond each of the boundary knots, whereas for the timescales \texttt{DMdur} and \texttt{tIns} where we have observation from a well-defined 0, we put knots at 0 and place the remaining knots so that the number of events is the same between each pair of knots as well as outside the boundary knots. \begin{Schunk} \begin{Sinput} > nk <- 5 > ( ai.kn <- with( subset(Si,lex.Xst=="Ins" & lex.Cst!=lex.Xst ), + quantile( Age+lex.dur , probs=(1:nk-0.5)/nk ) ) ) \end{Sinput} \begin{Soutput} 10% 30% 50% 70% 90% 23.23751 48.82218 58.63244 67.79028 78.88542 \end{Soutput} \begin{Sinput} > ( ad.kn <- with( subset(Si,lex.Xst=="Dead"), + quantile( Age+lex.dur , probs=(1:nk-0.5)/nk ) ) ) \end{Sinput} \begin{Soutput} 10% 30% 50% 70% 90% 61.91951 72.52731 78.43121 83.32348 90.15195 \end{Soutput} \begin{Sinput} > ( di.kn <- with( subset(Si,lex.Xst=="Ins" & lex.Cst!=lex.Xst ), + c(0,quantile( DMdur+lex.dur, probs=(1:(nk-1))/nk ) )) ) \end{Sinput} \begin{Soutput} 20% 40% 60% 80% 0.00000000 0.06570842 0.45448323 3.28761123 6.63764545 \end{Soutput} \begin{Sinput} > ( dd.kn <- with( subset(Si,lex.Xst=="Dead"), + c(0,quantile( DMdur+lex.dur, probs=(1:(nk-1))/nk ) )) ) \end{Sinput} \begin{Soutput} 20% 40% 60% 80% 0.0000000 0.7687885 2.1327858 4.0465435 6.5232033 \end{Soutput} \begin{Sinput} > ( ti.kn <- with( subset(Si,lex.Xst=="Dead(Ins)"), + c(0,quantile( t.Ins+lex.dur, probs=(1:(nk-1))/nk ) )) ) \end{Sinput} \begin{Soutput} 20% 40% 60% 80% 0.0000000 0.3093771 1.1307324 2.5489391 4.9117043 \end{Soutput} \end{Schunk} Note that when we tease out the event records for transition to \emph{transient} states (in this case \texttt{Ins}, that is \verb|lex.Xst=="Ins"|), we should add \verb|lex.Cst!=lex.Xst|, to include only transition records and avoiding including records of sojourn time in the transient state. We then fit Poisson models to transition rates, using the wrapper \texttt{Ns} from the \texttt{Epi} package to simplify the specification of the rates: \begin{Schunk} \begin{Sinput} > library( splines ) > DM.Ins <- glm( (lex.Xst=="Ins") ~ Ns( Age , knots=ai.kn ) + + Ns( DMdur, knots=di.kn ) + + I(Per-2000) + sex, + family=poisson, offset=log(lex.dur), + data = subset(Si,lex.Cst=="DM") ) > ci.exp( DM.Ins ) \end{Sinput} \begin{Soutput} exp(Est.) 2.5% 97.5% (Intercept) 1.37516629 1.21414923 1.55753699 Ns(Age, knots = ai.kn)1 0.23411761 0.19185266 0.28569349 Ns(Age, knots = ai.kn)2 0.23166177 0.19576557 0.27414000 Ns(Age, knots = ai.kn)3 0.02835009 0.02284379 0.03518363 Ns(Age, knots = ai.kn)4 0.38067392 0.32945713 0.43985278 Ns(DMdur, knots = di.kn)1 0.04462626 0.03373451 0.05903459 Ns(DMdur, knots = di.kn)2 0.22388988 0.19028663 0.26342723 Ns(DMdur, knots = di.kn)3 0.03379141 0.02574708 0.04434907 Ns(DMdur, knots = di.kn)4 0.47100646 0.40783317 0.54396529 I(Per - 2000) 0.97381513 0.96082049 0.98698552 sexF 0.73757407 0.66886782 0.81333785 \end{Soutput} \begin{Sinput} > class( DM.Ins ) \end{Sinput} \begin{Soutput} [1] "glm" "lm" \end{Soutput} \end{Schunk} We can also fit this model with a slightly simpler syntax using the \texttt{glm.Lexis} function: \begin{Schunk} \begin{Sinput} > DM.Ins <- glm.Lexis( Si, from = "DM", to = "Ins", + formula = ~ Ns( Age , knots=ai.kn ) + + Ns( DMdur, knots=di.kn ) + + I(Per-2000) + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object Si with log link: Rates for the transition: DM->Ins \end{Soutput} \begin{Sinput} > ci.exp( DM.Ins ) \end{Sinput} \begin{Soutput} exp(Est.) 2.5% 97.5% (Intercept) 1.37516630 1.21415038 1.55753552 Ns(Age, knots = ai.kn)1 0.23411761 0.19185214 0.28569426 Ns(Age, knots = ai.kn)2 0.23166177 0.19576473 0.27414118 Ns(Age, knots = ai.kn)3 0.02835009 0.02284374 0.03518371 Ns(Age, knots = ai.kn)4 0.38067392 0.32945601 0.43985427 Ns(DMdur, knots = di.kn)1 0.04462625 0.03373347 0.05903639 Ns(DMdur, knots = di.kn)2 0.22388988 0.19028599 0.26342813 Ns(DMdur, knots = di.kn)3 0.03379141 0.02574705 0.04434912 Ns(DMdur, knots = di.kn)4 0.47100646 0.40783201 0.54396683 I(Per - 2000) 0.97381513 0.96082027 0.98698574 sexF 0.73757407 0.66886641 0.81333956 \end{Soutput} \begin{Sinput} > class( DM.Ins ) \end{Sinput} \begin{Soutput} [1] "glm.lex" "glm" "lm" \end{Soutput} \end{Schunk} So we have a slightly simpler syntax, and we get an informative message of which transition(s) we are modeling. However we do not have \texttt{update} method for these objects. \begin{Schunk} \begin{Sinput} > DM.Dead <- glm.Lexis( Si, from = "DM", to = "Dead", + formula = ~ Ns( Age , knots=ad.kn ) + + Ns( DMdur, knots=dd.kn ) + + I(Per-2000) + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object Si with log link: Rates for the transition: DM->Dead \end{Soutput} \begin{Sinput} > Ins.Dead <- glm.Lexis( Si, from = "Ins", + formula = ~ Ns( Age , knots=ad.kn ) + + Ns( DMdur, knots=dd.kn ) + + Ns( t.Ins, knots=ti.kn ) + + I(Per-2000) + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object Si with log link: Rates for the transition: Ins->Dead(Ins) \end{Soutput} \end{Schunk} Note the similarity of the code used to fit the three models, is is mainly redefining the response variable (\texttt{to} state) and the subset of the data used (\texttt{from} state). Also note that the last model need no specification of \texttt{to}, the default is to model all transitions from the \texttt{from} state, and his case there is only one. \section{The mortality rates} This section discusses in some detail how to extract ad display the mortality rates from the models fitted. But it is not necessary for understanding how to use \texttt{simLexis} in practice. \subsection{Proportionality of mortality rates} Note that we have fitted separate models for the three transitions, there is no assumption of proportionality between the mortality rates from \texttt{DM} and \texttt{Ins}. However, there is nothing that prevents us from testing this assumption; we can just fit a model for the mortality rates in the entire data frame \texttt{Si}, and compare the deviance from this with the sum of the deviances from the separate models using the \texttt{glm.Lexis} function: \begin{Schunk} \begin{Sinput} > All.Dead <- glm.Lexis( Si, to = c("Dead(Ins)","Dead"), + formula = ~ Ns( Age , knots=ad.kn ) + + Ns( DMdur, knots=dd.kn ) + + lex.Cst + + I(Per-2000) + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object Si with log link: Rates for transitions: Ins->Dead(Ins), DM->Dead \end{Soutput} \begin{Sinput} > round( ci.exp( All.Dead ), 3 ) \end{Sinput} \begin{Soutput} exp(Est.) 2.5% 97.5% (Intercept) 0.057 0.049 0.065 Ns(Age, knots = ad.kn)1 4.101 3.462 4.858 Ns(Age, knots = ad.kn)2 4.661 4.064 5.346 Ns(Age, knots = ad.kn)3 15.434 13.548 17.583 Ns(Age, knots = ad.kn)4 7.509 6.695 8.421 Ns(DMdur, knots = dd.kn)1 0.466 0.384 0.565 Ns(DMdur, knots = dd.kn)2 0.642 0.563 0.731 Ns(DMdur, knots = dd.kn)3 0.229 0.165 0.318 Ns(DMdur, knots = dd.kn)4 0.796 0.713 0.888 lex.CstIns 2.168 1.947 2.415 I(Per - 2000) 0.965 0.954 0.977 sexF 0.665 0.614 0.721 \end{Soutput} \end{Schunk} Incidentally we could have dispensed with the \texttt{to=} argument too, because the default is to take \texttt{to} to be all absorbing states in the model. From the parameter values we would in a simple setting just claim that start of insulin-treatment was associated with a slightly more than doubling of mortality. The model \texttt{All.dead} assumes that the age- and DM-duration effects on mortality in the \texttt{DM} and \texttt{Ins} states are the same, and moreover that there is no effect of insulin duration, but merely a mortality that is larger by a multiplicative constant not depending on insulin duration. The model \texttt{DM.Dead} has 8 parameters to describe the dependency on age and DM duration, the model \texttt{Ins.Dead} has 12 for the same plus the insulin duration (a natural spline with $k$ knots gives $k-1$ parameters, and we chose $k=5$ above). We can compare the fit of the simple proportional hazards model with the fit of the separate models for the two mortality rates, by adding up the deviances and d.f. from these: \begin{Schunk} \begin{Sinput} > what <- c("null.deviance","df.null","deviance","df.residual") > ( rD <- unlist( DM.Dead[what] ) ) \end{Sinput} \begin{Soutput} null.deviance df.null deviance df.residual 22535.77 188727.00 20412.81 188717.00 \end{Soutput} \begin{Sinput} > ( rI <- unlist( Ins.Dead[what] ) ) \end{Sinput} \begin{Soutput} null.deviance df.null deviance df.residual 4867.127 35157.000 4211.735 35143.000 \end{Soutput} \begin{Sinput} > ( rA <- unlist( All.Dead[what] ) ) \end{Sinput} \begin{Soutput} null.deviance df.null deviance df.residual 27415.21 223885.00 24705.70 223874.00 \end{Soutput} \begin{Sinput} > round( c( dd <- rA-(rI+rD), "pVal"=1-pchisq(dd[3],dd[4]+1) ), 3 ) \end{Sinput} \begin{Soutput} null.deviance df.null deviance df.residual pVal.deviance 12.314 1.000 81.154 14.000 0.000 \end{Soutput} \end{Schunk} Thus we see there is a substantial non-proportionality of mortality rates from the two states; but a test provides no clue whatsoever to the particular \emph{shape} of the non-proportionality. To this end, we shall explore the predicted mortalities under the two models quantitatively in more detail. Note that the reason that there is a difference in the null deviances (and a difference of 1 in the null d.f.) is that the null deviance of \texttt{All.Dead} refer to a model with a single intercept, that is a model with constant and \emph{identical} mortality rates from the states \texttt{DM} and \texttt{Ins}, whereas the null models for \texttt{DM.Dead} and \texttt{Ins.Dead} have constant but \emph{different} mortality rates from the states \texttt{DM} and \texttt{Ins}. This is however irrelevant for the comparison of the \emph{residual} deviances. \subsection{How the mortality rates look} If we want to see how the mortality rates are modelled in \texttt{DM.Dead} and \texttt{Ins.Dead} in relation to \texttt{All.Dead}, we make a prediction of rates for say men diagnosed in different ages and going on insulin at different times after this. So we consider men diagnosed in ages 40, 50, 60 and 70, and who either never enter insulin treatment or do it 0, 2 or 5 years after diagnosis of DM. To this end we create a prediction data frame where we have observation times from diagnosis and 12 years on (longer would not make sense as this is the extent of the data). But we start by setting up an array to hold the predicted mortality rates, classified by diabetes duration, age at diabetes onset, time of insulin onset, and of course type of model. What we want to do is to plot the age-specific mortality rates for persons not on insulin, and for persons starting insulin at different times after DM. The mortality curves start at the age where the person gets diabetes and continues 12 years; for persons on insulin they start at the age when they initiate insulin. \begin{Schunk} \begin{Sinput} > pr.rates <- NArray( list( DMdur = seq(0,12,0.1), + DMage = 4:7*10, + r.Ins = c(NA,0,2,5), + model = c("DM/Ins","All"), + what = c("rate","lo","hi") ) ) > str( pr.rates ) \end{Sinput} \begin{Soutput} logi [1:121, 1:4, 1:4, 1:2, 1:3] NA NA NA NA NA NA ... - attr(*, "dimnames")=List of 5 ..$ DMdur: chr [1:121] "0" "0.1" "0.2" "0.3" ... ..$ DMage: chr [1:4] "40" "50" "60" "70" ..$ r.Ins: chr [1:4] NA "0" "2" "5" ..$ model: chr [1:2] "DM/Ins" "All" ..$ what : chr [1:3] "rate" "lo" "hi" \end{Soutput} \end{Schunk} For convenience the \texttt{Epi} package contains a function that computes predicted (log-)rates with c.i. --- it is merely a wrapper for \texttt{predict.glm}. So we set up the prediction data frame and modify it in loops over ages at onset and insulin onset in order to collect the predicted rates in different scenarios: \begin{Schunk} \begin{Sinput} > nd <- data.frame( DMdur = as.numeric( dimnames(pr.rates)[[1]] ), + lex.Cst = factor( 1, levels=1:4, + labels=levels(Si$lex.Cst) ), + sex = factor( 1, levels=1:2, labels=c("M","F")) ) \end{Sinput} \end{Schunk} Note that we did \emph{not} insert \texttt{lex.dur} as covariate in the prediction frame. This would be required if we used the \texttt{poisson} family with the \texttt{glm}, but the wrapper \texttt{glm.Lexis} uses the \texttt{poisreg} family, so \texttt{lex.dur} is ignored and predictions always comes in the (inverse) units of \texttt{lex.dur}. So we get rates per 1 person-year in the predictions. \begin{Schunk} \begin{Sinput} > for( ia in dimnames(pr.rates)[[2]] ) + { + dnew <- transform( nd, Age = as.numeric(ia)+DMdur, + Per = 1998+DMdur ) + pr.rates[,ia,1,"DM/Ins",] <- ci.pred( DM.Dead, newdata = dnew ) + pr.rates[,ia,1,"All" ,] <- ci.pred( All.Dead, newdata = dnew ) + for( ii in dimnames(pr.rates)[[3]][-1] ) + { + dnew = transform( dnew, lex.Cst = factor( 2, levels=1:4, + labels=levels(Si$lex.Cst) ), + t.Ins = ifelse( (DMdur-as.numeric(ii)) >= 0, + DMdur-as.numeric(ii), NA ) ) + pr.rates[,ia, ii ,"DM/Ins",] <- ci.pred( Ins.Dead, newdata = dnew ) + pr.rates[,ia, ii ,"All" ,] <- ci.pred( All.Dead, newdata = dnew ) + } + } \end{Sinput} \end{Schunk} So for each age at DM onset we make a plot of the mortality as function of current age both for those with no insulin treatment and those that start insulin treatment 0, 2 and 5 years after diabetes diagnosis, thus 4 curves (with c.i.). These curves are replicated with a different color for the simplified model. \begin{Schunk} \begin{Sinput} > par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1 ) > plot( NA, xlim=c(40,82), ylim=c(5,300), bty="n", + log="y", xlab="Age", ylab="Mortality rate per 1000 PY" ) > abline( v=seq(40,80,5), h=outer(1:9,10^(0:2),"*"), col=gray(0.8) ) > for( aa in 4:7*10 ) for( ii in 1:4 ) + matshade( aa+as.numeric(dimnames(pr.rates)[[1]]), + cbind( pr.rates[,paste(aa),ii,"DM/Ins",], + pr.rates[,paste(aa),ii,"All" ,] )*1000, + type="l", lty=1, lwd=2, + col=c("red","limegreen") ) \end{Sinput} \end{Schunk} \insfig{mort-int}{0.9}{Estimated mortality rates for male diabetes patients with no insulin (lower sets of curves) and insulin (upper curves), with DM onset in age 40, 50, 60 and 70. The red curves are from the models with separate age effects for persons with and without insulin, and a separate effect of insulin duration. The green curves are from the model with common age-effects and only a time-dependent effect of insulin, assuming no effect of insulin duration (the classical time-dependent variable approach). Hence the upper green curve is common for any time of insulin inception.} From figure \ref{fig:mort-int} we see that there is a substantial insulin-duration effect which is not accommodated by the simple model with only one time-dependent variable to describe the insulin effect. Note that the simple model (green curves) for those on insulin does not depend in insulin duration, and hence the mortality curves for those on insulin are just parallel to the mortality curves for those not on insulin, regardless of diabetes duration (or age) at the time of insulin initiation. This is the proportional hazards assumption. Thus the effect of insulin initiation is under-estimated for short duration of insulin and over-estimated for long duration of insulin. This is the major discrepancy between the two models, and illustrates the importance of being able to accommodate different time scales, but there is also a declining overall insulin effect by age which is not accommodated by the proportional hazards approach. Finally, this plot illustrates an important feature in reporting models with multiple timescales; all timescales must be represented in the predicted rates, only reporting the effect of one timescale, conditional on a fixed value of other timescales is misleading since all timescales by definition advance at the same pace. For example, the age-effect for a fixed value of insulin duration really is a misnomer since it does not correspond to any real person's follow-up, but to the mortality of persons in different ages but with the same duration of insulin use. \section{Input to the \texttt{simLexis} function} We want to estimate the cumulative probability of being in each of the 4 states, so that we can assess the fraction of diabetes pateints that go on insulin In order to simulate from the multistate model with the estimated transition rates, and get the follow-up of a hypothetical cohort, we must supply \emph{both} the transition rates and the structure of the model \emph{as well as} the initial cohort status to \texttt{simLexis}. \subsection{The transition object} We first put the models into an object representing the transitions; note this is a list of lists, the latter having \texttt{glm} objects as elements: \begin{Schunk} \begin{Sinput} > Tr <- list( "DM" = list( "Ins" = DM.Ins, + "Dead" = DM.Dead ), + "Ins" = list( "Dead(Ins)" = Ins.Dead ) ) \end{Sinput} \end{Schunk} Now we have the description of the rates and of the structure of the model. The \texttt{Tr} object defines the states and models for all transitions between them; the object \verb|Tr$A$B| is the model for the transition intensity from state \texttt{A} to state \texttt{B}. \subsection{The initial cohort} We now define an initial \texttt{Lexis} object of persons with all relevant covariates defined. Note that we use \texttt{NULL} as row indicator in the \texttt{Lexis} object we used for modeling; this conserves the \texttt{time.scale} and \texttt{time.since} attributes which are needed for the simulation: \begin{Schunk} \begin{Sinput} > str( ini <- Si[NULL,1:9] ) \end{Sinput} \begin{Soutput} Classes ‘Lexis’ and 'data.frame': 0 obs. of 9 variables: $ lex.id : int $ Per : num $ Age : num $ DMdur : num $ t.Ins : num $ lex.dur: num $ lex.Cst: Factor w/ 4 levels "DM","Ins","Dead",..: $ lex.Xst: Factor w/ 4 levels "DM","Ins","Dead",..: $ sex : Factor w/ 2 levels "M","F": - attr(*, "time.scales")= chr "Per" "Age" "DMdur" "t.Ins" - attr(*, "time.since")= chr "" "" "" "Ins" - attr(*, "breaks")=List of 4 ..$ Per : NULL ..$ Age : NULL ..$ DMdur: num 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 ... ..$ t.Ins: NULL \end{Soutput} \end{Schunk} We now have an empty \texttt{Lexis} object with attributes reflecting the timescales in the multistate model we want to simulate from. But we must enter some data to represent the initial state of the persons whose follow-up we want to simulate through the model; so fill in data for one man and one woman: \begin{Schunk} \begin{Sinput} > ini[1:2,"lex.id"] <- 1:2 > ini[1:2,"lex.Cst"] <- "DM" > ini[1:2,"Per"] <- 1995 > ini[1:2,"Age"] <- 60 > ini[1:2,"DMdur"] <- 5 > ini[1:2,"sex"] <- c("M","F") > ini \end{Sinput} \begin{Soutput} lex.id Per Age DMdur t.Ins lex.dur lex.Cst lex.Xst sex 1 1 1995 60 5 NA NA DM M 2 2 1995 60 5 NA NA DM F \end{Soutput} \end{Schunk} So the persons starts in age 60 in 1995 with 5 years of diabetes duration. Note that the \texttt{t.Ins} is \texttt{NA}, because this is a timescale that first comes alive if a transtion to \texttt{Ins} is simulated. \section{Simulation of the follow-up} Now we simulate life-courses of a 1000 of each of these persons using the estimated model. The \texttt{t.range} argument gives the times range where the integrated intensities (cumulative rates) are evaluated and where linear interpolation is used when simulating transition times. Note that this must be given in the same units as \texttt{lex.dur} in the \texttt{Lexis} object used for fitting the models for the transitions. It is not a parameter that can be easily determined from the \texttt{TR} object, hence it must be supplied by the user. \begin{Schunk} \begin{Sinput} > set.seed( 52381764 ) > Nsim <- 5000 > system.time( simL <- simLexis( Tr, + ini, + t.range = 12, + N = Nsim ) ) \end{Sinput} \begin{Soutput} user system elapsed 18.788 1.130 18.914 \end{Soutput} \end{Schunk} The result is a \texttt{Lexis} object --- a data frame representing the simulated follow-up of 10000 persons (5000 identical men and 5000 identical women) according to the rates we estimated from the original dataset. \begin{Schunk} \begin{Sinput} > summary( simL, by="sex" ) \end{Sinput} \begin{Soutput} $M Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 1438 2048 1514 0 5000 3562 36620.95 5000 Ins 0 1363 0 685 2048 685 10935.47 2048 Sum 1438 3411 1514 685 7048 4247 47556.41 5000 $F Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 2186 1689 1125 0 5000 2814 42181.63 5000 Ins 0 1321 0 368 1689 368 9535.20 1689 Sum 2186 3010 1125 368 6689 3182 51716.83 5000 \end{Soutput} \end{Schunk} \subsection{Using other models for simulation} \subsubsection{Proportional hazards Poisson model} We fitted a proportional mortality model \texttt{All.Dead} (which fitted worse than the other two), this is a model for \emph{both} the transition from \texttt{DM} to \texttt{Death} \emph{and} from \texttt{Ins} to \texttt{Dead(Ins)}, assuming that they are proportional. But it can easily be used in the simulation set-up, because the state is embedded in the model via the term \texttt{lex.Cst}, which is updated during the simulation. Simulation using this instead just requires that we supply a different transition object: \begin{Schunk} \begin{Sinput} > Tr.p <- list( "DM" = list( "Ins" = DM.Ins, + "Dead" = All.Dead ), + "Ins" = list( "Dead(Ins)" = All.Dead ) ) > system.time( simP <- simLexis( Tr.p, + ini, + t.range = 12, + N = Nsim ) ) \end{Sinput} \begin{Soutput} user system elapsed 17.604 0.988 17.625 \end{Soutput} \begin{Sinput} > summary( simP, by="sex" ) \end{Sinput} \begin{Soutput} $M Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 1633 1984 1383 0 5000 3367 37674.18 5000 Ins 0 1135 0 849 1984 849 9807.38 1984 Sum 1633 3119 1383 849 6984 4216 47481.56 5000 $F Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 2285 1695 1020 0 5000 2715 42892.52 5000 Ins 0 1191 0 504 1695 504 8833.70 1695 Sum 2285 2886 1020 504 6695 3219 51726.21 5000 \end{Soutput} \end{Schunk} \subsubsection{Proportional hazards Cox model} A third possibility would be to replace the two-time scale proportional mortality model by a one-time-scale Cox-model, using diabetes duration as time scale, and age at diagnosis of DM as (fixed) covariate: \begin{Schunk} \begin{Sinput} > library( survival ) > Cox.Dead <- coxph( Surv( DMdur, DMdur+lex.dur, + lex.Xst %in% c("Dead(Ins)","Dead")) ~ + Ns( Age-DMdur, knots=ad.kn ) + + I(lex.Cst=="Ins") + + I(Per-2000) + sex, + data = Si ) > round( ci.exp( Cox.Dead ), 3 ) \end{Sinput} \begin{Soutput} exp(Est.) 2.5% 97.5% Ns(Age - DMdur, knots = ad.kn)1 4.172 3.535 4.923 Ns(Age - DMdur, knots = ad.kn)2 4.502 3.824 5.301 Ns(Age - DMdur, knots = ad.kn)3 16.077 14.087 18.348 Ns(Age - DMdur, knots = ad.kn)4 7.479 6.501 8.605 I(lex.Cst == "Ins")TRUE 2.170 1.948 2.418 I(Per - 2000) 0.965 0.954 0.977 sexF 0.667 0.616 0.723 \end{Soutput} \end{Schunk} Note that in order for this model to be usable for simulation, it is necessary that we use the components of the \texttt{Lexis} object to specify the survival. Each record in the data frame \texttt{Si} represents follow up from \texttt{DMdur} to \texttt{DMdur+lex.dur}, so the model is a Cox model with diabetes duration as underlying timescale and age at diagnosis, \texttt{Age-DMdur}, as covariate. Also note that we used \texttt{I(lex.Cst=="Ins")} instead of just \texttt{lex.Cst}, because \texttt{coxph} assigns design matrix columns to all levels of \texttt{lex.Cst}, also those not present in data, which would give \texttt{NA}s among the parameter estimates and \texttt{NA}s as mortality outcomes. We see that the effect of insulin and the other covariates are pretty much the same as in the two-time-scale model. We can simulate from this model too; there is no restrictions on what type of model can be used for different transitions \begin{Schunk} \begin{Sinput} > Tr.c <- list( "DM" = list( "Ins" = Tr$DM$Ins, + "Dead" = Cox.Dead ), + "Ins" = list( "Dead(Ins)" = Cox.Dead ) ) > system.time( simC <- simLexis( Tr.c, + ini, + t.range = 12, + N = Nsim ) ) \end{Sinput} \begin{Soutput} user system elapsed 19.195 1.241 19.470 \end{Soutput} \begin{Sinput} > summary( simC, by="sex" ) \end{Sinput} \begin{Soutput} $M Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 1714 2039 1247 0 5000 3286 37280.04 5000 Ins 0 1348 0 691 2039 691 9990.38 2039 Sum 1714 3387 1247 691 7039 3977 47270.42 5000 $F Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 2332 1702 966 0 5000 2668 42168.20 5000 Ins 0 1313 0 389 1702 389 9083.14 1702 Sum 2332 3015 966 389 6702 3057 51251.34 5000 \end{Soutput} \end{Schunk} \section{Reporting the simulation results} We can now tabulate the number of persons in each state at a predefined set of times on a given time scale. Note that in order for this to be sensible, the \texttt{from} argument would normally be equal to the starting time for the simulated individuals. \begin{Schunk} \begin{Sinput} > system.time( + nSt <- nState( subset(simL,sex=="M"), + at=seq(0,11,0.2), from=1995, time.scale="Per" ) ) \end{Sinput} \begin{Soutput} user system elapsed 0.744 0.000 0.743 \end{Soutput} \begin{Sinput} > nSt[1:10,] \end{Sinput} \begin{Soutput} State when DM Ins Dead Dead(Ins) 1995 5000 0 0 0 1995.2 4932 38 29 1 1995.4 4843 93 62 2 1995.6 4773 137 87 3 1995.8 4702 179 116 3 1996 4621 226 148 5 1996.2 4547 269 179 5 1996.4 4469 309 212 10 1996.6 4407 342 237 14 1996.8 4322 386 275 17 \end{Soutput} \end{Schunk} We see that as time goes by, the 5000 men slowly move away from the starting state (\texttt{DM}). Based on this table (\texttt{nSt} is a table) we can now compute the fractions in each state, or, rather more relevant, the cumulative fraction across the states in some specified order, so that a plot of the stacked probabilities can be made, using either the default rather colorful layout, or a more minimalist version (both in figure \ref{fig:pstate0}): \begin{Schunk} \begin{Sinput} > pM <- pState( nSt, perm=c(1,2,4,3) ) > head( pM ) \end{Sinput} \begin{Soutput} State when DM Ins Dead(Ins) Dead 1995 1.0000 1.0000 1.0000 1 1995.2 0.9864 0.9940 0.9942 1 1995.4 0.9686 0.9872 0.9876 1 1995.6 0.9546 0.9820 0.9826 1 1995.8 0.9404 0.9762 0.9768 1 1996 0.9242 0.9694 0.9704 1 \end{Soutput} \begin{Sinput} > par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) > plot( pM ) > plot( pM, border="black", col="transparent", lwd=3 ) > text( rep(as.numeric(rownames(pM)[nrow(pM)-1]),ncol(pM)), + pM[nrow(pM),]-diff(c(0,pM[nrow(pM),]))/5, + colnames( pM ), adj=1 ) > box( col="white", lwd=3 ) > box() \end{Sinput} \end{Schunk} \insfig{pstate0}{1.0}{Default layout of the \textrm{\tt plot.pState} graph (left), and a version with the state probabilities as lines and annotation of states.} A more useful set-up of the graph would include a more through annotation and sensible choice of colors, as seen in figure \ref{fig:pstatex}: \begin{Schunk} \begin{Sinput} > clr <- c("limegreen","orange") > # expand with a lighter version of the two chosen colors > clx <- c( clr, rgb( t( col2rgb( clr[2:1] )*2 + rep(255,3) ) / 3, max=255 ) ) > par( mfrow=c(1,2), las=1, mar=c(3,3,4,2), mgp=c(3,1,0)/1.6 ) > # Men > plot( pM, col=clx, xlab="Date of FU" ) > lines( as.numeric(rownames(pM)), pM[,2], lwd=3 ) > mtext( "60 year old male, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) > mtext( "Survival curve", side=3, line=1.5, adj=0 ) > mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) > mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) > axis( side=4 ) > axis( side=4, at=1:19/20, labels=FALSE ) > axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) > # Women > pF <- pState( nState( subset(simL,sex=="F"), + at=seq(0,11,0.2), + from=1995, + time.scale="Per" ), + perm=c(1,2,4,3) ) > plot( pF, col=clx, xlab="Date of FU" ) > lines( as.numeric(rownames(pF)), pF[,2], lwd=3 ) > mtext( "60 year old female, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) > mtext( "Survival curve", side=3, line=1.5, adj=0 ) > mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) > mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) > axis( side=4 ) > axis( side=4, at=1:19/20, labels=FALSE ) > axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) \end{Sinput} \end{Schunk} \insfig{pstatex}{1.0}{\textrm{\tt plot.pState} graphs where persons ever on insulin are given in orange and persons never on insulin in green, and the overall survival (dead over the line) as a black line.} If we instead wanted to show the results on the age-scale, we would use age as timescale when constructing the probabilities; otherwise the code is pretty much the same as before (Figure \ref{fig:pstatey}): \begin{Schunk} \begin{Sinput} > par( mfrow=c(1,2), las=1, mar=c(3,3,4,2), mgp=c(3,1,0)/1.6 ) > # Men > pM <- pState( nState( subset(simL,sex=="M"), + at=seq(0,11,0.2), + from=60, + time.scale="Age" ), + perm=c(1,2,4,3) ) > plot( pM, col=clx, xlab="Age" ) > lines( as.numeric(rownames(pM)), pM[,2], lwd=3 ) > mtext( "60 year old male, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) > mtext( "Survival curve", side=3, line=1.5, adj=0 ) > mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) > mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) > axis( side=4 ) > axis( side=4, at=1:19/20, labels=FALSE ) > axis( side=4, at=1:19/20, labels=FALSE, tcl=-0.4 ) > axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) > # Women > pF <- pState( nState( subset(simL,sex=="F"), + at=seq(0,11,0.2), + from=60, + time.scale="Age" ), + perm=c(1,2,4,3) ) > plot( pF, col=clx, xlab="Age" ) > lines( as.numeric(rownames(pF)), pF[,2], lwd=3 ) > mtext( "60 year old female, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) > mtext( "Survival curve", side=3, line=1.5, adj=0 ) > mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) > mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) > axis( side=4 ) > axis( side=4, at=1:9/10, labels=FALSE ) > axis( side=4, at=1:19/20, labels=FALSE, tcl=-0.4 ) > axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) \end{Sinput} \end{Schunk} Note the several statements with \texttt{axis(side=4,...}; they are necessary to get the fine tick-marks in the right hand side of the plots that you will need in order to read off the probabilities at 2006 (or 71 years). \insfig{pstatey}{1.0}{\textrm{\tt plot.pState} graphs where persons ever on insulin are given in orange and persons never on insulin in green, and the overall survival (dead over the line) as a black line.} \subsection{Comparing predictions from different models} We have actually fitted different models for the transitions, and we have simulated Lexis objects from all three approaches, so we can plot these predictions on top of each other: \begin{Schunk} \begin{Sinput} > PrM <- pState( nState( subset(simP,sex=="M"), + at=seq(0,11,0.2), + from=60, + time.scale="Age" ), + perm=c(1,2,4,3) ) > PrF <- pState( nState( subset(simP,sex=="F"), + at=seq(0,11,0.2), + from=60, + time.scale="Age" ), + perm=c(1,2,4,3) ) > CoxM <- pState( nState( subset(simC,sex=="M"), + at=seq(0,11,0.2), + from=60, + time.scale="Age" ), + perm=c(1,2,4,3) ) > CoxF <- pState( nState( subset(simC,sex=="F"), + at=seq(0,11,0.2), + from=60, + time.scale="Age" ), + perm=c(1,2,4,3) ) > par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) > plot( pM, border="black", col="transparent", lwd=3 ) > lines( PrM, border="blue" , col="transparent", lwd=3 ) > lines( CoxM, border="red" , col="transparent", lwd=3 ) > text( 60.5, 0.05, "M" ) > box( lwd=5, col="white" ) ; box( lwd=2, col="black" ) > plot( pF, border="black", col="transparent", lwd=3 ) > lines( PrF, border="blue" , col="transparent", lwd=3 ) > lines( CoxF, border="red" , col="transparent", lwd=3 ) > text( 60.5, 0.05, "F" ) > box( lwd=5, col="white" ) ; box( lwd=2, col="black" ) \end{Sinput} \end{Schunk} \insfig{comp-0}{1.0}{Comparison of the simulated state occupancy probabilities using separate Poisson models for the mortality rates with and without insulin (black) and using proportional hazards Poisson models (blue) and Cox-models with diabetes duration as timescale and age at diabetes diagnosis as covariate (red).} From figure \ref{fig:comp-0} it is clear that the two proportional hazards models (blue and red curves) produce pretty much the same estimates of the state occupancy probabilities over time, but also that they relative to the model with separately estimated transition intensities overestimates the probability of being alive without insulin and underestimates the probabilities of being dead without insulin. However both the overall survival, and the fraction of persons on insulin are quite well in agreement with the more elaborate model. Thus the proportional hazards models overestimate the relative mortality of the insulin treated diabetes patients relative to the non-insulin treated. Interestingly, we also see a bump in the estimated probabilities from the Cox-model based model, but this is entirely an artifact that comes from the estimation method for the baseline hazard of the Cox-model that lets the (cumulative) hazard have large jumps at event times where the risk set is small. So also here it shows up that an assumption of continuous underlying hazards leads to more credible estimates. \chapter{Simulation of transitions in multistate models} \section{Theory} Suppose that the rate functions for the transitions out of the current state to, say, 3 different states are $\lambda_1$, $\lambda_2$ and $\lambda_3$, and the corresponding cumulative rates are $\Lambda_1$, $\Lambda_2$ and $\Lambda_3$, and we want to simulate an exit time and an exit state (that is either 1, 2 or 3). This can be done in two slightly different ways: \begin{enumerate} \item First time, then state: \begin{enumerate} \item Compute the survival function, $S(t) = \exp\bigl(-\Lambda_1(t)-\Lambda_2(t)-\Lambda_3(t)\bigr)$ \item Simulate a random U(0,1) variate, $u$, say. \item The simulated exit time is then the solution $t_u$ to the equation $S(t_u) = u \quad \Leftrightarrow \quad \sum_j\Lambda_j(t_u) = -\log(u)$. \item A simulated transition at $t_u$ is then found by simulating a random draw from the multinomial distribution with probabilities $p_i=\lambda_i(t_u) / \sum_j\lambda_j(t_u)$. \end{enumerate} \item Separate cumulative incidences: \begin{enumerate} \item Simulate 3 independent U(0,1) random variates $u_1$, $u_2$ and $u_3$. \item Solve the equations $\Lambda_i(t_i)=-\log(u_i), i=1,2,3$ and get $(t_1,t_2,t_3)$. \item The simulated survival time is then $\min(t_1,t_2,t_3)$, and the simulated transition is to the state corresponding to this, that is $k \in \{1,2,3\}$, where $t_k=\min(t_1,t_2,t_3)$ \end{enumerate} \end{enumerate} The intuitive argument is that with three possible transition there are 3 independent processes running, but only the first transition is observed. The latter approach is used in the implementation in \texttt{simLexis}. The formal argument for the equality of the two approaches goes as follows: \begin{enumerate} \item Equality of the transition times: \begin{enumerate} \item In the first approach we simulate from a distribution with cumulative rate $\Lambda_1(t)+\Lambda_2(t)+\Lambda_3(t)$, hence from a distribution with survival function: \begin{align*} S(t) & = \exp\bigl(-(\Lambda_1(t)+\Lambda_2(t)+\Lambda_3(t))\bigr) \\ & = \exp\bigl(-\Lambda_1(t)\bigr)\times \exp\bigl(-\Lambda_2(t)\bigr)\times \exp\bigl(-\Lambda_3(t)\bigr) \end{align*} \item In the second approach we choose the smallest of three independent survival times, with survival functions $\exp(-\Lambda_i), i=1,2,3$. Now, the survival function for the minimum of three independent survival times is: \begin{align*} S_\text{min}(t) & = \pmat{\min(t_1,t_2,t_3)>t} \\ & = \pmat{t_1>t} \times \pmat{t_2>t} \times \pmat{t_3>t} \\ & = \exp\bigl(-\Lambda_1(t)\bigr)\times \exp\bigl(-\Lambda_2(t)\bigr)\times \exp\bigl(-\Lambda_3(t)\bigr) \end{align*} which is the same survival function as derived above. \end{enumerate} \item Type of transition: \begin{enumerate} \item In the first instance the probability of a transition to state $i$, conditional on the transition time being $t$, is as known from standard probability theory: $\lambda_i(t)/\bigl(\lambda_1(t)+\lambda_2(t)+\lambda_3(t)\bigr)$. \item In the second approach we choose the transition corresponding to the the smallest of the transition times. So when we condition on the event that a transition takes place at time $t$, we have to show that the conditional probability that the smallest of the three simulated transition times was actually the $i$th, is as above. But conditional on \emph{survival} till $t$, the probabilities that events of type $1,2,3$ takes place in the interval $(t,t+\dif t)$ are $\lambda_1(t)\dif t$, $\lambda_2(t)\dif t$ and $\lambda_1(t)\dif t$, respectively (assuming that the probability of more than one event in the interval of length $\dif t$ is 0). Hence the conditional probabilities \emph{given a transition time} in $(t,t+\dif t)$ is: \[ \frac{\lambda_i(t)\dif t}{\lambda_1(t)\dif t+\lambda_2(t)\dif t+\lambda_3(t)\dif t}= \frac{\lambda_i(t)}{\lambda_1(t)+\lambda_2(t)+\lambda_3(t)} \] --- exactly as above. \end{enumerate} \end{enumerate} \section{Components of \texttt{simLexis}} This section explains the actually existing code for \texttt{simLexis}, as it is in the current version of \texttt{Epi}. % The following code sources the originally formatted code in % simLexis.R in order to make it printable with all the formatting and % comments in it. However the sourcing does not work when compiling % the vignettes in R CMD build. So when checking the code we comment % this out by putting eval=FALSE, and moreover, because it is only % simLexis that is exported, we also need to bring the functions simX, % sim1, lint, get.next and chop.lex into the workspace. So depending % on whether we actually construct the pdf for the inst/doc folder or % test (upload) the package, one of the following to chunks are run % with eval=FALSE and the other with eval=TRUE % When compiling the published vignette % When checking the package The function \texttt{simLexis} takes a \texttt{Lexis} object as input. This defines the initial state(s) and times of the start for a number of persons. Since the purpose is to simulate a history through the estimated multistate model, the input values of the outcome variables \texttt{lex.Xst} and \texttt{lex.dur} are ignored --- the aim is to simulate values for them. Note however that the attribute \texttt{time.since} must be present in the object. This is used for initializing timescales defined as time since entry into a particular state, it is a character vector of the same length as the \texttt{time.scales} attribute, with value equal to a state name if the corresponding time scale is defined as time since entry into that state. In this example the 4th timescale is time since entry into the \texttt{Ins} state, and hence: \begin{Schunk} \begin{Sinput} > cbind( + attr( ini, "time.scales" ), + attr( ini, "time.since" ) ) \end{Sinput} \begin{Soutput} [,1] [,2] [1,] "Per" "" [2,] "Age" "" [3,] "DMdur" "" [4,] "t.Ins" "Ins" \end{Soutput} \end{Schunk} \texttt{Lexis} objects will have this attribute set for time scales created using \texttt{cutLexis}. The other necessary argument is a transition object \texttt{Tr}, which is a list of lists. The elements of the lists should be \texttt{glm} objects derived by fitting Poisson models to a \texttt{Lexis} object representing follow-up data in a multistate model. It is assumed (but not checked) that timescales enter in the model via the timescales of the \texttt{Lexis} object. Formally, there are no assumptions about how \texttt{lex.dur} enters in the model. Optional arguments are \texttt{t.range}, \texttt{n.int} or \texttt{time.pts}, specifying the times after entry at which the cumulative rates will be computed (the maximum of which will be taken as the censoring time), and \texttt{N} a scalar or numerical vector of the number of persons with a given initial state each record of the \texttt{init} object should represent. The central part of the functions uses a \texttt{do.call} / \texttt{lapply} / \texttt{split} construction to do simulations for different initial states. This is the construction in the middle that calls \texttt{simX}. \texttt{simLexis} also calls \texttt{get.next} which is further detailed below. \begin{Schunk} \begin{Sinput} > simLexis \end{Sinput} \begin{Soutput} function (Tr, init, N = 1, lex.id, t.range = 20, n.int = 101, time.pts = seq(0, t.range, length.out = n.int)) { if (time.pts[1] != 0) stop("First time point must be 0, time.pts[1:3]= ", time.pts[1:3]) if (!missing(N)) { if (length(N) == 1) init <- init[rep(1:nrow(init), each = N), ] else init <- init[rep(1:nrow(init), N), ] } if (!missing(lex.id)) { if (length(lex.id) == nrow(init)) init$lex.id <- lex.id else init$lex.id <- 1:nrow(init) } else init$lex.id <- 1:nrow(init) if (is.null(tS <- attr(init, "time.scales"))) stop("No time.scales attribute for init") if (is.null(tF <- attr(init, "time.since"))) { attr(init, "time.since") <- tF <- rep("", tS) warning("'time.since' attribute set to blanks") } np <- length(time.pts) tr.st <- names(Tr) sf <- NULL nxt <- init[init$lex.Cst %in% tr.st, ] if (nrow(nxt) < nrow(init)) { tt <- table(init$lex.Cst) tt <- tt[tt > 0] nt <- length(tt) warning("\nSome initiators start in a absorbing state\n", "Initiator states represented are: ", paste(rbind(names(tt), rep(":", nt), paste(tt), rep(" ", nt)), collapse = ""), "\n", "Transient states are: ", paste(names(Tr), coll = " ")) if (nrow(nxt) == 0) stop("\nNo initiators in transient states!") } while (nrow(nxt) > 0) { nx <- do.call(rbind.data.frame, lapply(split(nxt, nxt$lex.Cst), simX, Tr, time.pts, tS)) sf <- rbind.data.frame(sf, nx) nxt <- get.next(nx, tr.st, tS, tF) } sf$lex.Xst <- factor(sf$lex.Xst, levels = levels(sf$lex.Cst)) sf$lex.Xst[is.na(sf$lex.Xst)] <- sf$lex.Cst[is.na(sf$lex.Xst)] nord <- match(c("lex.id", tS, "lex.dur", "lex.Cst", "lex.Xst"), names(sf)) noth <- setdiff(1:ncol(sf), nord) sf <- sf[order(sf$lex.id, sf[, tS[1]]), c(nord, noth)] rownames(sf) <- NULL attr(sf, "time.scales") <- tS attr(sf, "time.since") <- tF chop.lex(sf, tS, max(time.pts)) } \end{Soutput} \end{Schunk} \subsection{\texttt{simX}} \texttt{simX} is called by \texttt{simLexis} and simulates transition-times and -types for a set of patients assumed to be in the same state. It is called from \texttt{simLexis} with a data frame as argument, uses the state in \texttt{lex.Cst} to select the relevant component of \texttt{Tr} and compute predicted cumulative intensities for all states reachable from this state. Note that it is here the switch between \texttt{glm}, \texttt{coxph} and objects of class \texttt{function} is made. The dataset on which this prediction is done has \texttt{length(time.pts)} rows per person. \begin{Schunk} \begin{Sinput} > simX \end{Sinput} \begin{Soutput} function (nd, Tr, time.pts, tS) { np <- length(time.pts) nr <- nrow(nd) if (nr == 0) return(NULL) cst <- as.character(unique(nd$lex.Cst)) if (length(cst) > 1) stop("More than one lex.Cst present:\n", cst, "\n") prfrm <- nd[rep(1:nr, each = np), ] prfrm[, tS] <- prfrm[, tS] + rep(time.pts, nr) prfrm$lex.dur <- il <- min(diff(time.pts)) prfrp <- prfrm prfrp[, "lex.dur"] <- 1 prfrp[, tS] <- prfrp[, tS] + il/2 rt <- data.frame(lex.id = prfrm$lex.id) for (i in 1:length(Tr[[cst]])) { if (inherits(Tr[[cst]][[i]], "glm")) rt <- cbind(rt, predict(Tr[[cst]][[i]], type = "response", newdata = prfrp) * il) else if (inherits(Tr[[cst]][[i]], "coxph")) rt <- cbind(rt, predict(Tr[[cst]][[i]], type = "expected", newdata = prfrm)) else if (is.function(Tr[[cst]][[i]])) rt <- cbind(rt, Tr[[cst]][[i]](prfrm)) else stop("Invalid object supplied as transition, elements of the list must be either:\n", "- a glm(poisson) object fitted to a Lexis object\n", "- a coxph object fitted to a Lexis object\n", "- a function that takes a Lexis object as argument and returns\n", " average rates for each record in the same units as lex.dur.") } names(rt)[-1] <- names(Tr[[cst]]) xx <- match(c("lex.dur", "lex.Xst"), names(nd)) if (any(!is.na(xx))) nd <- nd[, -xx[!is.na(xx)]] merge(nd, do.call(rbind, lapply(split(rt, rt$lex.id), sim1, time.pts)), by = "lex.id") } \end{Soutput} \end{Schunk} As we see, \texttt{simX} calls \texttt{sim1} which simulates the transition for one person. \subsection{\texttt{sim1}} The predicted cumulative intensities are fed, person by person, to \texttt{sim1} --- again via a \texttt{do.call} / \texttt{lapply} / \texttt{split} construction --- and the resulting time and state is appended to the \texttt{nd} data frame. This way we have simulated \emph{one} transition (time and state) for each person: \begin{Schunk} \begin{Sinput} > sim1 \end{Sinput} \begin{Soutput} function (rt, time.pts) { ci <- apply(rbind(0, rt[, -1, drop = FALSE]), 2, cumsum)[1:nrow(rt), , drop = FALSE] tt <- uu <- -log(runif(ncol(ci))) for (i in 1:ncol(ci)) tt[i] <- lint(ci[, i], time.pts, uu[i]) data.frame(lex.id = rt[1, 1], lex.dur = min(tt, na.rm = TRUE), lex.Xst = factor(if (min(tt) < max(time.pts)) colnames(ci)[tt == min(tt)] else NA)) } \end{Soutput} \end{Schunk} The \texttt{sim1} function uses \texttt{lint} to do linear interpolation. \subsection{\texttt{lint}} We do not use \texttt{approx} to do the linear interpolation, because this function does not do the right thing if the cumulative incidences (\texttt{ci}) are constant across a number of times. Therefore we have a custom made linear interpolator that does the interpolation exploiting the fact the the \texttt{ci} is non-decreasing and \texttt{tt} is strictly monotonously increasing: \begin{Schunk} \begin{Sinput} > lint \end{Sinput} \begin{Soutput} function (ci, tt, u) { if (any(diff(ci) < 0) | any(diff(tt) < 0)) stop("Non-increasing arguments") c.u <- min(c(ci[ci > u], max(ci))) c.l <- max(c(ci[ci < u], min(ci))) t.u <- min(c(tt[ci > u], max(tt))) t.l <- max(c(tt[ci < u], min(tt))) ifelse(c.u == c.l, t.l, t.l + (u - c.l)/(c.u - c.l) * (t.u - t.l)) } \end{Soutput} \end{Schunk} \subsection{\texttt{get.next}} We must repeat the simulation operation on those that have a simulated entry to a transient state, and also make sure that any time scales defined as time since entry to one of these states be initialized to 0 before a call to \texttt{simX} is made for these persons. This accomplished by the function \texttt{get.next}: \begin{Schunk} \begin{Sinput} > get.next \end{Sinput} \begin{Soutput} function (sf, tr.st, tS, tF) { if (nrow(sf) == 0) return(sf) nxt <- sf[sf$lex.Xst %in% tr.st, ] if (nrow(nxt) == 0) return(nxt) nxt[, tS] <- nxt[, tS] + nxt$lex.dur wh <- tF for (i in 1:length(wh)) if (wh[i] != "") nxt[nxt$lex.Xst == wh[i], tS[i]] <- 0 nxt$lex.Cst <- nxt$lex.Xst return(nxt) } \end{Soutput} \end{Schunk} \subsection{\texttt{chop.lex}} The operation so far has censored individuals \texttt{max(time.pts)} after \emph{each} new entry to a transient state. In order to groom the output data we use \texttt{chop.lex} to censor all persons at the same designated time after \emph{initial} entry. \begin{Schunk} \begin{Sinput} > chop.lex \end{Sinput} \begin{Soutput} function (obj, tS, cens) { zz <- entry(obj, 1, by.id = TRUE) ww <- merge(obj, data.frame(lex.id = as.numeric(names(zz)), cens = zz + cens)) ww <- ww[ww[, tS[1]] < ww$cens, ] x.dur <- pmin(ww$lex.dur, ww[, "cens"] - ww[, tS[1]]) ww$lex.Xst[x.dur < ww$lex.dur] <- ww$lex.Cst[x.dur < ww$lex.dur] ww$lex.dur <- pmin(x.dur, ww$lex.dur) ww } \end{Soutput} \end{Schunk} \section{Probabilities from simulated \texttt{Lexis} objects} Once we have simulated a Lexis object we will of course want to use it for estimating probabilities, so basically we will want to enumerate the number of persons in each state at a pre-specified set of time points. \subsection{\texttt{nState}} Since we are dealing with multistate model with potentially multiple time scales, it is necessary to define the timescale (\texttt{time.scale}), the starting point on this timescale (\texttt{from}) and the points after this where we compute the number of occupants in each state, (\texttt{at}). \begin{Schunk} \begin{Sinput} > nState \end{Sinput} \begin{Soutput} function (obj, at, from, time.scale = 1) { tS <- check.time.scale(obj, time.scale) TT <- tmat(obj) absorb <- rownames(TT)[apply(!is.na(TT), 1, sum) == 0] transient <- setdiff(rownames(TT), absorb) tab.frm <- obj[rep(1:nrow(obj), each = length(at)), c(tS, "lex.dur", "lex.Cst", "lex.Xst")] tab.frm$when <- rep(at, nrow(obj)) + from tab.tr <- tab.frm[tab.frm[, tS] <= tab.frm$when & tab.frm[, tS] + tab.frm$lex.dur > tab.frm$when, ] tab.tr$State <- tab.tr$lex.Cst tab.ab <- tab.frm[tab.frm[, tS] + tab.frm$lex.dur <= tab.frm$when & tab.frm$lex.Xst %in% absorb, ] tab.ab$State <- tab.ab$lex.Xst with(rbind(tab.ab, tab.tr), table(when, State)) } \end{Soutput} \end{Schunk} \subsection{\texttt{pState}, \texttt{plot.pState} and \texttt{lines.pState}} In order to plot probabilities of state-occupancy it is useful to compute cumulative probabilities across states in any given order; this is done by the function \texttt{pState}, which returns a matrix of class \texttt{pState}: \begin{Schunk} \begin{Sinput} > pState \end{Sinput} \begin{Soutput} function (nSt, perm = 1:ncol(nSt)) { tt <- t(apply(nSt[, perm], 1, cumsum)) tt <- sweep(tt, 1, tt[, ncol(tt)], "/") class(tt) <- c("pState", "matrix") tt } \end{Soutput} \end{Schunk} There is also a \texttt{plot} and \texttt{lines} method for the resulting \texttt{pState} objects: \begin{Schunk} \begin{Sinput} > plot.pState \end{Sinput} \begin{Soutput} function (x, col = rainbow(ncol(x)), border = "transparent", xlab = "Time", ylim = 0:1, ylab = "Probability", ...) { matplot(as.numeric(rownames(x)), x, type = "n", ylim = ylim, yaxs = "i", xaxs = "i", xlab = xlab, ylab = ylab, ...) lines.pState(x, col = col, border = border, ...) } \end{Soutput} \begin{Sinput} > lines.pState \end{Sinput} \begin{Soutput} function (x, col = rainbow(ncol(x)), border = "transparent", ...) { nc <- ncol(x) col <- rep(col, nc)[1:nc] border <- rep(border, nc)[1:nc] pSt <- cbind(0, x) for (i in 2:ncol(pSt)) { polygon(c(as.numeric(rownames(pSt)), rev(as.numeric(rownames(pSt)))), c(pSt[, i], rev(pSt[, i - 1])), col = col[i - 1], border = border[i - 1], ...) } } \end{Soutput} \end{Schunk} \bibliographystyle{plain} \begin{thebibliography}{1} \bibitem{Carstensen.2011a} B~Carstensen and M~Plummer. \newblock Using {L}exis objects for multi-state models in {R}. \newblock {\em Journal of Statistical Software}, 38(6):1--18, 1 2011. \bibitem{Iacobelli.2013} S~Iacobelli and B~Carstensen. \newblock {Multiple time scales in multi-state models}. \newblock {\em Stat Med}, 32(30):5315--5327, Dec 2013. \bibitem{Plummer.2011} M~Plummer and B~Carstensen. \newblock Lexis: An {R} class for epidemiological studies with long-term follow-up. \newblock {\em Journal of Statistical Software}, 38(5):1--12, 1 2011. \end{thebibliography} \addcontentsline{toc}{chapter}{References} \end{document} Epi/vignettes/useful.tex0000644000176200001440000002363113430576324015040 0ustar liggesusers% This is a file of useful extra commands snatched from % Michael Hills, David Clayton, Bendix Carstensen & Esa Laara. % % Commands to draw observation lines on follow-up diagrams % % Horizontal lines % \providecommand{\hfail}[1]{\begin{picture}(250,5) \put(0,0){\line(1,0){#1}} \put(#1,0){\circle*{5}} \end{picture}} \providecommand{\hcens}[1]{\begin{picture}(250,5) \put(0,0){\line(1,0){#1}} \put(#1,0){\line(0,1){2.5}} \put(#1,0){\line(0,-1){2.5}} \end{picture}} % % Diagonals for Lexis diagrams % \providecommand{\dfail}[1]{\begin{picture}(250,250) \put(0,0){\line(1,1){#1}} \put(#1,#1){\circle*{5}} \end{picture}} \providecommand{\dcens}[1]{\begin{picture}(250,250) \put(0,0){\line(1,1){#1}} % \put(#1,#1){\line(0,1){2.5}} % \put(#1,#1){\line(0,-1){2.5}} % BxC Changed this to an open circle instead of a line \put(#1,#1){\circle{5}} 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\providecommand{\R}{{\textsf{\textbf{R}}}} \providecommand{\sas}{\textsl{\textbf{SAS}}} \providecommand{\SAS}{\textsl{\textbf{SAS}}} %\providecommand{\gap}[0]{\\[5pt]} %\providecommand{\blank}[0]{$\;\,$} % Conditional independence sign from Philip Dawid \providecommand{\cip}{\mbox{$\perp\!\!\!\perp$}} %%% Commands to comment out parts of the text \providecommand{\GLEM}[1]{} \providecommand{\FORGETIT}[1]{} \providecommand{\OMIT}[1]{} %%% Insert output from program in small text %%% (requires package verbatim) \providecommand{\insoutsmall}[1]{ \small \renewcommand{\baselinestretch}{0.8} \verbatiminput{#1} \renewcommand{\baselinestretch}{1.0} \normalsize } \providecommand{\insoutfoot}[1]{ \footnotesize \renewcommand{\baselinestretch}{0.8} \verbatiminput{#1} \renewcommand{\baselinestretch}{1.0} \normalsize } \providecommand{\insout}[1]{ \scriptsize \renewcommand{\baselinestretch}{0.8} \verbatiminput{#1} \renewcommand{\baselinestretch}{1.0} \normalsize } \providecommand{\insouttiny}[1]{ \tiny \renewcommand{\baselinestretch}{0.8} \verbatiminput{#1} \renewcommand{\baselinestretch}{1.0} \normalsize } % From Esa: \providecommand{\T}{\text{\rm \small{T}}} \providecommand{\id}{\operatorname{id}} \providecommand{\Dev}{\operatorname{Dev}} \providecommand{\Bin}{\operatorname{Bin}} \providecommand{\probit}{\operatorname{probit}} \providecommand{\cloglog}{\operatorname{cloglog}} % Special commands to include output from R, Bugs and Stata \providecommand{\Rin}[2]{ \subsection{\texttt{#1.R}} #2 \insout{./R/#1.Rout} } \providecommand{\Statain}[2]{ \subsection{\texttt{#1.do}} #2 \insout{./do/#1.log} } \providecommand{\Bugsin}[2]{ \subsection{\texttt{#1.bug}} #2 \insout{./bugs/#1.bug} } \newlength{\wdth} \providecommand{\fxbl}[1]{\settowidth{\wdth}{#1} \makebox[\wdth]{}} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End: Epi/vignettes/flup.tex0000644000176200001440000025476514003562712014512 0ustar liggesusers%\VignetteIndexEntry{Follow-up data with the Lexis functions in Epi} \documentclass[a4paper,dvipsnames,twoside,12pt]{report} \newcommand{\Title}{Follow-up data with the\\ \texttt{Lexis} functions in \texttt{Epi}} \newcommand{\Tit}{Follow-up with \texttt{Lexis}} \newcommand{\Version}{Version 6} \newcommand{\Dates}{August 2019} \newcommand{\Where}{SDCC} \newcommand{\Homepage}{\url{http://bendixcarstensen.com/} } \newcommand{\Faculty}{\begin{tabular}{rl} Bendix Carstensen & Steno Diabetes Center Copenhagen, Gentofte, Denmark\\ & {\small \& Department of Biostatistics, University of Copenhagen} \\ & \texttt{b@bxc.dk} \\ & \url{http://BendixCarstensen.com} \\[1em] \end{tabular}} \input{topreport} \renewcommand{\rwpre}{./flup} \chapter*{Introduction} \addcontentsline{toc}{chapter}{Introduction} This is an introduction to the \texttt{Lexis} machinery in the \texttt{Epi} package. The machinery is intended for representation and manipulation of follow-up data (event history data) from studies where exact dates of events are known. It accommodates follow-up through multiple states and on multiple time scales. This vignette uses an example from the \texttt{Epi} package to illustrate the set-up of a simple \texttt{Lexis} object (a data frame of follow-up intervals), as well as the subdivision of follow-up intervals needed for multistate representation and analysis of transition rates. The first chapter is exclusively on manipulation of the follow-up representation, but it points to the subsequent chapter where analysis is based on a \texttt{Lexis} representation with very small follow-up intervals. Chapter 2 uses analysis of mortality rates among Danish diabetes patients (available in the \texttt{Epi} package) currently on insulin treatment or not to illustrate the use of the the \texttt{Lexis} machinery. I owe much thanks to my colleague Lars Jorge Diaz for careful reading and many constructive suggestions. \section{History} The \texttt{Lexis} machinery in the \texttt{Epi} package was first conceived by Martyn Plummer\cite{Plummer.2011,Carstensen.2011a}, and since its first appearance in the \texttt{Epi} package in 2008 it has been expanded with a number of utilities. An overview of these can be found in the last chapter of this note: ``\texttt{Lexis} functions''. \chapter{Representation of follow-up data in the \texttt{Epi} package} In the \texttt{Epi}-package, follow-up data is represented by adding some extra variables to a data frame. Such a data frame is called a \texttt{Lexis} object. The tools for handling follow-up data then use the structure of this for special plots, tabulations and modeling. Follow-up data basically consists of a time of entry, a time of exit and an indication of the status at exit (normally either ``alive'' or ``dead'') for each person. Implicitly is also assumed a status \emph{during} the follow-up (usually ``alive''). \begin{figure}[htbp] \centering \setlength{\unitlength}{1pt} \begin{picture}(210,70)(0,75) %\scriptsize \thicklines \put( 0,80){\makebox(0,0)[r]{Age-scale}} \put( 50,80){\line(1,0){150}} \put( 50,80){\line(0,1){5}} \put(100,80){\line(0,1){5}} \put(150,80){\line(0,1){5}} \put(200,80){\line(0,1){5}} \put( 50,77){\makebox(0,0)[t]{35}} \put(100,77){\makebox(0,0)[t]{40}} \put(150,77){\makebox(0,0)[t]{45}} \put(200,77){\makebox(0,0)[t]{50}} \put( 0,115){\makebox(0,0)[r]{Follow-up}} \put( 80,105){\makebox(0,0)[r]{\small Two}} \put( 90,105){\line(1,0){87}} \put( 90,100){\line(0,1){10}} \put(100,100){\line(0,1){10}} \put(150,100){\line(0,1){10}} \put(180,105){\circle{6}} \put( 95,110){\makebox(0,0)[b]{1}} \put(125,110){\makebox(0,0)[b]{5}} \put(165,110){\makebox(0,0)[b]{3}} \put( 50,130){\makebox(0,0)[r]{\small One}} \put( 60,130){\line(1,0){70}} \put( 60,125){\line(0,1){10}} \put(100,125){\line(0,1){10}} \put(130,130){\circle*{6}} \put( 80,135){\makebox(0,0)[b]{4}} \put(115,135){\makebox(0,0)[b]{3}} \end{picture} \caption{\it Follow-up of two persons} \label{fig:fu2} \end{figure} \section{Time scales} A time scale is a variable that varies deterministically \emph{within} each person during follow-up, \textit{e.g.}: \begin{itemize} \item Age \item Calendar time \item Time since start of treatment \item Time since relapse \end{itemize} All time scales advance at the same pace, so the time followed is the same on all time scales. Therefore, it will suffice to use only the entry point on each of the time scales, for example: \begin{itemize} \item Age at entry \item Date of entry \item Time at treatment (\emph{at} treatment this is 0) \item Time at relapse (\emph{at} relapse this is 0) \end{itemize} For illustration we need to load the \texttt{Epi} package: \begin{Schunk} \begin{Sinput} > library(Epi) > print( sessionInfo(), l=F ) \end{Sinput} \begin{Soutput} R version 3.6.3 (2020-02-29) Platform: x86_64-pc-linux-gnu (64-bit) Running under: Ubuntu 14.04.6 LTS Matrix products: default BLAS: /usr/lib/openblas-base/libopenblas.so.0 LAPACK: /usr/lib/lapack/liblapack.so.3.0 attached base packages: [1] utils datasets graphics grDevices stats methods base other attached packages: [1] Epi_2.43 loaded via a namespace (and not attached): [1] Rcpp_1.0.3 magrittr_1.5 splines_3.6.3 MASS_7.3-53 [5] tidyselect_0.2.5 lattice_0.20-41 R6_2.4.1 rlang_0.4.4 [9] plyr_1.8.5 dplyr_0.8.4 cmprsk_2.2-7 tools_3.6.3 [13] parallel_3.6.3 grid_3.6.3 data.table_1.12.0 nlme_3.1-149 [17] mgcv_1.8-33 survival_3.2-7 assertthat_0.2.1 tibble_2.1.3 [21] etm_1.0.4 numDeriv_2016.8-1 crayon_1.3.4 Matrix_1.2-18 [25] purrr_0.3.0 glue_1.3.1 compiler_3.6.3 pillar_1.4.3 [29] zoo_1.8-4 pkgconfig_2.0.3 \end{Soutput} \end{Schunk} In the \texttt{Epi} package, follow-up in a cohort is represented in a \texttt{Lexis} object. As mentioned, a \texttt{Lexis} object is a data frame with some extra structure representing the follow-up. For the \texttt{DMlate} data --- follow-up of diabetes patients in Denmark recording date of birth, date of diabetes, date of insulin use, date of first oral drug use and date of death --- we can construct a \texttt{Lexis} object by: \begin{Schunk} \begin{Sinput} > data( DMlate ) > head( DMlate ) \end{Sinput} \begin{Soutput} sex dobth dodm dodth dooad doins dox 50185 F 1940.256 1998.917 NA NA NA 2009.997 307563 M 1939.218 2003.309 NA 2007.446 NA 2009.997 294104 F 1918.301 2004.552 NA NA NA 2009.997 336439 F 1965.225 2009.261 NA NA NA 2009.997 245651 M 1932.877 2008.653 NA NA NA 2009.997 216824 F 1927.870 2007.886 2009.923 NA NA 2009.923 \end{Soutput} \begin{Sinput} > dmL <- Lexis( entry = list( per=dodm, + age=dodm-dobth, + tfD=0 ), + exit = list( per=dox ), + exit.status = factor( !is.na(dodth), labels=c("DM","Dead") ), + data = DMlate ) \end{Sinput} \begin{Soutput} NOTE: entry.status has been set to "DM" for all. NOTE: Dropping 4 rows with duration of follow up < tol \end{Soutput} \begin{Sinput} > timeScales(dmL) \end{Sinput} \begin{Soutput} [1] "per" "age" "tfD" \end{Soutput} \end{Schunk} (The excluded persons are persons with date of diabetes equal to date of death.) The \texttt{entry} argument is a \emph{named} list with the entry points on each of the time scales we want to use. It defines the names of the time scales and the entry points of the follow-up of each person. The \texttt{exit} argument gives the exit time on \emph{one} of the time scales, so the name of the element in this list must match one of the names of the \texttt{entry} list. This is sufficient, because the follow-up time on all time scales is the same, in this case $\mathtt{dox}$-$\mathtt{dodm}$. The \texttt{exit.status} is a categorical variable (a \emph{factor}) that indicates the exit status --- in this case whether the person (still) is in state \texttt{DM} or exits to \texttt{Dead} at the end of follow-up. In principle we should also indicate the \texttt{entry.status}, but the default is to assume that all persons enter in the \emph{first} of the mentioned \texttt{exit.state}s --- in this case \texttt{DM}, because $\mathtt{FALSE}<\mathtt{TRUE}$. Now take a look at the result: \begin{Schunk} \begin{Sinput} > str( dmL ) \end{Sinput} \begin{Soutput} Classes ‘Lexis’ and 'data.frame': 9996 obs. of 14 variables: $ per : num 1999 2003 2005 2009 2009 ... $ age : num 58.7 64.1 86.3 44 75.8 ... $ tfD : num 0 0 0 0 0 0 0 0 0 0 ... $ lex.dur: num 11.08 6.689 5.446 0.736 1.344 ... $ lex.Cst: Factor w/ 2 levels "DM","Dead": 1 1 1 1 1 1 1 1 1 1 ... $ lex.Xst: Factor w/ 2 levels "DM","Dead": 1 1 1 1 1 2 1 1 2 1 ... $ lex.id : int 1 2 3 4 5 6 7 8 9 10 ... $ sex : Factor w/ 2 levels "M","F": 2 1 2 2 1 2 1 1 2 1 ... $ dobth : num 1940 1939 1918 1965 1933 ... $ dodm : num 1999 2003 2005 2009 2009 ... $ dodth : num NA NA NA NA NA ... $ dooad : num NA 2007 NA NA NA ... $ doins : num NA NA NA NA NA NA NA NA NA NA ... $ dox : num 2010 2010 2010 2010 2010 ... - attr(*, "time.scales")= chr "per" "age" "tfD" - attr(*, "time.since")= chr "" "" "" - attr(*, "breaks")=List of 3 ..$ per: NULL ..$ age: NULL ..$ tfD: NULL \end{Soutput} \begin{Sinput} > head( dmL )[,1:10] \end{Sinput} \begin{Soutput} per age tfD lex.dur lex.Cst lex.Xst lex.id sex dobth dodm 50185 1998.917 58.66119 0 11.0800821 DM DM 1 F 1940.256 1998.917 307563 2003.309 64.09035 0 6.6885695 DM DM 2 M 1939.218 2003.309 294104 2004.552 86.25051 0 5.4455852 DM DM 3 F 1918.301 2004.552 336439 2009.261 44.03559 0 0.7364819 DM DM 4 F 1965.225 2009.261 245651 2008.653 75.77550 0 1.3442847 DM DM 5 M 1932.877 2008.653 216824 2007.886 80.01643 0 2.0369610 DM Dead 6 F 1927.870 2007.886 \end{Soutput} \end{Schunk} The \texttt{Lexis} object \texttt{dmL} has a variable for each time scale which is the entry point on this time scale. The follow-up time is in the variable \texttt{lex.dur} (\texttt{dur}ation). Note that the exit status is in the variable \texttt{lex.Xst} (e\texttt{X}it \texttt{st}ate. The variable \texttt{lex.Cst} is the state where the follow-up takes place (\texttt{C}urrent \texttt{st}ate), in this case \texttt{DM} (alive with diabetes) for all persons. This implies that \emph{censored} observations are characterized by having $\mathtt{lex.Cst}=\mathtt{lex.Xst}$. There is a \texttt{summary} function for \texttt{Lexis} objects that lists the number of transitions and records as well as the total amount of follow-up time; it also (optionally) prints information about the names of the variables that constitute the time scales: \begin{Schunk} \begin{Sinput} > summary.Lexis( dmL, timeScales=TRUE ) \end{Sinput} \begin{Soutput} Transitions: To From DM Dead Records: Events: Risk time: Persons: DM 7497 2499 9996 2499 54273.27 9996 Timescales: per age tfD "" "" "" \end{Soutput} \end{Schunk} It is possible to get a visualization of the follow-up along the time scales chosen by using the \texttt{plot} method for \texttt{Lexis} objects. \texttt{dmL} is an object of \emph{class} \texttt{Lexis}, so using the function \texttt{plot()} on it means that \R\ will look for the function \texttt{plot.Lexis} and use this function. \begin{Schunk} \begin{Sinput} > plot( dmL ) \end{Sinput} \end{Schunk} The function allows quite a bit of control over the output, and a \texttt{points.Lexis} function allows plotting of the endpoints of follow-up: \begin{Schunk} \begin{Sinput} > par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) > plot( dmL, 1:2, lwd=1, col=c("blue","red")[dmL$sex], + grid=TRUE, lty.grid=1, col.grid=gray(0.7), + xlim=1960+c(0,60), xaxs="i", + ylim= 40+c(0,60), yaxs="i", las=1 ) > points( dmL, 1:2, pch=c(NA,3)[dmL$lex.Xst], + col="lightgray", lwd=3, cex=0.3 ) > points( dmL, 1:2, pch=c(NA,3)[dmL$lex.Xst], + col=c("blue","red")[dmL$sex], lwd=1, cex=0.3 ) > box(bty='o') \end{Sinput} \end{Schunk} In the above code you will note that the values of the arguments \texttt{col} and \texttt{pch} are indexed by factors, using the convention in \R\ that the index is taken as \emph{number of the level} of the supplied factor. Thus \texttt{c("blue","red")[dmL\$sex]} is \texttt{"blue"} when \texttt{sex} is \texttt{M} (the first level). The results of these two plotting commands are in figure \ref{fig:Lexis-diagram}, p. \pageref{fig:Lexis-diagram}. \begin{figure}[tb] \centering \includegraphics[width=0.35\textwidth]{flup-dmL1} \includegraphics[width=0.63\textwidth]{flup-dmL2} \caption{\it Lexis diagram of the \textrm{\tt DMlate} dataset; left panel is the default version, right panel: plot with some bells and whistles. The red lines are for women, blue for men, crosses indicate deaths.} \label{fig:Lexis-diagram} \end{figure} \section{Splitting the follow-up time along a time scale} In next chapter we shall conduct statistical analysis of mortality rates, and a prerequisite for parametric analysis of rates is that follow-up time is subdivided in smaller intervals, where we can reasonably assume that rates are constant. The follow-up time in a cohort can be subdivided (``split'') along a time scale, for example current age. This is achieved by the \texttt{splitLexis} (note that it is \emph{not} called \texttt{split.Lexis}). This requires that the time scale and the breakpoints on this time scale are supplied. Try: \begin{Schunk} \begin{Sinput} > dmS1 <- splitLexis( dmL, "age", breaks=seq(0,100,5) ) > summary( dmL ) \end{Sinput} \begin{Soutput} Transitions: To From DM Dead Records: Events: Risk time: Persons: DM 7497 2499 9996 2499 54273.27 9996 \end{Soutput} \begin{Sinput} > summary( dmS1 ) \end{Sinput} \begin{Soutput} Transitions: To From DM Dead Records: Events: Risk time: Persons: DM 18328 2499 20827 2499 54273.27 9996 \end{Soutput} \end{Schunk} We see that the number of persons and events and the amount of follow-up is the same in the two data sets; only the number of records differ --- the extra records all have \texttt{lex.Cst}=\texttt{DM} and \texttt{lex.Xst}=\texttt{DM}. To see how records are split for each individual, it is useful to list the results for a few individuals (whom we selected with a view to the illustrative usefulness): \begin{Schunk} \begin{Sinput} > wh.id <- c(9,27,52,484) > subset( dmL , lex.id %in% wh.id )[,1:10] \end{Sinput} \begin{Soutput} per age tfD lex.dur lex.Cst lex.Xst lex.id sex dobth dodm 430048 1998.956 61.87269 0 9.508556 DM Dead 9 F 1937.083 1998.956 22671 2000.042 52.71184 0 9.954825 DM DM 27 M 1947.331 2000.042 338459 1998.249 61.85626 0 11.748118 DM DM 52 F 1936.393 1998.249 274124 1998.260 62.37919 0 10.929500 DM Dead 484 F 1935.881 1998.260 \end{Soutput} \begin{Sinput} > subset( dmS1, lex.id %in% wh.id )[,1:10] \end{Sinput} \begin{Soutput} lex.id per age tfD lex.dur lex.Cst lex.Xst sex dobth dodm 14 9 1998.956 61.87269 0.000000 3.127310 DM DM F 1937.083 1998.956 15 9 2002.083 65.00000 3.127310 5.000000 DM DM F 1937.083 1998.956 16 9 2007.083 70.00000 8.127310 1.381246 DM Dead F 1937.083 1998.956 54 27 2000.042 52.71184 0.000000 2.288159 DM DM M 1947.331 2000.042 55 27 2002.331 55.00000 2.288159 5.000000 DM DM M 1947.331 2000.042 56 27 2007.331 60.00000 7.288159 2.666667 DM DM M 1947.331 2000.042 108 52 1998.249 61.85626 0.000000 3.143737 DM DM F 1936.393 1998.249 109 52 2001.393 65.00000 3.143737 5.000000 DM DM F 1936.393 1998.249 110 52 2006.393 70.00000 8.143737 3.604381 DM DM F 1936.393 1998.249 1004 484 1998.260 62.37919 0.000000 2.620808 DM DM F 1935.881 1998.260 1005 484 2000.881 65.00000 2.620808 5.000000 DM DM F 1935.881 1998.260 1006 484 2005.881 70.00000 7.620808 3.308693 DM Dead F 1935.881 1998.260 \end{Soutput} \end{Schunk} The resulting object, \texttt{dmS1}, is again a \texttt{Lexis} object, and the follow-up may be split further along another time scale, for example diabetes duration, \texttt{tfD}. Subsequently we list the results for the chosen individuals: \begin{Schunk} \begin{Sinput} > dmS2 <- splitLexis( dmS1, "tfD", breaks=c(0,1,2,5,10,20,30,40) ) > subset( dmS2, lex.id %in% wh.id )[,1:10] \end{Sinput} \begin{Soutput} lex.id per age tfD lex.dur lex.Cst lex.Xst sex dobth dodm 31 9 1998.956 61.87269 0.000000 1.0000000 DM DM F 1937.083 1998.956 32 9 1999.956 62.87269 1.000000 1.0000000 DM DM F 1937.083 1998.956 33 9 2000.956 63.87269 2.000000 1.1273101 DM DM F 1937.083 1998.956 34 9 2002.083 65.00000 3.127310 1.8726899 DM DM F 1937.083 1998.956 35 9 2003.956 66.87269 5.000000 3.1273101 DM DM F 1937.083 1998.956 36 9 2007.083 70.00000 8.127310 1.3812457 DM Dead F 1937.083 1998.956 111 27 2000.042 52.71184 0.000000 1.0000000 DM DM M 1947.331 2000.042 112 27 2001.042 53.71184 1.000000 1.0000000 DM DM M 1947.331 2000.042 113 27 2002.042 54.71184 2.000000 0.2881588 DM DM M 1947.331 2000.042 114 27 2002.331 55.00000 2.288159 2.7118412 DM DM M 1947.331 2000.042 115 27 2005.042 57.71184 5.000000 2.2881588 DM DM M 1947.331 2000.042 116 27 2007.331 60.00000 7.288159 2.6666667 DM DM M 1947.331 2000.042 229 52 1998.249 61.85626 0.000000 1.0000000 DM DM F 1936.393 1998.249 230 52 1999.249 62.85626 1.000000 1.0000000 DM DM F 1936.393 1998.249 231 52 2000.249 63.85626 2.000000 1.1437372 DM DM F 1936.393 1998.249 232 52 2001.393 65.00000 3.143737 1.8562628 DM DM F 1936.393 1998.249 233 52 2003.249 66.85626 5.000000 3.1437372 DM DM F 1936.393 1998.249 234 52 2006.393 70.00000 8.143737 1.8562628 DM DM F 1936.393 1998.249 235 52 2008.249 71.85626 10.000000 1.7481177 DM DM F 1936.393 1998.249 2084 484 1998.260 62.37919 0.000000 1.0000000 DM DM F 1935.881 1998.260 2085 484 1999.260 63.37919 1.000000 1.0000000 DM DM F 1935.881 1998.260 2086 484 2000.260 64.37919 2.000000 0.6208077 DM DM F 1935.881 1998.260 2087 484 2000.881 65.00000 2.620808 2.3791923 DM DM F 1935.881 1998.260 2088 484 2003.260 67.37919 5.000000 2.6208077 DM DM F 1935.881 1998.260 2089 484 2005.881 70.00000 7.620808 2.3791923 DM DM F 1935.881 1998.260 2090 484 2008.260 72.37919 10.000000 0.9295003 DM Dead F 1935.881 1998.260 \end{Soutput} \end{Schunk} A more efficient (and more intuitive) way of making this double split is to use the \texttt{splitMulti} function from the \texttt{popEpi} package: \begin{Schunk} \begin{Sinput} > library( popEpi ) > dmM <- splitMulti( dmL, age = seq(0,100,5), + tfD = c(0,1,2,5,10,20,30,40), + drop = FALSE ) > summary( dmS2 ) \end{Sinput} \begin{Soutput} Transitions: To From DM Dead Records: Events: Risk time: Persons: DM 40897 2499 43396 2499 54273.27 9996 \end{Soutput} \begin{Sinput} > summary( dmM ) \end{Sinput} \begin{Soutput} Transitions: To From DM Dead Records: Events: Risk time: Persons: DM 40897 2499 43396 2499 54273.27 9996 \end{Soutput} \end{Schunk} Note we used the argument \texttt{drop=FALSE} which will retain follow-up also outside the window defined by the breaks. Otherwise the default for \texttt{splitMulti} would be to drop follow-up outside \texttt{age} [0,100] and \texttt{tfD} [0,40]. This clipping behaviour is not available in \texttt{splitLexis}, nevertheless this may be exactly what we want in some situations. So we see that the two ways of splitting data yields the same amount of follow-up, but the results are not identical: \begin{Schunk} \begin{Sinput} > identical( dmS2, dmM ) \end{Sinput} \begin{Soutput} [1] FALSE \end{Soutput} \begin{Sinput} > class( dmS2 ) \end{Sinput} \begin{Soutput} [1] "Lexis" "data.frame" \end{Soutput} \begin{Sinput} > class( dmM ) \end{Sinput} \begin{Soutput} [1] "Lexis" "data.table" "data.frame" \end{Soutput} \end{Schunk} As we see, this is because the \texttt{dmM} object also is a \texttt{data.table} object; the \texttt{splitMulti} uses the \texttt{data.table} machinery which makes the splitting substantially faster --- this is of particular interest if you operate on large data sets ($>100,000$ records). Thus the recommended way of splitting follow-up time is by \texttt{splitMulti}. But you should be aware that the result is a \texttt{data.table} object, which in some circumstances behaves slightly different from \texttt{data.frame}s. See the manual for \texttt{data.table}. \section{Cutting follow up time at dates of intermediate events} If we have a recording of the date of a specific event as for example recovery or relapse, we may classify follow-up time as being before or after this intermediate event, but it requires that follow-up records that straddle the event be cut in two and placed in separate records, one representing follow-up \emph{before} the intermediate event, and another representing follow-up \emph{after} the intermediate event. This is achieved with the function \texttt{cutLexis}, which takes three arguments: the time point of the intermediate event, the time scale that this point refers to, and the value of the (new) state following the date. Optionally, we may also define a new time scale with the argument \texttt{new.scale=}. We are interested in the time before and after inception of insulin use, which occurs at the date \texttt{doins}: \begin{Schunk} \begin{Sinput} > whc <- c(names(dmL)[1:7],"dodm","doins") # WHich Columns do we want to see? > subset( dmL, lex.id %in% wh.id )[,whc] \end{Sinput} \begin{Soutput} per age tfD lex.dur lex.Cst lex.Xst lex.id dodm doins 430048 1998.956 61.87269 0 9.508556 DM Dead 9 1998.956 NA 22671 2000.042 52.71184 0 9.954825 DM DM 27 2000.042 NA 338459 1998.249 61.85626 0 11.748118 DM DM 52 1998.249 2004.804 274124 1998.260 62.37919 0 10.929500 DM Dead 484 1998.260 2003.960 \end{Soutput} \begin{Sinput} > dmC <- cutLexis( data = dmL, + cut = dmL$doins, + timescale = "per", + new.state = "Ins", + new.scale = "tfI", + precursor.states = "DM" ) > whc <- c(names(dmL)[1:8],"doins") # WHich Columns do we want to see? > subset( dmC, lex.id %in% wh.id )[,whc] \end{Sinput} \begin{Soutput} per age tfD lex.dur lex.Cst lex.Xst lex.id sex doins 9 1998.956 61.87269 0.000000 9.508556 DM Dead 9 F NA 27 2000.042 52.71184 0.000000 9.954825 DM DM 27 M NA 52 1998.249 61.85626 0.000000 6.554415 DM Ins 52 F 2004.804 10048 2004.804 68.41068 6.554415 5.193703 Ins Ins 52 F 2004.804 484 1998.260 62.37919 0.000000 5.700205 DM Ins 484 F 2003.960 10480 2003.960 68.07940 5.700205 5.229295 Ins Dead 484 F 2003.960 \end{Soutput} \end{Schunk} (The \texttt{precursor.states=} argument is explained below). Note that the process of cutting time is simplified by having all types of events referred to the calendar time scale. This is a generally applicable advice in handling follow-up data: Get all event times as \emph{dates}, location of events and follow-up on other time scales can then easily be derived from this. Note that individual 52 has had his follow-up cut at 6.55 years from diabetes diagnosis and individual 484 at 5.70 years from diabetes diagnosis. This dataset could then be split along the time scales as we did before with \texttt{dmL}. The result of this can also be achieved by cutting the split dataset \texttt{dmS2} instead of \texttt{dmL}: \begin{Schunk} \begin{Sinput} > dmS2C <- cutLexis( data = dmS2, + cut = dmS2$doins, + timescale = "per", + new.state = "Ins", + new.scale = "tfI", + precursor.states = "DM" ) > subset( dmS2C, lex.id %in% wh.id )[,whc] \end{Sinput} \begin{Soutput} per age tfD lex.dur lex.Cst lex.Xst lex.id sex doins 31 1998.956 61.87269 0.000000 1.0000000 DM DM 9 F NA 32 1999.956 62.87269 1.000000 1.0000000 DM DM 9 F NA 33 2000.956 63.87269 2.000000 1.1273101 DM DM 9 F NA 34 2002.083 65.00000 3.127310 1.8726899 DM DM 9 F NA 35 2003.956 66.87269 5.000000 3.1273101 DM DM 9 F NA 36 2007.083 70.00000 8.127310 1.3812457 DM Dead 9 F NA 111 2000.042 52.71184 0.000000 1.0000000 DM DM 27 M NA 112 2001.042 53.71184 1.000000 1.0000000 DM DM 27 M NA 113 2002.042 54.71184 2.000000 0.2881588 DM DM 27 M NA 114 2002.331 55.00000 2.288159 2.7118412 DM DM 27 M NA 115 2005.042 57.71184 5.000000 2.2881588 DM DM 27 M NA 116 2007.331 60.00000 7.288159 2.6666667 DM DM 27 M NA 229 1998.249 61.85626 0.000000 1.0000000 DM DM 52 F 2004.804 230 1999.249 62.85626 1.000000 1.0000000 DM DM 52 F 2004.804 231 2000.249 63.85626 2.000000 1.1437372 DM DM 52 F 2004.804 232 2001.393 65.00000 3.143737 1.8562628 DM DM 52 F 2004.804 233 2003.249 66.85626 5.000000 1.5544148 DM Ins 52 F 2004.804 43629 2004.804 68.41068 6.554415 1.5893224 Ins Ins 52 F 2004.804 43630 2006.393 70.00000 8.143737 1.8562628 Ins Ins 52 F 2004.804 43631 2008.249 71.85626 10.000000 1.7481177 Ins Ins 52 F 2004.804 2084 1998.260 62.37919 0.000000 1.0000000 DM DM 484 F 2003.960 2085 1999.260 63.37919 1.000000 1.0000000 DM DM 484 F 2003.960 2086 2000.260 64.37919 2.000000 0.6208077 DM DM 484 F 2003.960 2087 2000.881 65.00000 2.620808 2.3791923 DM DM 484 F 2003.960 2088 2003.260 67.37919 5.000000 0.7002053 DM Ins 484 F 2003.960 45484 2003.960 68.07940 5.700205 1.9206023 Ins Ins 484 F 2003.960 45485 2005.881 70.00000 7.620808 2.3791923 Ins Ins 484 F 2003.960 45486 2008.260 72.37919 10.000000 0.9295003 Ins Dead 484 F 2003.960 \end{Soutput} \end{Schunk} Thus it does not matter in which order we use \texttt{splitLexis} and \texttt{cutLexis}. Mathematicians would say that \texttt{splitLexis} and \texttt{cutLexis} are commutative. Note in \texttt{lex.id}=484, that follow-up subsequent to the event is classified as being in state \texttt{Ins}, but that the final transition to state \texttt{Dead} is preserved. This is the point of the \texttt{precursor.states=} argument. It names the states (in this case \texttt{DM}) that will be over-written by \texttt{new.state} (in this case \texttt{Ins}), while the state \texttt{Dead} should not be updated even if it is after the time where the persons moves to state \texttt{Ins}. In other words, only state \texttt{DM} is a precursor to state \texttt{Ins}, state \texttt{Dead} is always subsequent to state \texttt{Ins}. Note that we defined a new time scale, \texttt{tfI}, using the argument \texttt{new.scale=tfI}. This has a special status relative to the other three time scales, it is defined as time since entry into a state, namely \texttt{Ins}, this is noted in the time scale part of the summary of \texttt{Lexis} object --- the information sits in the attribute \texttt{time.since} of the \texttt{Lexis} object, which can be accessed by the function \texttt{timeSince()} or through the \texttt{summary()}: \begin{Schunk} \begin{Sinput} > summary( dmS2C, timeScales=TRUE ) \end{Sinput} \begin{Soutput} Transitions: To From DM Ins Dead Records: Events: Risk time: Persons: DM 35135 1694 2048 38877 3742 45885.49 9899 Ins 0 5762 451 6213 451 8387.77 1791 Sum 35135 7456 2499 45090 4193 54273.27 9996 Timescales: per age tfD tfI "" "" "" "Ins" \end{Soutput} \end{Schunk} Finally we can get a quick overview of the states and transitions by using \texttt{boxes} --- \texttt{scale.R} scales transition rates to rates per 1000 PY: \begin{Schunk} \begin{Sinput} > boxes( dmC, boxpos=TRUE, scale.R=1000, show.BE=TRUE ) \end{Sinput} \end{Schunk} \insfig{box1}{0.8}{States, person years, transitions and rates in the cut dataset. The numbers \emph{in} the boxes are person-years and the number of persons \texttt{B}eginning, resp. \texttt{E}nding their follow-up in each state (triggered by \textrm{\tt show.BE=TRUE}). The numbers at the arrows are the number of transitions and transition rates per 1000 (triggered by \textrm{\tt scale.R=1000}).} \chapter{Modeling rates from \texttt{Lexis} objects} \section{Covariates} In the dataset \texttt{dmS2C} there are three types of covariates that can be used to describe mortality rates: \begin{enumerate} \item time-dependent covariates \item time scales \item fixed covariates \end{enumerate} There is only one time-dependent covariate here, namely \texttt{lex.Cst}, the current state of the person's follow up; it takes the values \texttt{DM} and \texttt{Ins} according to whether the person has ever purchased insulin at a given time of follow-up. The time-scales are obvious candidates for explanatory variables for the rates, notably age and time from diagnosis (duration of diabetes) and insulin. \subsection{Time scales as covariates} If we want to model the effect of the time scale variables on occurrence rates, we will for each interval use either the value of the left endpoint in each interval or the middle. There is a function \texttt{timeBand} which returns either of these: \begin{Schunk} \begin{Sinput} > timeBand( dmS2C, "age", "middle" )[1:10] \end{Sinput} \begin{Soutput} [1] 57.5 57.5 62.5 62.5 62.5 67.5 67.5 62.5 67.5 67.5 \end{Soutput} \begin{Sinput} > # For nice printing and column labelling we use the data.frame() function: > data.frame( dmS2C[,c("per","age","tfD","lex.dur")], + mid.age=timeBand( dmS2C, "age", "middle" ), + mid.t=timeBand( dmS2C, "tfD", "middle" ), + left.t=timeBand( dmS2C, "tfD", "left" ), + right.t=timeBand( dmS2C, "tfD", "right" ), + fact.t=timeBand( dmS2C, "tfD", "factor" ) )[1:15,] \end{Sinput} \begin{Soutput} per age tfD lex.dur mid.age mid.t left.t right.t fact.t 1 1998.917 58.66119 0.0000000 1.00000000 57.5 0.5 0 1 (0,1] 2 1999.917 59.66119 1.0000000 0.33880903 57.5 1.5 1 2 (1,2] 3 2000.256 60.00000 1.3388090 0.66119097 62.5 1.5 1 2 (1,2] 4 2000.917 60.66119 2.0000000 3.00000000 62.5 3.5 2 5 (2,5] 5 2003.917 63.66119 5.0000000 1.33880903 62.5 7.5 5 10 (5,10] 6 2005.256 65.00000 6.3388090 3.66119097 67.5 7.5 5 10 (5,10] 7 2008.917 68.66119 10.0000000 1.08008214 67.5 15.0 10 20 (10,20] 8 2003.309 64.09035 0.0000000 0.90965092 62.5 0.5 0 1 (0,1] 9 2004.218 65.00000 0.9096509 0.09034908 67.5 0.5 0 1 (0,1] 10 2004.309 65.09035 1.0000000 1.00000000 67.5 1.5 1 2 (1,2] 11 2005.309 66.09035 2.0000000 3.00000000 67.5 3.5 2 5 (2,5] 12 2008.309 69.09035 5.0000000 0.90965092 67.5 7.5 5 10 (5,10] 13 2009.218 70.00000 5.9096509 0.77891855 72.5 7.5 5 10 (5,10] 14 2004.552 86.25051 0.0000000 1.00000000 87.5 0.5 0 1 (0,1] 15 2005.552 87.25051 1.0000000 1.00000000 87.5 1.5 1 2 (1,2] \end{Soutput} \end{Schunk} Note that the values of these functions are characteristics of the intervals defined by \texttt{breaks=}, \emph{not} the midpoints nor left or right endpoints of the actual follow-up intervals (which would be \texttt{tfD} and \texttt{tfD+lex.dur}, respectively). These functions are intended for modeling time scale variables as factors (categorical variables) in which case the coding must be independent of the censoring and mortality pattern --- it should only depend on the chosen grouping of the time scale. Modeling time scales as \emph{quantitative} should not be based on these codings but directly on the values of the time-scale variables, notably the left endpoints of the intervals. \subsection{Differences between time scales} Apparently, the only fixed variable is \texttt{sex}, but formally the dates of birth (\texttt{dobth}), diagnosis (\texttt{dodm}) and first insulin purchase (\texttt{doins}) are fixed covariates too. They can be constructed as origins of time scales referred to the calendar time scale. Likewise, and possibly of greater interest, we can consider these origins on the age scale, calculated as the difference between age and another time scale. These would then be age at birth (hardly relevant since it is the same for all persons), age at diabetes diagnosis and age at insulin treatment. \subsection{Keeping the relation between time scales} The midpoint (as well as the right interval endpoint) should be used with caution if the variable age at diagnosis \texttt{dodm-dobth} is modeled too; the age at diabetes is logically equal to the difference between current age (\texttt{age}) and time since diabetes diagnosis (\texttt{tfD}): \begin{Schunk} \begin{Sinput} > summary( (dmS2$age-dmS2$tfD) - (dmS2$dodm-dmS2$dobth) ) \end{Sinput} \begin{Soutput} Min. 1st Qu. Median Mean 3rd Qu. Max. 0 0 0 0 0 0 \end{Soutput} \end{Schunk} This calculation refers to the \emph{start} of each interval --- which are in the time scale variables in the \texttt{Lexis} object. But when using the middle of the intervals, this relationship is not preserved: \begin{Schunk} \begin{Sinput} > summary( timeBand( dmS2, "age", "middle" ) - + timeBand( dmS2, "tfD", "middle" ) - (dmS2$dodm-dmS2$dobth) ) \end{Sinput} \begin{Soutput} Min. 1st Qu. Median Mean 3rd Qu. Max. -7.4870 -2.0862 -0.3765 Inf 1.3641 Inf \end{Soutput} \end{Schunk} If all three variables are to be included in a model, we must make sure that the \emph{substantial} relationship between the variables be maintained. One way is to recompute age at diabetes diagnosis from the two midpoint variables, but more straightforward would be to use the left endpoint of the intervals, that is the time scale variables in the \texttt{Lexis} object. If we dissolve the relationship between the variables \texttt{age}, \texttt{tfD} and age at diagnosis by grouping we may obtain identifiability of the three separate effects, but it will be at the price of an arbitrary allocation of a linear trend between them. For the sake of clarity, consider current age, $a$, duration of disease, $d$ and age at diagnosis $e$, where \[ \text{current age} = \text{age at diagnosis} + \text{disease duration}, \quad \text{\ie} \quad a=e+d \quad \Leftrightarrow \quad e+d-a=0 \] If we model the effect of the quantitative variables $a$, $e$ and $d$ on the log-rates by three functions $f$, $g$ and $h$: $ \log(\lambda)=f(a)+g(d)+h(e) $ then for any $\kappa$: \begin{align*} \log(\lambda) & = f(a)+g(d)+h(e)+\kappa(e+d-a)\\ & = \big(f(a)-\kappa a \big)+ \big(g(d)+\kappa d \big)+ \big(h(e)+\kappa e \big) \\ & = \tilde f(a)+ \tilde g(d)+ \tilde h(e) \end{align*} In practical modeling this will turn up as a singular model matrix with one parameter aliased, corresponding to some arbitrarily chosen value of $\kappa$ (depending on software conventions for singular models). This phenomenon is well known from age-period-cohort models. Thus we see that we can move any slope around between the three terms, so if we achieve identifiability by using grouping of one of the variables we will in reality have settled for a particular value of $\kappa$, without known why we chose just that. The solution is to resort to predictions which are independent of the particular parametrization or choose a particular parametrization with explicit constraints. \section{Modeling of rates} As mentioned, the purpose of subdividing follow-up data in smaller intervals is to be able to model effects of time scale variables as parametric functions. When we split along a time scale we can get intervals that are as small as we want; if they are sufficiently small, an assumption of constant rates in each interval becomes reasonable. In a model that assumes a constant occurrence rate in each of the intervals the likelihood contribution from each interval is the same as the likelihood contribution from a Poisson variate $D$, say, with mean $\lambda \ell$ where $\lambda$ is the rate and $\ell$ is the interval length, and where the value of the variate $D$ is 1 or 0 according to whether an event has occurred or not. Moreover, the likelihood contributions from all follow-up intervals from a single person are \emph{conditionally} independent (conditional on having survived till the start of the interval in question). This implies that the total contribution to the likelihood from a single person is a product of terms, and hence the same as the likelihood of a number of independent Poisson terms, one from each interval. Note that variables are neither Poisson distributed (\eg they can only ever assume values 0 or 1) nor independent --- it is only the likelihood for the follow-up data that happens to be the same as the likelihood from independent Poisson variates. Different models can have the same likelihood, a model cannot be inferred from the likelihood. Parametric modeling of the rates is obtained by using the \emph{values} of the time scales for each interval as \emph{quantitative} explanatory variables, using for example splines. And of course also the values of the fixed covariates and the time-dependent variables for each interval. Thus the model will be one where the rate is assumed constant in each (small) interval, but where a parametric form of the \emph{size} of the rate in each interval is imposed by the model, using the time scale as a quantitative covariate. \subsection{Interval length} In the first chapter we illustrated cutting and splitting by listing the results for a few individuals across a number of intervals. For illustrational purposes we used 5-year age bands to avoid excessive listings, but since the doubling time for mortality on the age scale is only slightly larger than 5 years, the assumption about constant rates in each interval would be pretty far fetched if we were to use 5 year intervals. Thus, for modeling purposes we split the follow-up in 3 month intervals. When we use intervals of 3 months length it is superfluous to split along multiple time scales --- the precise location of tightly spaced splits will be irrelevant from any practical point of view. \texttt{splitLexis} and \texttt{splitMulti} will allocate the actual split times for all of the time scale variables, so these can be used directly in modeling. So we split the cut dataset in 3 months intervals along the age scale: \begin{Schunk} \begin{Sinput} > dmCs <- splitMulti( dmC, age = seq(0,110,1/4) ) > summary( dmCs, t=T ) \end{Sinput} \begin{Soutput} Transitions: To From DM Ins Dead Records: Events: Risk time: Persons: DM 189669 1694 2048 193411 3742 45885.49 9899 Ins 0 34886 451 35337 451 8387.77 1791 Sum 189669 36580 2499 228748 4193 54273.27 9996 Timescales: per age tfD tfI "" "" "" "Ins" \end{Soutput} \end{Schunk} We see that we now have 228,748 records and 9996 persons, so about 23 records per person. The total risk time is 54,275 years, a bit less than 3 months on average per record as expected. \subsection{Practicalities for splines} In this study we want to look at how mortality depend on age (\texttt{age}) and time since start of insulin use (\texttt{tfI}). If we want to use splines in the description we must allocate knots for anchoring the splines at each of the time scales, either by some \textit{ad hoc} method or by using some sort of penalized splines as for example by \texttt{gam}; the latter will not be treated here; it belongs in the realm of the \texttt{mgcv} package. Here we shall use the former approach and allocate 5 knots on each of the time-scales. We allocate knots so that we have the events evenly distributed between the knots. Since the insulin state starts at 0 for all individuals we include 0 as the first knot, such that any set of natural splines with these knots will have the value 0 at 0 on the time scale. \begin{Schunk} \begin{Sinput} > ( a.kn <- with( subset( dmCs, lex.Xst=="Dead" ), + quantile( age+lex.dur, (1:5-0.5)/5 ) ) ) \end{Sinput} \begin{Soutput} 10% 30% 50% 70% 90% 60.29350 71.31937 77.72758 82.72745 89.86393 \end{Soutput} \begin{Sinput} > ( i.kn <- c( 0, + with( subset( dmCs, lex.Xst=="Dead" & lex.Cst=="Ins" ), + quantile( tfI+lex.dur, (1:4)/5 ) ) ) ) \end{Sinput} \begin{Soutput} 20% 40% 60% 80% 0.0000000 0.3093771 1.1307324 2.5489391 4.9117043 \end{Soutput} \end{Schunk} In the \texttt{Epi} package there is a convenience wrapper, \texttt{Ns}, for the \texttt{n}atural \texttt{s}pline generator \texttt{ns}, that takes the smallest and the largest of a set of supplied knots to be the boundary knots, so the explicit definition of the boundary knots becomes superfluous. Note that it is a feature of the \texttt{Ns} (via the features of \texttt{ns}) that any generated spline function is 0 at the leftmost knot. \subsection{Poisson models} A model that describes mortality rates as only a function of age would then be: \begin{Schunk} \begin{Sinput} > ma <- glm( (lex.Xst=="Dead") ~ Ns(age,knots=a.kn), + family = poisson, + offset = log(lex.dur), + data = dmCs ) > summary( ma ) \end{Sinput} \begin{Soutput} Call: glm(formula = (lex.Xst == "Dead") ~ Ns(age, knots = a.kn), family = poisson, data = dmCs, offset = log(lex.dur)) Deviance Residuals: Min 1Q Median 3Q Max -0.5883 -0.1688 -0.1144 -0.0766 4.5958 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -3.82830 0.03861 -99.16 <2e-16 Ns(age, knots = a.kn)1 1.36254 0.08723 15.62 <2e-16 Ns(age, knots = a.kn)2 1.49446 0.06845 21.83 <2e-16 Ns(age, knots = a.kn)3 2.63557 0.07058 37.34 <2e-16 Ns(age, knots = a.kn)4 1.94173 0.05769 33.66 <2e-16 (Dispersion parameter for poisson family taken to be 1) Null deviance: 27719 on 228747 degrees of freedom Residual deviance: 25423 on 228743 degrees of freedom AIC: 30431 Number of Fisher Scoring iterations: 8 \end{Soutput} \end{Schunk} The offset, \texttt{log(lex.dur)} comes from the fact that the likelihood for the follow-up data during $\ell$ time is the same as that for independent Poisson variates with mean $\lambda \ell$, and that the default link function for the Poisson family is the log, so that we are using a linear model for the log-mean, $\log(\lambda) + \log(\ell)$. But when we want a model for the log-rate ($\log(\lambda)$), the term $\log(\ell)$ must still be included as a covariate, but with regression coefficient fixed to 1; a so-called \emph{offset}. This is however a technicality; it just exploits that the likelihood of a particular Poisson model and that of the rates model is the same. In the \texttt{Epi} package is a \texttt{glm} family, \texttt{poisreg} that has a more intuitive interface, where the response is a 2-column matrix of events and person-time, respectively. This is in concert with the fact that the outcome variable in follow-up studies is bivariate: (event, risk time). \begin{Schunk} \begin{Sinput} > Ma <- glm( cbind(lex.Xst=="Dead",lex.dur) ~ Ns(age,knots=a.kn), + family = poisreg, data = dmCs ) > summary( Ma ) \end{Sinput} \begin{Soutput} Call: glm(formula = cbind(lex.Xst == "Dead", lex.dur) ~ Ns(age, knots = a.kn), family = poisreg, data = dmCs) Deviance Residuals: Min 1Q Median 3Q Max -0.5883 -0.1688 -0.1144 -0.0766 4.5958 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -3.82830 0.03861 -99.15 <2e-16 Ns(age, knots = a.kn)1 1.36254 0.08723 15.62 <2e-16 Ns(age, knots = a.kn)2 1.49446 0.06845 21.83 <2e-16 Ns(age, knots = a.kn)3 2.63557 0.07058 37.34 <2e-16 Ns(age, knots = a.kn)4 1.94173 0.05769 33.66 <2e-16 (Dispersion parameter for poisson family taken to be 1) Null deviance: 27719 on 228747 degrees of freedom Residual deviance: 25423 on 228743 degrees of freedom AIC: 30431 Number of Fisher Scoring iterations: 7 \end{Soutput} \end{Schunk} Exploiting the multistate structure in the \texttt{Lexis} object there is a multistate convenience wrapper for \texttt{glm} with the \texttt{poisreg} family, that just requires specification of the transitions in terms of \texttt{from} and \texttt{to}. Although it is called \texttt{glm.Lexis} it is \emph{not} an S3 method for \texttt{Lexis} objects: \begin{Schunk} \begin{Sinput} > Xa <- glm.Lexis( dmCs, from="DM", to="Dead", + formula = ~ Ns(age,knots=a.kn) ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object dmCs with log link: Rates for the transition: DM->Dead \end{Soutput} \end{Schunk} The result is a \texttt{glm} object but with an extra attribute, \texttt{Lexis}: \begin{Schunk} \begin{Sinput} > attr( Xa, "Lexis" ) \end{Sinput} \begin{Soutput} $data [1] "dmCs" $trans [1] "DM->Dead" $formula ~Ns(age, knots = a.kn) $scale [1] 1 \end{Soutput} \end{Schunk} There are similar wrappers for \texttt{gam} and \texttt{coxph} models, \texttt{gam.Lexis} and \texttt{coxph.Lexis}, but these will not be elaborated in detail. The \texttt{from=} and \texttt{to=} can even be omitted, in which case all possible transitions \emph{into} any of the absorbing states is modeled: \begin{Schunk} \begin{Sinput} > xa <- glm.Lexis( dmCs, formula = ~ Ns(age,knots=a.kn) ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object dmCs with log link: Rates for transitions: DM->Dead, Ins->Dead \end{Soutput} \end{Schunk} We can check if the four models fitted are the same: \begin{Schunk} \begin{Sinput} > c( deviance(ma), deviance(Ma), deviance(Xa), deviance(xa) ) \end{Sinput} \begin{Soutput} [1] 25422.92 25422.92 20902.31 25422.92 \end{Soutput} \end{Schunk} Oops! the model \texttt{Xa} is apparently not the same as the other three? This is because the explicit specification \verb|from="DM", to="Dead"|, omits modeling contributions from the $\mathtt{Ins}\rightarrow\mathtt{Dead}$ transition --- the output actually said so --- see also figure \ref{fig:box1} on p. \pageref{fig:box1}. The other three models all use both transitions --- and assume that the two transition rates are the same, \ie that start of insulin has no effect on mortality. We shall relax this assumption later. The parameters from the model do not have any direct interpretation \textit{per se}, but we can compute the estimated mortality rates for a range of ages using \texttt{ci.pred} with a suitably defined prediction data frame. Note that if we use the \texttt{poisson} family of models, we must specify all covariates in the model, including the variable in the offset, \texttt{lex.dur} (remember that this was a covariate with coefficient fixed at 1). We set the latter to 1000, because we want the mortality rates per 1000 person-years. Using the \texttt{poisreg} family, the prediction will ignore any value of \texttt{lex.dur} specified in the prediction data frame, the returned rates will be per unit in which \texttt{lex.dur} is recorded. \begin{Schunk} \begin{Sinput} > nd <- data.frame( age=40:85, lex.dur=1000 ) > pr.0 <- ci.pred( ma, newdata = nd ) # mortality per 100 PY > pr.a <- ci.pred( Ma, newdata = nd )*1000 # mortality per 100 PY > summary(pr.0/pr.a) \end{Sinput} \begin{Soutput} Estimate 2.5% 97.5% Min. :1 Min. :1 Min. :1 1st Qu.:1 1st Qu.:1 1st Qu.:1 Median :1 Median :1 Median :1 Mean :1 Mean :1 Mean :1 3rd Qu.:1 3rd Qu.:1 3rd Qu.:1 Max. :1 Max. :1 Max. :1 \end{Soutput} \begin{Sinput} > matshade( nd$age, pr.a, plot=TRUE, + type="l", lty=1, + log="y", xlab="Age (years)", + ylab="DM mortality per 1000 PY") \end{Sinput} \end{Schunk} \insfig{pr-a}{0.8}{Mortality among Danish diabetes patients by age with 95\% CI as shaded area. We see that the rates increase linearly on the log-scale, that is exponentially by age.} \section{Time dependent covariate} A Poisson model approach to mortality by insulin status, would be to assume that the rate-ratio between patients on insulin and not on insulin is a fixed quantity, independent of time since start of insulin, independent of age. This is commonly termed a proportional hazards assumption, because the rates (hazards) in the two groups are proportional along the age (baseline time) scale. \begin{Schunk} \begin{Sinput} > pm <- glm( cbind(lex.Xst=="Dead",lex.dur) ~ Ns(age,knots=a.kn) + + lex.Cst + sex, + family=poisreg, data = dmCs ) > round( ci.exp( pm ), 3 ) \end{Sinput} \begin{Soutput} exp(Est.) 2.5% 97.5% (Intercept) 0.022 0.021 0.024 Ns(age, knots = a.kn)1 4.248 3.581 5.040 Ns(age, knots = a.kn)2 5.008 4.376 5.731 Ns(age, knots = a.kn)3 16.832 14.624 19.373 Ns(age, knots = a.kn)4 7.994 7.126 8.968 lex.CstIns 1.985 1.791 2.200 sexF 0.668 0.617 0.724 \end{Soutput} \end{Schunk} So we see that persons on insulin have about twice the mortality of persons not on insulin and that women have 2/3 the mortality of men. \subsection{Time since insulin start} If we want to test whether the excess mortality depends on the time since start if insulin treatment, we can add a spline terms in \texttt{tfI}. But since \texttt{tfI} is a time scale defined as time since entry into a new state (\texttt{Ins}), the variable \texttt{tfI} will be missing for those in the \texttt{DM} state, so before modeling we must set the \texttt{NA}s to 0, which we do with \texttt{tsNA20} (acronym for \texttt{t}ime\texttt{s}cale \texttt{NA}s to zero): \begin{Schunk} \begin{Sinput} > pm <- glm( cbind(lex.Xst=="Dead",lex.dur) ~ Ns(age,knots=a.kn) + + Ns(tfI,knots=i.kn) + + lex.Cst + sex, + family=poisreg, data = tsNA20(dmCs) ) \end{Sinput} \end{Schunk} As noted before we could do this simpler with \texttt{glm.Lexis}, even without the \texttt{from=} and \texttt{to=} arguments, because we are modeling all transitions \emph{into} the absorbing state (\texttt{Dead}): \begin{Schunk} \begin{Sinput} > Pm <- glm.Lexis( tsNA20(dmCs), + form = ~ Ns(age,knots=a.kn) + + Ns(tfI,knots=i.kn) + + lex.Cst + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object tsNA20(dmCs) with log link: Rates for transitions: DM->Dead, Ins->Dead \end{Soutput} \begin{Sinput} > c( deviance(Pm), deviance(pm) ) \end{Sinput} \begin{Soutput} [1] 25096.33 25096.33 \end{Soutput} \begin{Sinput} > identical( model.matrix(Pm), model.matrix(pm) ) \end{Sinput} \begin{Soutput} [1] TRUE \end{Soutput} \end{Schunk} The coding of the effect of \texttt{tfI} is so that the value is 0 at 0, so the meaning of the estimate of the effect of \texttt{lex.Cst} is the RR between persons with and without insulin, immediately after start of insulin: \begin{Schunk} \begin{Sinput} > round( ci.exp( Pm, subset="ex" ), 3 ) \end{Sinput} \begin{Soutput} exp(Est.) 2.5% 97.5% lex.CstIns 5.632 4.430 7.16 sexF 0.674 0.622 0.73 \end{Soutput} \end{Schunk} We see that the effect of sex is pretty much the same as before, but the effect of \texttt{lex.Cst} is much larger, it now refers to a different quantity, namely the RR at \texttt{tfI}=0. If we want to see the effect of time since insulin, it is best viewed jointly with the effect of age: \begin{Schunk} \begin{Sinput} > ndI <- data.frame( expand.grid( tfI=c(NA,seq(0,15,0.1)), + ai=seq(40,80,10) ), + sex="M", + lex.Cst="Ins" ) > ndI <- transform( ndI, age=ai+tfI ) > head( ndI ) \end{Sinput} \begin{Soutput} tfI ai sex lex.Cst age 1 NA 40 M Ins NA 2 0.0 40 M Ins 40.0 3 0.1 40 M Ins 40.1 4 0.2 40 M Ins 40.2 5 0.3 40 M Ins 40.3 6 0.4 40 M Ins 40.4 \end{Soutput} \begin{Sinput} > ndA <- data.frame( age= seq(40,100,0.1), tfI=0, lex.Cst="DM", sex="M" ) > pri <- ci.pred( Pm, ndI ) * 1000 > pra <- ci.pred( Pm, ndA ) * 1000 > matshade( ndI$age, pri, plot=TRUE, las=1, + xlab="Age (years)", ylab="DM mortality per 1000 PY", + log="y", lty=1, col="blue" ) > matshade( ndA$age, pra ) \end{Sinput} \end{Schunk} \insfig{ins-time}{0.8}{Mortality rates of persons on insulin, starting insulin at ages 40,50,\ldots,80 (blue), compared with persons not on insulin (black curve). Shaded areas are 95\% CI.} In figure \ref{fig:ins-time}, p. \pageref{fig:ins-time}, we see that mortality is high just after insulin start, but falls by almost a factor 3 during the first year. Also we see that there is a tendency that mortality in a given age is smallest for those with the longest duration of insulin use. \section{The Cox model} Note that in the Cox-model the age is used as response variable, slightly counter-intuitive. Hence the age part of the linear predictors is not in that model: \begin{Schunk} \begin{Sinput} > library( survival ) > cm <- coxph( Surv(age,age+lex.dur,lex.Xst=="Dead") ~ + Ns(tfI,knots=i.kn) + lex.Cst + sex, + data = tsNA20(dmCs) ) \end{Sinput} \end{Schunk} There is also a multistate wrapper for Cox models, requiring a l.h.s. side for the \texttt{formula=} argument: \begin{Schunk} \begin{Sinput} > Cm <- coxph.Lexis( tsNA20(dmCs), + form= age ~ Ns(tfI,knots=i.kn) + lex.Cst + sex ) \end{Sinput} \begin{Soutput} survival::coxph analysis of Lexis object tsNA20(dmCs): Rates for transitions DM->Dead, Ins->Dead Baseline timescale: age \end{Soutput} \begin{Sinput} > cbind( ci.exp( cm ), ci.exp( Cm ) ) \end{Sinput} \begin{Soutput} exp(Est.) 2.5% 97.5% exp(Est.) 2.5% 97.5% Ns(tfI, knots = i.kn)1 0.2984062 0.19417148 0.4585960 0.2984062 0.19417148 0.4585960 Ns(tfI, knots = i.kn)2 0.3871151 0.29011380 0.5165495 0.3871151 0.29011380 0.5165495 Ns(tfI, knots = i.kn)3 0.1239128 0.06287008 0.2442238 0.1239128 0.06287008 0.2442238 Ns(tfI, knots = i.kn)4 0.4405121 0.34839015 0.5569932 0.4405121 0.34839015 0.5569932 lex.CstIns 5.6700284 4.45011220 7.2243623 5.6700284 4.45011220 7.2243623 lex.CstDead 1.0000000 1.00000000 1.0000000 1.0000000 1.00000000 1.0000000 sexF 0.6753202 0.62316569 0.7318397 0.6753202 0.62316569 0.7318397 \end{Soutput} \end{Schunk} We can compare the estimates from the Cox model with those from the Poisson model --- we must add \texttt{NA}s because the Cox-model does not give the parameters for the baseline time scale (\texttt{age}), but also remove one of the parameters, because \texttt{coxph} parametrizes factors (in this case \texttt{lex.Cst}) by all defined levels and not only by the levels present in the dataset at hand (note the line of \texttt{1.0000000}s in the print above): \begin{Schunk} \begin{Sinput} > round( cbind( ci.exp( Pm ), + rbind( matrix(NA,5,3), + ci.exp( cm )[-6,] ) ), 3 ) \end{Sinput} \begin{Soutput} exp(Est.) 2.5% 97.5% exp(Est.) 2.5% 97.5% (Intercept) 0.022 0.021 0.024 NA NA NA Ns(age, knots = a.kn)1 4.208 3.546 4.993 NA NA NA Ns(age, knots = a.kn)2 5.012 4.380 5.736 NA NA NA Ns(age, knots = a.kn)3 16.560 14.386 19.063 NA NA NA Ns(age, knots = a.kn)4 7.921 7.061 8.885 NA NA NA Ns(tfI, knots = i.kn)1 0.298 0.194 0.458 0.298 0.194 0.459 Ns(tfI, knots = i.kn)2 0.385 0.289 0.514 0.387 0.290 0.517 Ns(tfI, knots = i.kn)3 0.125 0.064 0.246 0.124 0.063 0.244 Ns(tfI, knots = i.kn)4 0.438 0.346 0.553 0.441 0.348 0.557 lex.CstIns 5.632 4.430 7.160 5.670 4.450 7.224 sexF 0.674 0.622 0.730 0.675 0.623 0.732 \end{Soutput} \end{Schunk} Thus we see that the Poisson and Cox gives pretty much the same results. You may argue that Cox requires a smaller dataset, because there is no need to subdivide data in small intervals \emph{before} insulin use. But certainly the time \emph{after} insulin inception need to be if the effect of this time should be modeled. The drawback of the Cox-modeling is that it is not possible to show the absolute rates as we did in figure \ref{fig:ins-time} on \pageref{fig:ins-time}. \section{Marginal effect of time since insulin} When we plot the marginal effect of \texttt{tfI} from the two models we get pretty much the same; here we plot the RR relative to \texttt{tfI}=2 years. Note that we are deriving the RR as the ratio of two sets of predictions, from the data frames \texttt{nd} and \texttt{nr} --- for further details consult the help page for \texttt{ci.lin}, specifically the use of a list as the \texttt{ctr.mat} argument: \begin{Schunk} \begin{Sinput} > nd <- data.frame( tfI=seq(0,15,,151), lex.Cst="Ins", sex="M" ) > nr <- data.frame( tfI= 2 , lex.Cst="Ins", sex="M" ) > ppr <- ci.exp( pm, list(nd,nr), xvars="age" ) > cpr <- ci.exp( cm, list(nd,nr) ) > par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) > matshade( nd$tfI, cbind(ppr,cpr), plot=T, + lty=c(1,2), log="y", + xlab="Time since insulin (years)", ylab="Rate ratio") > abline( h=1, lty=3 ) \end{Sinput} \end{Schunk} \insfig{Ieff}{0.8}{The naked duration effects relative to 2 years of duration, black from Poisson model, red from Cox model. The two sets of estimates are identical, and so are the standard errors, so the two shaded areas overlap almost perfectly.} In figure \ref{fig:Ieff}, p. \pageref{fig:Ieff}, we see that the duration effect is exactly the same from the two modeling approaches. We will also want the RR relative to the non-insulin users --- recall these are coded 0 on the \texttt{tfI} variable: \begin{Schunk} \begin{Sinput} > nd <- data.frame( tfI=seq(0,15,,151), lex.Cst="Ins", sex="M" ) > nr <- data.frame( tfI= 0 , lex.Cst="DM" , sex="M" ) > ppr <- ci.exp( pm, list(nd,nr), xvars="age" ) > cpr <- ci.exp( cm, list(nd,nr) ) > par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) > matshade( nd$tfI, cbind(ppr,cpr), + xlab="Time since insulin (years)", + ylab="Rate ratio relative to non-Insulin", + lty=c(1,2), log="y", plot=T ) \end{Sinput} \end{Schunk} \insfig{IeffR}{0.8}{Insulin duration effect (state \textrm{\tt Ins}) relative to no insulin (state \textrm{\tt DM}), black from Poisson model, red from Cox model. The \emph{shape} is the same as the previous figure, but the RR is now relative to non-insulin, instead of relative to insulin users at 2 years duration. The two sets of estimates are identical, and so are the standard errors, so the two shaded areas overlap almost perfectly.} In figure \ref{fig:IeffR}, p. \pageref{fig:IeffR}, we see the effect of increasing duration of insulin use \emph{for a fixed age} which is a bit artificial, so we would like to see the \emph{joint} effects of age and insulin duration. What we cannot see is how the duration affects mortality relative to \texttt{current} age (at the age attained at the same time as the attained \texttt{tfI}). Another way of interpreting this curve is as the rate ratio relative to a person not on insulin, so we see that the RR (or hazard ratio, HR as some call it) is over 5 at the start of insulin (the \texttt{lex.Cst} estimate), and decreases to about 1.5 in the long term. Both figure \ref{fig:Ieff} and \ref{fig:IeffR} indicate a declining RR by insulin duration, but only from figure \ref{fig:ins-time} it is visible that mortality actually is \emph{in}creasing by age after some 2 years after insulin start. This point would not be available if we had only fitted a Cox model where we did not have access to the baseline hazard as a function of age. \section{Age$\times$duration interaction} The model we fitted assumes that the RR is the same regardless of the age at start of insulin --- the hazards are multiplicative. Sometimes this is termed the proportional hazards assumption: For \emph{any} fixed age the HR is the same as a function of time since insulin, and vice versa. A more correct term would be ``main effects model'' --- there is no interaction between age (the baseline time scale) and other covariates. So there is really no need for the term ``proportional hazards''; well defined and precise statistical terms for it has existed for aeons. \subsection{Age at insulin start} In order to check the consistency of the multiplicativity assumption across the spectrum of age at insulin inception, we can fit an interaction model. One approach to this would be using a non-linear effect of age at insulin use (for convenience we use the same knots as for age) --- note that the prediction data frames are the same as we used above, because we do not compute age at insulin use as a separate variable, but rather enter it as the difference between current age (\texttt{age}) and insulin duration (\texttt{tfI}). At first glance we might think of doing: \begin{Schunk} \begin{Sinput} > imx <- glm.Lexis( tsNA20(dmCs), + formula = ~ Ns(age ,knots=a.kn) + + Ns( tfI,knots=i.kn) + + Ns(age-tfI,knots=a.kn) + + lex.Cst + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object tsNA20(dmCs) with log link: Rates for transitions: DM->Dead, Ins->Dead \end{Soutput} \end{Schunk} But this will fit a model with a rate-ratio between persons with and without insulin that depends only on age at insulin start for the time \emph{after} insulin start, the RR at \texttt{tfI}=0 will be the same at any age, which really is not the type of interaction we wanted. We want the \texttt{age-tfI} term to be specific for the insulin exposed so we may use one of two other approaches, that are conceptually alike but mathematically different: \begin{Schunk} \begin{Sinput} > Im <- glm.Lexis( tsNA20(dmCs), + formula = ~ Ns(age ,knots=a.kn) + + Ns( tfI,knots=i.kn) + + Ns((age-tfI)*(lex.Cst=="Ins"),knots=a.kn) + + lex.Cst + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object tsNA20(dmCs) with log link: Rates for transitions: DM->Dead, Ins->Dead \end{Soutput} \begin{Sinput} > im <- glm.Lexis( tsNA20(dmCs), + formula = ~ Ns(age ,knots=a.kn) + + Ns( tfI,knots=i.kn) + + lex.Cst:Ns(age-tfI,knots=a.kn) + + lex.Cst + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object tsNA20(dmCs) with log link: Rates for transitions: DM->Dead, Ins->Dead \end{Soutput} \end{Schunk} The first model (\texttt{Im}) has a common age-effect (\texttt{Ns(age,...}) for persons with and without diabetes and a RR depending on insulin duration \texttt{tfI} and age at insulin (\texttt{age-tfI}). Since the linear effect of these two terms are in the model as well, a linear trend in the RR by current age (\texttt{age}) is accommodated as well. The second model allows age-effects that differ non-linearly between person with and without insulin, because the interaction term \texttt{lex.Cst:Ns(age-tfI...} for persons not on insulin is merely an age term (since \texttt{tfI} is coded 0 for all follow-up not on insulin). We can compare the models fitted: \begin{Schunk} \begin{Sinput} > anova( imx, Im, im, test='Chisq') \end{Sinput} \begin{Soutput} Analysis of Deviance Table Model 1: cbind(trt(Lx$lex.Cst, Lx$lex.Xst) %in% trnam, Lx$lex.dur) ~ Ns(age, knots = a.kn) + Ns(tfI, knots = i.kn) + Ns(age - tfI, knots = a.kn) + lex.Cst + sex Model 2: cbind(trt(Lx$lex.Cst, Lx$lex.Xst) %in% trnam, Lx$lex.dur) ~ Ns(age, knots = a.kn) + Ns(tfI, knots = i.kn) + Ns((age - tfI) * (lex.Cst == "Ins"), knots = a.kn) + lex.Cst + sex Model 3: cbind(trt(Lx$lex.Cst, Lx$lex.Xst) %in% trnam, Lx$lex.dur) ~ Ns(age, knots = a.kn) + Ns(tfI, knots = i.kn) + lex.Cst:Ns(age - tfI, knots = a.kn) + lex.Cst + sex Resid. Df Resid. Dev Df Deviance Pr(>Chi) 1 228734 25096 2 228733 25087 1 8.9631 0.002755 3 228730 25082 3 4.6804 0.196749 \end{Soutput} \end{Schunk} so we see that the models indeed are different, and moreover that the last model does not provide substantial further improvement, by allowing non-linear RR along the age-scale. We can illustrate the different estimated rates from the three models in figure \ref{fig:dur-int}, p. \pageref{fig:dur-int}: \begin{Schunk} \begin{Sinput} > pxi <- ci.pred( imx, ndI ) > pxa <- ci.pred( imx, ndA ) > pIi <- ci.pred( Im , ndI ) > pIa <- ci.pred( Im , ndA ) > pii <- ci.pred( im , ndI ) > pia <- ci.pred( im , ndA ) > par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) > matshade( ndI$age, cbind( pxi, pIi, pii)*1000, plot=T, log="y", + xlab="Age", ylab="Mortality per 1000 PY", + lty=1, lwd=2, col=c("blue","forestgreen","red"), alpha=0.1 ) > matshade( ndA$age, cbind( pxa, pIa, pia)*1000, + lty=1, lwd=2, col=c("blue","forestgreen","red"), alpha=0.1 ) \end{Sinput} \end{Schunk} \insfig{dur-int}{0.8}{Age at insulin as interaction between age and duration. Blue curves are from the naive interaction model \textrm{\tt imx} with identical $\RR$ at \textrm{\tt tfI}=0 at any age; green curves are from the interaction model with age at insulin, from the model \textrm{\tt Im} with only linear differences by age, and red lines from the full interaction model \textrm{\tt im}.} We can also plot the RRs only from these models (figure \ref{fig:dur-int-RR}, p. \pageref{fig:dur-int-RR}); for this we need the reference frames, and the machinery from \texttt{ci.exp} allowing a list of two data frames: \begin{Schunk} \begin{Sinput} > ndR <- transform( ndI, tfI=0, lex.Cst="DM" ) > cbind( head(ndI), head(ndR) ) \end{Sinput} \begin{Soutput} tfI ai sex lex.Cst age tfI ai sex lex.Cst age 1 NA 40 M Ins NA 0 40 M DM NA 2 0.0 40 M Ins 40.0 0 40 M DM 40.0 3 0.1 40 M Ins 40.1 0 40 M DM 40.1 4 0.2 40 M Ins 40.2 0 40 M DM 40.2 5 0.3 40 M Ins 40.3 0 40 M DM 40.3 6 0.4 40 M Ins 40.4 0 40 M DM 40.4 \end{Soutput} \begin{Sinput} > Rxi <- ci.exp( imx, list(ndI,ndR) ) > Rii <- ci.exp( im , list(ndI,ndR) ) > RIi <- ci.exp( Im , list(ndI,ndR) ) > par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) > matshade( ndI$age, cbind( Rxi, RIi, Rii), plot=T, log="y", + xlab="Age (years)", ylab="Rate ratio vs, non-Insulin", + lty=1, lwd=2, col=c("blue","forestgreen","red"), alpha=0.1 ) > abline( h=1 ) > abline( h=ci.exp(imx,subset="lex.Cst")[,1], lty="25", col="blue" ) \end{Sinput} \end{Schunk} \insfig{dur-int-RR}{0.9}{RR from three different interaction models. The horizontal dotted line is at the estimated effect of \textrm{\tt lex.Cst}, to illustrate that the first model (blue) constrains this initial HR to be constant across age. The green curves are the extended interaction model, and the red the full one.} \clearpage \subsection{General interaction} As a final illustration we may want to explore a different kind of interaction, not defined from the duration --- here we simplify the interaction by not using the second-last knot in the interaction terms --- figure \ref{fig:splint}, p. \pageref{fig:splint}. Note again that the prediction code is the same: \begin{Schunk} \begin{Sinput} > gm <- glm.Lexis( tsNA20(dmCs), + formula = ~ Ns(age,knots=a.kn) + + Ns(tfI,knots=i.kn) + + lex.Cst:Ns(age,knots=a.kn):Ns(tfI,knots=i.kn) + + lex.Cst + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object tsNA20(dmCs) with log link: Rates for transitions: DM->Dead, Ins->Dead \end{Soutput} \begin{Sinput} > pgi <- ci.pred( gm, ndI ) > pga <- ci.pred( gm, ndA ) > par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) > matshade( ndI$age, cbind( pgi, pii )*1000, plot=T, + lty=c("solid","21"), lend="butt", lwd=2, log="y", + xlab="Age (years)", ylab="Mortality rates per 1000 PY", + alpha=c(0.2,0.1), col=c("black","red") ) > matshade( ndA$age, cbind( pga, pia )*1000, + lty=c("solid","21"), lend="butt", lwd=2, + alpha=c(0.2,0.1), col=c("black","red") ) \end{Sinput} \end{Schunk} \insfig{splint}{0.8}{Spline-by-spline interaction between age and duration (model \textrm{\tt gm}, black), and the interaction using a non-linear effect of age at entry (model \textrm{\tt im}, red), corresponding to the red curves in figure \ref{fig:dur-int}.} This is in figure \ref{fig:splint}, p. \pageref{fig:splint}. \subsection{Evaluating interactions} Here we see that the interaction effect is such that in the older ages the length of insulin use has an increasing effect on mortality. Even though there is no statistically significant interaction between age and time since start of insulin, it would be illustrative to show the RR as a function of age at insulin and age at follow-up: \begin{Schunk} \begin{Sinput} > ndR <- transform( ndI, lex.Cst="DM", tfI=0 ) > iRR <- ci.exp( im, ctr.mat=list(ndI,ndR) ) > gRR <- ci.exp( gm, ctr.mat=list(ndI,ndR) ) > par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) > matshade( ndI$age, cbind(gRR,iRR), lty=1, log="y", plot=TRUE, + xlab="Age (years)", ylab="Rate ratio: Ins vs. non-Ins", + col=c("black","red") ) > abline( h=1 ) \end{Sinput} \end{Schunk} \insfig{RR-int}{0.8}{The effect of duration of insulin use at different ages of follow-up (and age at insulin start). Estimates are from the model with an interaction term using a non-linear effect of age at insulin start (model \textrm{\tt im}, red) and using a general spline interactions (model \textrm{\tt gm}, black). It appears that the general interaction over-models a bit.} This is in figure \ref{fig:RR-int}, p. \pageref{fig:RR-int}. The advantage of the parametric modeling (be that with age at insulin or general spline interaction) is that it is straight-forward to \emph{test} whether we have an interaction. \section{Separate models} In the above we insisted on making a joint model for the \texttt{DM}$\rightarrow$\texttt{Dead} and the \texttt{Ins}$\rightarrow$\texttt{Dead} transitions, but with the complications demonstrated it would actually have been more sensible to model the two transitions separately: \begin{Schunk} \begin{Sinput} > dmd <- glm.Lexis( dmCs, + from="DM", to="Dead", + formula = ~ Ns(age,knots=a.kn) + + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object dmCs with log link: Rates for the transition: DM->Dead \end{Soutput} \begin{Sinput} > ind <- glm.Lexis( dmCs, + from="Ins", to="Dead", + formula = ~ Ns(age,knots=a.kn) + + Ns(tfI,knots=i.kn) + + Ns(age-tfI,knots=a.kn) + + sex ) \end{Sinput} \begin{Soutput} stats::glm Poisson analysis of Lexis object dmCs with log link: Rates for the transition: Ins->Dead \end{Soutput} \begin{Sinput} > ini <- ci.pred( ind, ndI ) > dmi <- ci.pred( dmd, ndI ) > dma <- ci.pred( dmd, ndA ) \end{Sinput} \end{Schunk} The estimated mortality rates are shown in figure \ref{fig:sep-mort}, p. \pageref{fig:sep-mort}, using: \begin{Schunk} \begin{Sinput} > par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") > matshade( ndI$age, ini*1000, plot=TRUE, log="y", + xlab="Age (years)", ylab="Mortality rates per 1000 PY", + lwd=2, col="red" ) > matshade( ndA$age, dma*1000, + lwd=2, col="black" ) \end{Sinput} \end{Schunk} The estimated RRs are computed using that the estimates from the two models are uncorrelated, and hence qualify for \texttt{ci.ratio} (this and the previous graph appear in figure \ref{fig:Ins-noIns}, p. \pageref{fig:Ins-noIns}) \begin{Schunk} \begin{Sinput} > par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") > matshade( ndI$age, ci.ratio(ini,dmi), plot=TRUE, log="y", + xlab="Age (years)", ylab="RR insulin vs. no insulin", + lwd=2, col="red" ) > abline( h=1 ) \end{Sinput} \end{Schunk} \begin{figure}[tb] \centering \includegraphics[width=0.49\textwidth]{flup-sep-mort} \includegraphics[width=0.49\textwidth]{flup-sep-HR} \caption{\it Left panel: Mortality rates from separate models for the two mortality transitions; the \textrm{\tt DM}$\rightarrow$\textrm{\tt Dead} transition modeled by age alone; \textrm{\tt Ins}$\rightarrow$\textrm{\tt Dead} transition modeled with spline effects of current age, time since insulin and and age at insulin. \newline Right panel: Mortality HR of insulin vs. no insulin.} \label{fig:Ins-noIns} \end{figure} \chapter{More states} \section{Subdividing states} It may be of interest to subdivide the states following the intermediate event according to whether the event has occurred or not. This will enable us to address the question of the fraction of the patients that ever go on insulin. This is done by the argument \texttt{split.states=TRUE}. \begin{Schunk} \begin{Sinput} > dmCs <- cutLexis( data = dmS2, + cut = dmS2$doins, + timescale = "per", + new.state = "Ins", + new.scale = "tfI", + precursor.states = "DM", + split.states = TRUE ) > summary( dmCs ) \end{Sinput} \begin{Soutput} Transitions: To From DM Ins Dead Dead(Ins) Records: Events: Risk time: Persons: DM 35135 1694 2048 0 38877 3742 45885.49 9899 Ins 0 5762 0 451 6213 451 8387.77 1791 Sum 35135 7456 2048 451 45090 4193 54273.27 9996 \end{Soutput} \end{Schunk} We can illustrate the numbers and the transitions (figure \ref{fig:box4}, p. \pageref{fig:box4}) \begin{Schunk} \begin{Sinput} > boxes( dmCs, boxpos=list(x=c(15,15,85,85), + y=c(85,15,85,15)), + scale.R=1000, show.BE=TRUE ) \end{Sinput} \end{Schunk} \insfig{box4}{0.7}{Transitions between 4 states: the numbers \emph{in} the boxes are person-years (middle), and below the number of persons who start, respectively end their follow-up in each of the states.} Note that it is only the mortality rates that we have been modeling, namely the transitions \texttt{DM}$\rightarrow$\texttt{Dead} and \texttt{Ins}$\rightarrow$\texttt{Dead(Ins)}. If we were to model the cumulative risk of using insulin we would also need a model for the DM$\rightarrow$Ins transition. Subsequent to that we would then compute the probability of being in each state conditional on suitable starting conditions. With models where transition rates depend on several time scales this is not a trivial task. This is treated in more detail in the vignette on \texttt{simLexis}. \section{Multiple intermediate events} We may be interested in starting either insulin or OAD (oral anti-diabetic drugs), thus giving rise to more states and more time scales. This can be accomplished by the \texttt{mcutLexis} function, that generalizes \texttt{cutLexis}: \begin{Schunk} \begin{Sinput} > dmM <- mcutLexis( dmL, + timescale = "per", + wh = c("doins","dooad"), + new.states = c("Ins","OAD"), + new.scales = c("tfI","tfO"), + precursor.states = "DM", + ties.resolve = TRUE ) \end{Sinput} \begin{Soutput} NOTE: 15 records with tied events times resolved (adding 0.01 random uniform), so results are only reproducible if the random number seed was set. \end{Soutput} \begin{Sinput} > summary( dmM, t=T ) \end{Sinput} \begin{Soutput} Transitions: To From DM Dead OAD Ins OAD-Ins Ins-OAD Records: Events: Risk time: Persons: DM 2830 1056 2957 689 0 0 7532 4702 22920.34 7532 OAD 0 992 3327 0 1005 0 5324 1997 22965.24 5324 Ins 0 152 0 462 0 172 786 324 3883.06 786 OAD-Ins 0 266 0 0 739 0 1005 266 3770.53 1005 Ins-OAD 0 33 0 0 0 139 172 33 734.09 172 Sum 2830 2499 6284 1151 1744 311 14819 7322 54273.27 9996 Timescales: per age tfD tfI tfO "" "" "" "Ins" "OAD" \end{Soutput} \end{Schunk} We see that we now have two time scales defined as entry since into states. \begin{Schunk} \begin{Sinput} > wh <- c(subset(dmM,lex.Cst=="Ins-OAD")$lex.id[1:2], + subset(dmM,lex.Cst=="OAD-Ins")$lex.id[1:2]) > options( width=110 ) > print( subset( dmM, lex.id %in% wh )[,c('lex.id',names(dmM[1:8]),c("doins","dooad"))], + digits=6, row.names=FALSE ) \end{Sinput} \begin{Soutput} lex.id tfI tfO per age tfD lex.dur lex.Cst lex.Xst doins dooad 18 NA NA 1996.75 61.7221 0.0000000 1.16906229 DM OAD 2005.99 1997.92 18 NA 0.00000 1997.92 62.8912 1.1690623 8.07939767 OAD OAD-Ins 2005.99 1997.92 18 0.00000000 8.07940 2005.99 70.9706 9.2484600 4.00273785 OAD-Ins OAD-Ins 2005.99 1997.92 25 NA NA 2003.69 60.3422 0.0000000 1.88090349 DM OAD 2008.64 2005.57 25 NA 0.00000 2005.57 62.2231 1.8809035 3.06913073 OAD OAD-Ins 2008.64 2005.57 25 0.00000000 3.06913 2008.64 65.2923 4.9500342 1.35797399 OAD-Ins OAD-Ins 2008.64 2005.57 20 NA NA 2009.25 53.2183 0.0000000 0.04071988 DM Ins 2009.29 2009.29 20 0.00000000 NA 2009.29 53.2591 0.0407199 0.00131847 Ins Ins-OAD 2009.29 2009.29 20 0.00131847 0.00000 2009.29 53.2604 0.0420383 0.70813277 Ins-OAD Ins-OAD 2009.29 2009.29 38 NA NA 2008.37 63.9316 0.0000000 0.09308693 DM Ins 2008.46 2008.67 38 0.00000000 NA 2008.46 64.0246 0.0930869 0.21355236 Ins Ins-OAD 2008.46 2008.67 38 0.21355236 0.00000 2008.67 64.2382 0.3066393 1.32511978 Ins-OAD Dead 2008.46 2008.67 \end{Soutput} \end{Schunk} We can also illustrate the transitions to the different states, as in figure \ref{fig:mbox}: \begin{Schunk} \begin{Sinput} > boxes( dmM, boxpos=list(x=c(15,80,40,40,85,85), + y=c(50,50,90,10,90,10)), + scale.R=1000, show.BE=TRUE ) \end{Sinput} \end{Schunk} \insfig{mbox}{1.0}{Boxes for the \textrm{\tt dmM} object. The numbers \emph{in} the boxes are person-years (middle), and below the number of persons who start, respectively end their follow-up in each of the states.} We may not be interested in whether persons were prescribed insulin before OAD or vice versa, in which case we would combine the levels with both insulin and OAD to one, regardless of order (figure \ref{fig:mboxr}): \begin{Schunk} \begin{Sinput} > summary( dmMr <- Relevel( dmM, list('OAD+Ins'=5:6), first=FALSE) ) \end{Sinput} \begin{Soutput} Transitions: To From DM Dead OAD Ins OAD+Ins Records: Events: Risk time: Persons: DM 2830 1056 2957 689 0 7532 4702 22920.34 7532 OAD 0 992 3327 0 1005 5324 1997 22965.24 5324 Ins 0 152 0 462 172 786 324 3883.06 786 OAD+Ins 0 299 0 0 878 1177 299 4504.62 1177 Sum 2830 2499 6284 1151 2055 14819 7322 54273.27 9996 \end{Soutput} \begin{Sinput} > boxes( dmMr, boxpos=list(x=c(15,50,15,85,85), + y=c(85,50,15,85,15)), + scale.R=1000, show.BE=TRUE ) \end{Sinput} \end{Schunk} \insfig{mboxr}{1.0}{Boxes for the \textrm{\tt dmMr} object with collapsed states. The numbers \emph{in} the boxes are person-years (middle), and below the number of persons who start, respectively end their follow-up in each of the states.} Diagrams as those in figures \ref{fig:mbox} and \ref{fig:mboxr} gives an overview of the possible transitions, which states it might be relevant to collapse, and which transitions to model and how. The actual modeling of the transition rates is straightforward; split the data along some timescale and then use \texttt{glm.Lexis} or \texttt{gam.Lexis}, where it is possible to select the transitions modelled. This is also possible with the \texttt{coxph.Lexis} function, but it requires that a single time scale be selected as the baseline time scale, and the effect of this will not be accessible. \chapter{\texttt{Lexis} functions} The \texttt{Lexis} machinery has evolved over time since it was first introduced in a workable version in \texttt{Epi\_1.0.5} in August 2008. Over the years there have been additions of tools for handling multistate data. Here is a list of the current functions relating to \texttt{Lexis} objects with a very brief description; it does not replace the documentation. Unless otherwise stated, functions named \texttt{something.Lexis} (with a ``\texttt{.}'') are S3 methods for \texttt{Lexis} objects, so you can skip the ``\texttt{.Lexis}'' in daily use. \setlist{noitemsep} \begin{description} \item[Define]\ \\ \begin{description} \item[\texttt{Lexis}] defines a \texttt{Lexis} object \end{description} \item[Cut and split]\ \\ \begin{description} \item[\texttt{cutLexis}] cut follow-up at intermediate event \item[\texttt{mcutLexis}] cut follow-up at several intermediate events \item[\texttt{countLexis}] cut follow-up at intermediate event count the no. events so far \item[\texttt{splitLexis}] split follow up along a time scale \item[\texttt{splitMulti}] split follow up along a time scale --- from the \texttt{popEpi} package, faster and has simpler syntax than \texttt{splitLexis} \item[\texttt{addCov.Lexis}] add clinical measurements at a given date to a \texttt{Lexis} object \end{description} \item[Boxes and plots]\ \\ \begin{description} \item[\texttt{boxes.Lexis}] draw a diagram of states and transitions \item[\texttt{plot.Lexis}] draw a standard Lexis diagram \item[\texttt{points.Lexis}] add points to a Lexis diagram \item[\texttt{lines.Lexis}] add lines to a Lexis diagram \item[\texttt{PY.ann.Lexis}] annotate life lines in a Lexis diagram \end{description} \item[Summarize and query]\ \\ \begin{description} \item[\texttt{summary.Lexis}] overview of transitions, risk time etc. \item[\texttt{levels.Lexis}] what are the states in the \texttt{Lexis} object \item[\texttt{nid.Lexis}] number of persons in the \texttt{Lexis} object --- how many unique values of \texttt{lex.id} are present \item[\texttt{entry}] entry time \item[\texttt{exit}] exit time \item[\texttt{status}] status at entry or exit \item[\texttt{timeBand}] factor of time bands \item[\texttt{timeScales}] what time scales are in the \texttt{Lexis} object \item[\texttt{timeSince}] what time scales are defined as time since a given state \item[\texttt{breaks}] what breaks are currently defined \item[\texttt{absorbing}] what are the absorbing states \item[\texttt{transient}] what are the transient states \item[\texttt{preceding}, \texttt{before}] which states precede this \item[\texttt{succeeding}, \texttt{after}] which states can follow this \item[\texttt{tmat.Lexis}] transition matrix for the \texttt{Lexis} object \end{description} \item[Manipulate]\ \\ \begin{description} \item[\texttt{subset.Lexis}, \texttt{[}] subset of a \texttt{Lexis} object \item[\texttt{merge.Lexis}] merges a \texttt{Lexis} objects with a \texttt{data.frame} \item[\texttt{cbind.Lexis}] bind a \texttt{data.frame} to a \texttt{Lexis} object \item[\texttt{rbind.Lexis}] put two \texttt{Lexis} objects head-to-foot \item[\texttt{transform.Lexis}] transform and add variables \item[\texttt{tsNA20}] turn \texttt{NA}s to 0s for time scales \item[\texttt{Relevel.Lexis}, \texttt{factorize.Lexis}] reorder and combine states \item[\texttt{rm.tr}] remove transitions from a \texttt{Lexis} object \item[\texttt{bootLexis}] bootstrap sample of \emph{persons} (\texttt{lex.id}) in the \texttt{Lexis} object \end{description} \item[Simulate]\ \\ \begin{description} \item[\texttt{simLexis}] simulate a \texttt{Lexis} object from specified transition rate models \item[\texttt{nState}, \texttt{pState}] count state occupancy from a simulated \texttt{Lexis} object \item[\texttt{plot.pState}, \texttt{lines.pState}] plot state occupancy from a \texttt{pState} object \end{description} \item[Stack]\ \\ \begin{description} \item[\texttt{stack.Lexis}] make a stacked object for simultaneous analysis of transitions --- returns a \texttt{stacked.Lexis} object \item[\texttt{subset.stacked.Lexis}] subsets of a \texttt{stacked.Lexis} object \item[\texttt{transform.stacked.Lexis}] transform a \texttt{stacked.Lexis} object \end{description} \item[Interface to other packages]\ \\ \begin{description} \item[\texttt{msdata.Lexis}] interface to \texttt{mstate} package \item[\texttt{etm.Lexis}] interface to \texttt{etm} package \item[\texttt{crr.Lexis}] interface to \texttt{cmprsk} package \end{description} \item[Statistical models] --- these are \emph{not} S3 methods \begin{description} \item[\texttt{glm.Lexis}] fit a \texttt{glm} model using the \texttt{poisreg} family to (hopefully) time split data \item[\texttt{gam.Lexis}] fit a \texttt{gam} model (from the \texttt{mgcv} package) using the \texttt{poisreg} family to (hopefully) time split data \item[\texttt{coxph.Lexis}] fit a Cox model to follow-up in a \texttt{Lexis} object \end{description} \end{description} \renewcommand{\bibname}{References} \bibliographystyle{plain} \begin{thebibliography}{1} \bibitem{Carstensen.2011a} B~Carstensen and M~Plummer. \newblock Using {L}exis objects for multi-state models in {R}. \newblock {\em Journal of Statistical Software}, 38(6):1--18, 1 2011. %% \bibitem{Iacobelli.2013} %% S~Iacobelli and B~Carstensen. %% \newblock {Multiple time scales in multi-state models}. %% \newblock {\em Stat Med}, 32(30):5315--5327, Dec 2013. \bibitem{Plummer.2011} M~Plummer and B~Carstensen. \newblock Lexis: An {R} class for epidemiological studies with long-term follow-up. \newblock {\em Journal of Statistical Software}, 38(5):1--12, 1 2011. \end{thebibliography} \addcontentsline{toc}{chapter}{\bibname} \end{document} Epi/vignettes/topreport.tex0000644000176200001440000001061413250443225015561 0ustar liggesusers%---------------------------------------------------------------------- % Packages %\usepackage[inline]{showlabels} %\usepackage[latin1]{inputenc} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[english]{babel} \usepackage[font=it,labelfont=normalfont]{caption} \usepackage[colorlinks,urlcolor=blue,linkcolor=red,citecolor=Maroon]{hyperref} \usepackage[ae,hyper]{Rd} \usepackage[dvipsnames]{xcolor} \usepackage[super]{nth} % \usepackage[retainorgcmds]{IEEEtrantools} \usepackage[noae]{Sweave} \usepackage{makeidx,floatflt,amsmath,amsfonts,amsbsy,enumitem,dcolumn,needspace} \usepackage{ifthen,calc,eso-pic,everyshi} \usepackage{booktabs,longtable,rotating,graphicx,subfig} \usepackage{pdfpages,verbatim,fancyhdr,datetime,afterpage} \usepackage[abspath]{currfile} % \usepackage{times} \renewcommand{\textfraction}{0.0} \renewcommand{\topfraction}{1.0} \renewcommand{\bottomfraction}{1.0} \renewcommand{\floatpagefraction}{0.9} % \usepackage{mslapa} \definecolor{blaa}{RGB}{99,99,255} \DeclareGraphicsExtensions{.png,.pdf,.jpg} % Make the Sweave output nicer (slightly mor compact) \DefineVerbatimEnvironment{Sinput}{Verbatim}{fontsize=\small,fontshape=sl,formatcom=\color{BlueViolet}} \DefineVerbatimEnvironment{Soutput}{Verbatim}{fontsize=\small,formatcom=\color{Sepia},xleftmargin=0em} \DefineVerbatimEnvironment{Scode}{Verbatim}{fontsize=\small} \fvset{listparameters={\setlength{\topsep}{-0.1ex}}} \renewenvironment{Schunk}% {\renewcommand{\baselinestretch}{0.87} \vspace{\topsep}}% {\renewcommand{\baselinestretch}{1.00} \vspace{\topsep}} % \renewenvironment{knitrout} % {\renewcommand{\baselinestretch}{0.87}} % {\renewcommand{\baselinestretch}{1.00}} \input{useful} %---------------------------------------------------------------------- % Set up layout of pages \oddsidemargin 1mm \evensidemargin 1mm \topmargin -10mm \headheight 8mm \headsep 5mm \textheight 240mm \textwidth 165mm %\footheight 5mm \footskip 15mm \renewcommand{\topfraction}{0.9} \renewcommand{\bottomfraction}{0.9} \renewcommand{\textfraction}{0.1} \renewcommand{\floatpagefraction}{0.9} \renewcommand{\headrulewidth}{0.1pt} \setcounter{secnumdepth}{2} \setcounter{tocdepth}{3} %---------------------------------------------------------------------- % How to insert a figure in a .rnw file \newcommand{\rwpre}{./graph/gr} \newcommand{\insfig}[3]{ \begin{figure}[h] \centering \includegraphics[width=#2\textwidth]{\rwpre-#1} % \caption{#3} \caption{#3\hfill\mbox{\footnotesize \textrm{\tt \rwpre-#1}}} \label{fig:#1} % \afterpage{\clearpage} \end{figure}} \newcommand{\linput}[1]{ % \clearpage \afterpage{\hfill \ldots now input from \texttt{#1.tex}\\} \fancyfoot[OR,EL]{\footnotesize \texttt{#1.tex}} \input{#1}} %---------------------------------------------------------------------- % Here is the document starting with the titlepage \begin{document} %---------------------------------------------------------------------- % The title page \setcounter{page}{1} \pagenumbering{roman} \pagestyle{plain} \thispagestyle{empty} % \vspace*{0.05\textheight} \flushright % The blank below here is necessary in order not to muck up the % linespacing in title if it has more than 2 lines {\Huge \bfseries \Title }\ \\[-1.5ex] \noindent\textcolor{blaa}{\rule[-1ex]{\textwidth}{5pt}}\\[2.5ex] \large \Where \\ \Dates \\ \Homepage \\ \Version \\[1em] \normalsize Compiled \today,\ \currenttime\\ from: \texttt{\currfileabspath}\\[1em] % \input{wordcount} \normalsize \vfill \Faculty % End of titlepage % \newpage %---------------------------------------------------------------------- % Table of contents \tableofcontents % \listoftables % \listoffigures \clearpage % \begingroup % \let\clearpage\relax % \listoftables % \listoffigures % \endgroup %---------------------------------------------------------------------- % General text layout \raggedright \parindent 1em \parskip 0ex \cleardoublepage %---------------------------------------------------------------------- % General page style \pagenumbering{arabic} \setcounter{page}{1} \pagestyle{fancy} \renewcommand{\chaptermark}[1]{\markboth{\textsl{#1}}{}} \renewcommand{\sectionmark}[1]{\markright{\thesection\ \textsl{#1}}{}} \fancyhead[EL]{\bf \thepage \quad \rm \rightmark} \fancyhead[ER]{\rm \Tit} \fancyhead[OL]{\rm \leftmark} \fancyhead[OR]{\rm \rightmark \quad \bf \thepage} \fancyfoot{} Epi/vignettes/yll.rnw0000644000176200001440000005272614003562347014347 0ustar liggesusers%\VignetteIndexEntry{Years of life lost (YLL)} \SweaveOpts{results=verbatim,keep.source=TRUE,include=FALSE,eps=FALSE} \documentclass[a4paper,twoside,12pt]{report} \newcommand{\Title}{Years of Life Lost (YLL) to disease\\Diabetes in DK as example} \newcommand{\Tit}{YLL} \newcommand{\Version}{February 1.2} \newcommand{\Dates}{November 2017} \newcommand{\Where}{SDC} \newcommand{\Homepage}{\url{http://bendixcarstensen.com/Epi}} \newcommand{\Faculty}{\begin{tabular}{rl} Bendix Carstensen & Steno Diabetes Center, Gentofte, Denmark\\ & {\small \& Department of Biostatistics, University of Copenhagen} \\ & \texttt{b@bxc.dk}\\ & \url{http://BendixCarstensen.com} \\[1em] \end{tabular}} \input{topreport} <>= options( width=90, SweaveHooks=list( fig=function() par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") ) ) @ % \renewcommand{\rwpre}{./yll} \chapter{Theory and technicalities} This vignette for the \texttt{Epi} package describes the probabilistic and demographic background for and technical implementation of the \texttt{erl} and \texttt{yll} functions that computes the expected residual life time and years of life lost in an illness-death model. \section{Years of life lost (YLL)} \ldots to diabetes or any other disease for that matter. The general concept in calculation of ``years lost to\ldots'' is the comparison of the expected lifetime between two groups of persons; one with and one without disease (in this example DM). The expected lifetime is the area under the survival curve, so basically the exercise requires that two survival curves that are deemed relevant be available. The years of life lost is therefore just the area between the survival curves for those ``Well'', $S_W(t)$, and for those ``Diseased'', $S_D(t)$: \[ \YLL = \int_0^\infty S_W(t) - S_D(t) \dif t \] The time $t$ could of course be age, but it could also be ``time after age 50'' and the survival curves compared would then be survival curves \emph{conditional} on survival till age 50, and the YLL would be the years of life lost for a 50-year old person with diabetes. If we are referring to the expected lifetime we will more precisely use the label expected residual lifetime, ERL. \section{Constructing the survival curves} YLL can be computed in two different ways, depending on the way the survival curve and hence the expected lifetime of a person \emph{without} diabetes is computed: \begin{itemize} \item Assume that the ``Well'' persons are \emph{immune} to disease --- using only the non-DM mortality rates throughout for calculation of expected life time. \item Assume that the ``Well'' persons \emph{can} acquire the disease and thereby see an increased mortality, thus involving all three rates shown in figure \ref{fig:states}. \end{itemize} The former gives a higher YLL because the comparison is to persons assumed immune to DM (and yet with the same mortality as non-immune prior to diagnosis), the latter gives a more realistic picture of the comparison of group of persons with and without diabetes at a given age that can be interpreted in the real world. The differences can be illustrated by figure \ref{fig:states}; the immune approach corresponds to an assumption of $\lambda(t)=0$ in the calculation of the survival curve for a person in the ``Well'' state. Calculation of the survival of a diseased person already in the ``DM'' state is unaffected by assumptions about $\lambda$. <>= library( Epi ) TM <- matrix(NA,4,4) rownames(TM) <- colnames(TM) <- c("Well","DM","Dead","Dead(DM)") TM[1,2:3] <- TM[2,4] <- 1 zz <- boxes( TM, boxpos=list(x=c(20,80,20,80),y=c(80,80,20,20)), wm=1.5, hm=4 ) @ <>= zz$Arrowtext <- c( expression(lambda), expression(mu[W]), expression(mu[D][M]) ) boxes( zz ) @ % \insfig{states}{0.7}{Illness-death model describing diabetes incidence and -mortality.} \subsection{Total mortality --- a shortcut?} A practical crude shortcut could be to compare the ERL in the diabetic population to the ERL for the \emph{entire} population (that is use the total mortality ignoring diabetes status). Note however that this approach also counts the mortality of persons that acquired the disease earlier, thus making the comparison population on average more ill than the population we aim at, namely those well at a given time, which only then become more gradually ill. How large these effects are can however be empirically explored, as we shall do later. \subsection{Disease duration} In the exposition above there is no explicit provision for the effect of disease duration, but if we were able to devise mortality rates for any combination of age and duration, this could be taken into account. There are however severe limitations in this as we in principle would want to have duration effects as long as the age-effects --- in principle for all $(a,d)$ where $d\leq A$, where $A$ is the age at which we condition. So even if we were only to compute ERL from age, say, 40 we would still need duration effects up to 60 years (namely to age 100). The incorporation of duration effects is in principle trivial from a computational point of view, but we would be forced to entertain models predicting duration effects way beyond what is actually observed disease duration in any practical case. \subsection{Computing integrals} The practical calculations of survival curves, ERL and YLL involves calculation of (cumulative) integrals of rates and functions of these as we shall see below. This is easy if we have a closed form expression of the function, so its value may be computed at any time point --- this will be the case if we model rates by smooth parametric functions. Computing the (cumulative) integral of a function is done as follows: \begin{itemize} \item Compute the value of the function (mortality rate for example) at the midpoints of a sequence of narrow equidistant intervals --- for example one- or three month intervals of age, say. \item Take the cumulative sum of these values multiplied by the interval length --- this will be a very close approximation to the cumulative integral evaluated at the end of each interval. \item If the intervals are really small (like 1/100 year), the distinction between the value at the middle and at the end of each interval becomes irrelevant. \end{itemize} Note that in the above it is assumed that the rates are given in units corresponding to the interval length --- or more precisely, as the cumulative rates over the interval. \section{Survival functions in the illness-death model} The survival functions for persons in the ``Well'' state can be computed under two fundamentally different scenarios, depending on whether persons in the ``Well'' state are assumed to be immune to the disease ($\lambda(a)=0$) or not. \subsection{Immune approach} In this case both survival functions for person in the two states are the usual simple transformation of the cumulative mortality rates: \[ S_W(a) = \exp\left(-\int_0^a\!\!\mu_W(u) \dif u \right), \qquad S_D(a) = \exp\left(-\int_0^a\!\!\mu_D(u) \dif u \right) \] \subsubsection{Conditional survival functions} If we want the \emph{conditional} survival functions given survival to age $A$, say, they are just: \[ S_W(a|A) = S_W(a)/S_W(A), \qquad S_D(a|A) = S_D(a)/S_D(A) \] \subsection{Non-immune approach} For a diseased person, the survival function in this states is the same as above, but the survival function for a person without disease (at age 0) is (see figure \ref{fig:states}): \[ S(a) = \ptxt{Well}\!(a) + \ptxt{DM}\!(a) \] In the appendix of the paper \cite{Carstensen.2008c} is an indication of how to compute the probability of being in any of the four states shown in figure \ref{fig:states}, which I shall repeat here: In terms of the rates, the probability of being in the ``Well'' box is simply the probability of escaping both death (at a rate of $\mu_W(a)$) and diabetes (at a rate of $\lambda(a)$): \[ \ptxt{Well}(a) = \exp\left(\!-\int_0^a\!\!\mu_W(u)+\lambda(u) \right) \dif u \] The probability of being alive with diabetes at age $a$, is computed given that diabetes occurred at age $s$ ($s>= data( DMepi ) @ % The dataset \texttt{DMepi} contains diabetes events, deaths and person-years for persons without diabetes and deaths and person-years for persons with diabetes: <<>>= str( DMepi ) head( DMepi ) @ % For each combination of sex, age, period and date of birth in 1 year age groups, we have the person-years in the ``Well'' (\texttt{Y.nD}) and the ``DM'' (\texttt{Y.DM}) states, as well as the number of deaths from these (\texttt{D.nD}, \texttt{D.DM}) and the number of incident diabetes cases from the ``Well'' state (\texttt{X}). In order to compute the years of life lost to diabetes and how this has changed over time, we fit models for the mortality and incidence of both groups (and of course, separately for men and women). The models we use will be age-period-cohort models \cite{Carstensen.2007a} providing estimated mortality rates for ages 0--99 and dates 1.1.1996--1.1.2016. First we transform the age and period variables to reflect the mean age and period in each of the Lexis triangles. We also compute the total number of deaths and amount of risk time, as we are going to model the total mortality as well. Finally we restrict the dataset to ages over 30 only: <<>>= DMepi <- transform( subset( DMepi, A>30 ), D.T = D.nD + D.DM, Y.T = Y.nD + Y.DM ) head(DMepi) @ % With the correct age and period coding in the Lexis triangles, we fit models for the mortalities and incidences. Note that we for comparative purposes also fit a model for the \emph{total} mortality, ignoring the <<>>= # Knots used in all models ( a.kn <- seq(40,95,,6) ) ( p.kn <- seq(1997,2015,,4) ) ( c.kn <- seq(1910,1976,,6) ) # Check the number of events between knots ae <- xtabs( cbind(D.nD,D.DM,X) ~ cut(A,c(30,a.kn,Inf)) + sex, data=DMepi ) ftable( addmargins(ae,1), col.vars=3:2 ) pe <- xtabs( cbind(D.nD,D.DM,X) ~ cut(P,c(1990,p.kn,Inf)) + sex, data=DMepi ) ftable( addmargins(pe,1), col.vars=3:2 ) ce <- xtabs( cbind(D.nD,D.DM,X) ~ cut(P-A,c(-Inf,c.kn,Inf)) + sex, data=DMepi ) ftable( addmargins(ce,1), col.vars=3:2 ) # Fit an APC-model for all transitions, seperately for men and women mW.m <- glm( D.nD ~ -1 + Ns(A ,knots=a.kn,int=TRUE) + Ns( P,knots=p.kn,ref=2005) + Ns(P-A,knots=c.kn,ref=1950), offset = log(Y.nD), family = poisson, data = subset( DMepi, sex=="M" ) ) mD.m <- update( mW.m, D.DM ~ . , offset=log(Y.DM) ) mT.m <- update( mW.m, D.T ~ . , offset=log(Y.T ) ) lW.m <- update( mW.m, X ~ . ) # Model for women mW.f <- update( mW.m, data = subset( DMepi, sex=="F" ) ) mD.f <- update( mD.m, data = subset( DMepi, sex=="F" ) ) mT.f <- update( mT.m, data = subset( DMepi, sex=="F" ) ) lW.f <- update( lW.m, data = subset( DMepi, sex=="F" ) ) @ % \section{Residual life time and years lost to DM} We now collect the estimated years of life lost classified by method (immune assumption or not), sex, age and calendar time: <<>>= a.ref <- 30:90 p.ref <- 1996:2016 aYLL <- NArray( list( type = c("Imm","Tot","Sus"), sex = levels( DMepi$sex ), age = a.ref, date = p.ref ) ) str( aYLL ) system.time( for( ip in p.ref ) { nd <- data.frame( A = seq(30,90,0.2)+0.1, P = ip, Y.nD = 1, Y.DM = 1, Y.T = 1 ) muW.m <- ci.pred( mW.m, nd )[,1] muD.m <- ci.pred( mD.m, nd )[,1] muT.m <- ci.pred( mT.m, nd )[,1] lam.m <- ci.pred( lW.m, nd )[,1] muW.f <- ci.pred( mW.f, nd )[,1] muD.f <- ci.pred( mD.f, nd )[,1] muT.f <- ci.pred( mT.f, nd )[,1] lam.f <- ci.pred( lW.f, nd )[,1] aYLL["Imm","M",,paste(ip)] <- yll( int=0.2, muW.m, muD.m, lam=NULL, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Imm","F",,paste(ip)] <- yll( int=0.2, muW.f, muD.f, lam=NULL, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Tot","M",,paste(ip)] <- yll( int=0.2, muT.m, muD.m, lam=NULL, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Tot","F",,paste(ip)] <- yll( int=0.2, muT.f, muD.f, lam=NULL, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Sus","M",,paste(ip)] <- yll( int=0.2, muW.m, muD.m, lam=lam.m, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Sus","F",,paste(ip)] <- yll( int=0.2, muW.f, muD.f, lam=lam.f, A=a.ref, age.in=30, note=FALSE )[-1] } ) round( ftable( aYLL[,,seq(1,61,10),], col.vars=c(3,2) ), 1 ) @ % We now have the relevant points for the graph showing YLL to diabetes for men and women by age, and calendar year, both under the immunity and susceptibility models for the calculation of YLL. <>= plyll <- function(wh){ par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, bty="n", las=1 ) matplot( a.ref, aYLL[wh,"M",,], type="l", lty=1, col="blue", lwd=1:2, ylim=c(0,12), xlab="Age", ylab="Years lost to DM", yaxs="i" ) abline(v=50,h=1:10,col=gray(0.7)) text( 90, 11, "Men", col="blue", adj=1 ) text( 40, aYLL[wh,"M","40","1996"], "1996", adj=c(0,0), col="blue" ) text( 43, aYLL[wh,"M","44","2016"], "2016", adj=c(1,1), col="blue" ) matplot( a.ref, aYLL[wh,"F",,], type="l", lty=1, col="red", lwd=1:2, ylim=c(0,12), xlab="Age", ylab="Years lost to DM", yaxs="i" ) abline(v=50,h=1:10,col=gray(0.7)) text( 90, 11, "Women", col="red", adj=1 ) text( 40, aYLL[wh,"F","40","1996"], "1996", adj=c(0,0), col="red" ) text( 43, aYLL[wh,"F","44","2016"], "2016", adj=c(1,1), col="red" ) } plyll("Imm") @ % <>= plyll("Tot") @ % <>= plyll("Sus") @ % \begin{figure}[h] \centering \includegraphics[width=\textwidth]{yll-imm} \caption{Years of life lost to DM: the difference in expected residual life time at different ages between persons with and without diabetes, assuming the persons without diabetes at a given age remain free from diabetes (immunity assumption --- not reasonable). The lines refer to date of evaluation; the top lines refer to 1.1.1996 the bottom ones to 1.1.2016. Blue curves are men, red women.} \label{fig:imm} \end{figure} \begin{figure}[h] \centering \includegraphics[width=\textwidth]{yll-sus} \caption{Years of life lost to DM: the difference in expected residual life time at different ages between persons with and without diabetes, allowing the persons without diabetes at a given to contract diabetes and thus be subject to higher mortality. The lines refer to date of evaluation; the top lines refer to 1.1.1996 the bottom ones to 1.1.2016. Blue curves are men, red women.} \label{fig:sus} \end{figure} \begin{figure}[h] \centering \includegraphics[width=\textwidth]{yll-tot} \caption{Years of life lost to DM: the difference in expected residual life time at different ages between persons with and without diabetes. Allowance for susceptibility is approximated by using the total population mortality instead of non-DM mortality. The lines refer to date of evaluation; the top lines refer to 1.1.1996 the bottom ones to 1.1.2016. Blue curves are men, red women.} \label{fig:tot} \end{figure} From figure \ref{fig:sus} we see that for men aged 50 the years lost to diabetes has decreased from a bit over 8 to a bit less than 6 years, and for women from 8.5 to 5 years; so a greater improvement for women. \chapter{Practical implementation} We have devised functions that wraps these formulae up for practical use. \section{Function definitions} % The following code sources the originally formatted code in erl.R in % order to make it printable with all the formatting and comments in % it. However the sourcing does not work when compiling the vignettes % in R CMD build. So when checking the code we comment this out by % putting eval=FALSE. So depending on whether we actually construct % the pdf for the inst/doc folder or test (upload) the package, one of % the following two chunks are run with eval=FALSE and the other with % eval=TRUE. <>= source( "../R/erl.R", keep.source=TRUE ) @ % % When checking the package <>= surv1 <- Epi::surv1 surv2 <- Epi::surv2 erl1 <- Epi::erl1 erl <- Epi::erl yll <- Epi::yll @ % When using the functions it is assumed that the functions $\mu_W$, $\mu_D$ and $\lambda$ are given as vectors corresponding to equidistantly (usually tightly) spaced ages from 0 to $K$ where K is the age where everyone can safely be assumed dead. \texttt{surv1} is a simple function that computes the survival function from a vector of mortality rates, and optionally the conditional survival given being alive at prespecified ages: <<>>= surv1 @ % \texttt{erl1} basically just expands the result of \texttt{surv1} with a column of expected residual life times: <<>>= erl1 @ % We also define a function, \texttt{surv2}, that computes the survival function for a non-diseased person that may become diseased with rate \texttt{lam} and after that die at a rate of \texttt{muD} (corresponding to the formulae above). This is the sane way of handling years of life lost to a particular illness: <<>>= surv2 @ % Finally we devised a function using these to compute the expected residual lifetime at select ages: <<>>= erl @ % \ldots and a wrapper for this if we only want the years of life lost returned: <<>>= yll @ % \bibliographystyle{plain} \begin{thebibliography}{1} \bibitem{Carstensen.2007a} B~Carstensen. \newblock Age-{P}eriod-{C}ohort models for the {L}exis diagram. \newblock {\em Statistics in Medicine}, 26(15):3018--3045, 2007. \bibitem{Carstensen.2008c} B~Carstensen, JK~Kristensen, P~Ottosen, and K~Borch-Johnsen. \newblock The {D}anish {N}ational {D}iabetes {R}egister: {T}rends in incidence, prevalence and mortality. \newblock {\em Diabetologia}, 51:2187--2196, 2008. \end{thebibliography} \addcontentsline{toc}{chapter}{References} \end{document} Epi/vignettes/fixall0000755000176200001440000000125314003553264014207 0ustar liggesusers# Before this is run, do this: # 1) run rw on simLexis and yll with eval=TRUE in the lines with # CHANGE1 in order to get a version with properly formatted # code. # 2) Move the .tex files to sL.tex and yl.tex, and compile. # 3) Swap TRUE and FALSE in the CHANGE1/2 lines in the rnw files. # Then we are ready for the following: rt crisk rw crisk bl crisk cp crisk.R ../inst/doc cp crisk.pdf ../inst/doc rw flup rt flup bl flup cp flup.R ../inst/doc cp flup.pdf ../inst/doc rt simLexis rw simLexis bl simLexis cp simLexis.R ../inst/doc/simLexis.R cp sL.pdf ../inst/doc/simLexis.pdf rt yll rw yll bl yll cp yll.R ../inst/doc/yll.R cp yl.pdf ../inst/doc/yll.pdf kleanEpi/vignettes/flup.rnw0000644000176200001440000016705013522040203014475 0ustar liggesusers%\VignetteIndexEntry{Follow-up data with the Lexis functions in Epi} \SweaveOpts{results=verbatim,keep.source=TRUE,include=FALSE,eps=FALSE} \documentclass[a4paper,dvipsnames,twoside,12pt]{report} \newcommand{\Title}{Follow-up data with the\\ \texttt{Lexis} functions in \texttt{Epi}} \newcommand{\Tit}{Follow-up with \texttt{Lexis}} \newcommand{\Version}{Version 6} \newcommand{\Dates}{August 2019} \newcommand{\Where}{SDCC} \newcommand{\Homepage}{\url{http://bendixcarstensen.com/} } \newcommand{\Faculty}{\begin{tabular}{rl} Bendix Carstensen & Steno Diabetes Center Copenhagen, Gentofte, Denmark\\ & {\small \& Department of Biostatistics, University of Copenhagen} \\ & \texttt{b@bxc.dk} \\ & \url{http://BendixCarstensen.com} \\[1em] \end{tabular}} \input{topreport} \renewcommand{\rwpre}{./flup} <>= options( width=90, SweaveHooks=list( fig=function() par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") ) ) @ % \chapter*{Introduction} \addcontentsline{toc}{chapter}{Introduction} This is an introduction to the \texttt{Lexis} machinery in the \texttt{Epi} package. The machinery is intended for representation and manipulation of follow-up data (event history data) from studies where exact dates of events are known. It accommodates follow-up through multiple states and on multiple time scales. This vignette uses an example from the \texttt{Epi} package to illustrate the set-up of a simple \texttt{Lexis} object (a data frame of follow-up intervals), as well as the subdivision of follow-up intervals needed for multistate representation and analysis of transition rates. The first chapter is exclusively on manipulation of the follow-up representation, but it points to the subsequent chapter where analysis is based on a \texttt{Lexis} representation with very small follow-up intervals. Chapter 2 uses analysis of mortality rates among Danish diabetes patients (available in the \texttt{Epi} package) currently on insulin treatment or not to illustrate the use of the the \texttt{Lexis} machinery. I owe much thanks to my colleague Lars Jorge Diaz for careful reading and many constructive suggestions. \section{History} The \texttt{Lexis} machinery in the \texttt{Epi} package was first conceived by Martyn Plummer\cite{Plummer.2011,Carstensen.2011a}, and since its first appearance in the \texttt{Epi} package in 2008 it has been expanded with a number of utilities. An overview of these can be found in the last chapter of this note: ``\texttt{Lexis} functions''. \chapter{Representation of follow-up data in the \texttt{Epi} package} In the \texttt{Epi}-package, follow-up data is represented by adding some extra variables to a data frame. Such a data frame is called a \texttt{Lexis} object. The tools for handling follow-up data then use the structure of this for special plots, tabulations and modeling. Follow-up data basically consists of a time of entry, a time of exit and an indication of the status at exit (normally either ``alive'' or ``dead'') for each person. Implicitly is also assumed a status \emph{during} the follow-up (usually ``alive''). \begin{figure}[htbp] \centering \setlength{\unitlength}{1pt} \begin{picture}(210,70)(0,75) %\scriptsize \thicklines \put( 0,80){\makebox(0,0)[r]{Age-scale}} \put( 50,80){\line(1,0){150}} \put( 50,80){\line(0,1){5}} \put(100,80){\line(0,1){5}} \put(150,80){\line(0,1){5}} \put(200,80){\line(0,1){5}} \put( 50,77){\makebox(0,0)[t]{35}} \put(100,77){\makebox(0,0)[t]{40}} \put(150,77){\makebox(0,0)[t]{45}} \put(200,77){\makebox(0,0)[t]{50}} \put( 0,115){\makebox(0,0)[r]{Follow-up}} \put( 80,105){\makebox(0,0)[r]{\small Two}} \put( 90,105){\line(1,0){87}} \put( 90,100){\line(0,1){10}} \put(100,100){\line(0,1){10}} \put(150,100){\line(0,1){10}} \put(180,105){\circle{6}} \put( 95,110){\makebox(0,0)[b]{1}} \put(125,110){\makebox(0,0)[b]{5}} \put(165,110){\makebox(0,0)[b]{3}} \put( 50,130){\makebox(0,0)[r]{\small One}} \put( 60,130){\line(1,0){70}} \put( 60,125){\line(0,1){10}} \put(100,125){\line(0,1){10}} \put(130,130){\circle*{6}} \put( 80,135){\makebox(0,0)[b]{4}} \put(115,135){\makebox(0,0)[b]{3}} \end{picture} \caption{\it Follow-up of two persons} \label{fig:fu2} \end{figure} \section{Time scales} A time scale is a variable that varies deterministically \emph{within} each person during follow-up, \textit{e.g.}: \begin{itemize} \item Age \item Calendar time \item Time since start of treatment \item Time since relapse \end{itemize} All time scales advance at the same pace, so the time followed is the same on all time scales. Therefore, it will suffice to use only the entry point on each of the time scales, for example: \begin{itemize} \item Age at entry \item Date of entry \item Time at treatment (\emph{at} treatment this is 0) \item Time at relapse (\emph{at} relapse this is 0) \end{itemize} For illustration we need to load the \texttt{Epi} package: <<>>= library(Epi) print( sessionInfo(), l=F ) @ % In the \texttt{Epi} package, follow-up in a cohort is represented in a \texttt{Lexis} object. As mentioned, a \texttt{Lexis} object is a data frame with some extra structure representing the follow-up. For the \texttt{DMlate} data --- follow-up of diabetes patients in Denmark recording date of birth, date of diabetes, date of insulin use, date of first oral drug use and date of death --- we can construct a \texttt{Lexis} object by: <<>>= data( DMlate ) head( DMlate ) dmL <- Lexis( entry = list( per=dodm, age=dodm-dobth, tfD=0 ), exit = list( per=dox ), exit.status = factor( !is.na(dodth), labels=c("DM","Dead") ), data = DMlate ) timeScales(dmL) @ % (The excluded persons are persons with date of diabetes equal to date of death.) The \texttt{entry} argument is a \emph{named} list with the entry points on each of the time scales we want to use. It defines the names of the time scales and the entry points of the follow-up of each person. The \texttt{exit} argument gives the exit time on \emph{one} of the time scales, so the name of the element in this list must match one of the names of the \texttt{entry} list. This is sufficient, because the follow-up time on all time scales is the same, in this case $\mathtt{dox}$-$\mathtt{dodm}$. The \texttt{exit.status} is a categorical variable (a \emph{factor}) that indicates the exit status --- in this case whether the person (still) is in state \texttt{DM} or exits to \texttt{Dead} at the end of follow-up. In principle we should also indicate the \texttt{entry.status}, but the default is to assume that all persons enter in the \emph{first} of the mentioned \texttt{exit.state}s --- in this case \texttt{DM}, because $\mathtt{FALSE}<\mathtt{TRUE}$. Now take a look at the result: <<>>= str( dmL ) head( dmL )[,1:10] @ % The \texttt{Lexis} object \texttt{dmL} has a variable for each time scale which is the entry point on this time scale. The follow-up time is in the variable \texttt{lex.dur} (\texttt{dur}ation). Note that the exit status is in the variable \texttt{lex.Xst} (e\texttt{X}it \texttt{st}ate. The variable \texttt{lex.Cst} is the state where the follow-up takes place (\texttt{C}urrent \texttt{st}ate), in this case \texttt{DM} (alive with diabetes) for all persons. This implies that \emph{censored} observations are characterized by having $\mathtt{lex.Cst}=\mathtt{lex.Xst}$. There is a \texttt{summary} function for \texttt{Lexis} objects that lists the number of transitions and records as well as the total amount of follow-up time; it also (optionally) prints information about the names of the variables that constitute the time scales: <<>>= summary.Lexis( dmL, timeScales=TRUE ) @ % It is possible to get a visualization of the follow-up along the time scales chosen by using the \texttt{plot} method for \texttt{Lexis} objects. \texttt{dmL} is an object of \emph{class} \texttt{Lexis}, so using the function \texttt{plot()} on it means that \R\ will look for the function \texttt{plot.Lexis} and use this function. <>= plot( dmL ) @ % The function allows quite a bit of control over the output, and a \texttt{points.Lexis} function allows plotting of the endpoints of follow-up: <>= par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) plot( dmL, 1:2, lwd=1, col=c("blue","red")[dmL$sex], grid=TRUE, lty.grid=1, col.grid=gray(0.7), xlim=1960+c(0,60), xaxs="i", ylim= 40+c(0,60), yaxs="i", las=1 ) points( dmL, 1:2, pch=c(NA,3)[dmL$lex.Xst], col="lightgray", lwd=3, cex=0.3 ) points( dmL, 1:2, pch=c(NA,3)[dmL$lex.Xst], col=c("blue","red")[dmL$sex], lwd=1, cex=0.3 ) box(bty='o') @ % In the above code you will note that the values of the arguments \texttt{col} and \texttt{pch} are indexed by factors, using the convention in \R\ that the index is taken as \emph{number of the level} of the supplied factor. Thus \texttt{c("blue","red")[dmL\$sex]} is \texttt{"blue"} when \texttt{sex} is \texttt{M} (the first level). The results of these two plotting commands are in figure \ref{fig:Lexis-diagram}, p. \pageref{fig:Lexis-diagram}. \begin{figure}[tb] \centering \includegraphics[width=0.35\textwidth]{flup-dmL1} \includegraphics[width=0.63\textwidth]{flup-dmL2} \caption{\it Lexis diagram of the \textrm{\tt DMlate} dataset; left panel is the default version, right panel: plot with some bells and whistles. The red lines are for women, blue for men, crosses indicate deaths.} \label{fig:Lexis-diagram} \end{figure} \section{Splitting the follow-up time along a time scale} In next chapter we shall conduct statistical analysis of mortality rates, and a prerequisite for parametric analysis of rates is that follow-up time is subdivided in smaller intervals, where we can reasonably assume that rates are constant. The follow-up time in a cohort can be subdivided (``split'') along a time scale, for example current age. This is achieved by the \texttt{splitLexis} (note that it is \emph{not} called \texttt{split.Lexis}). This requires that the time scale and the breakpoints on this time scale are supplied. Try: <<>>= dmS1 <- splitLexis( dmL, "age", breaks=seq(0,100,5) ) summary( dmL ) summary( dmS1 ) @ % We see that the number of persons and events and the amount of follow-up is the same in the two data sets; only the number of records differ --- the extra records all have \texttt{lex.Cst}=\texttt{DM} and \texttt{lex.Xst}=\texttt{DM}. To see how records are split for each individual, it is useful to list the results for a few individuals (whom we selected with a view to the illustrative usefulness): <<>>= wh.id <- c(9,27,52,484) subset( dmL , lex.id %in% wh.id )[,1:10] subset( dmS1, lex.id %in% wh.id )[,1:10] @ % The resulting object, \texttt{dmS1}, is again a \texttt{Lexis} object, and the follow-up may be split further along another time scale, for example diabetes duration, \texttt{tfD}. Subsequently we list the results for the chosen individuals: <<>>= dmS2 <- splitLexis( dmS1, "tfD", breaks=c(0,1,2,5,10,20,30,40) ) subset( dmS2, lex.id %in% wh.id )[,1:10] @ % A more efficient (and more intuitive) way of making this double split is to use the \texttt{splitMulti} function from the \texttt{popEpi} package: <<>>= library( popEpi ) dmM <- splitMulti( dmL, age = seq(0,100,5), tfD = c(0,1,2,5,10,20,30,40), drop = FALSE ) summary( dmS2 ) summary( dmM ) @ % Note we used the argument \texttt{drop=FALSE} which will retain follow-up also outside the window defined by the breaks. Otherwise the default for \texttt{splitMulti} would be to drop follow-up outside \texttt{age} [0,100] and \texttt{tfD} [0,40]. This clipping behaviour is not available in \texttt{splitLexis}, nevertheless this may be exactly what we want in some situations. So we see that the two ways of splitting data yields the same amount of follow-up, but the results are not identical: <<>>= identical( dmS2, dmM ) class( dmS2 ) class( dmM ) @ % As we see, this is because the \texttt{dmM} object also is a \texttt{data.table} object; the \texttt{splitMulti} uses the \texttt{data.table} machinery which makes the splitting substantially faster --- this is of particular interest if you operate on large data sets ($>100,000$ records). Thus the recommended way of splitting follow-up time is by \texttt{splitMulti}. But you should be aware that the result is a \texttt{data.table} object, which in some circumstances behaves slightly different from \texttt{data.frame}s. See the manual for \texttt{data.table}. \section{Cutting follow up time at dates of intermediate events} If we have a recording of the date of a specific event as for example recovery or relapse, we may classify follow-up time as being before or after this intermediate event, but it requires that follow-up records that straddle the event be cut in two and placed in separate records, one representing follow-up \emph{before} the intermediate event, and another representing follow-up \emph{after} the intermediate event. This is achieved with the function \texttt{cutLexis}, which takes three arguments: the time point of the intermediate event, the time scale that this point refers to, and the value of the (new) state following the date. Optionally, we may also define a new time scale with the argument \texttt{new.scale=}. We are interested in the time before and after inception of insulin use, which occurs at the date \texttt{doins}: <<>>= whc <- c(names(dmL)[1:7],"dodm","doins") # WHich Columns do we want to see? subset( dmL, lex.id %in% wh.id )[,whc] dmC <- cutLexis( data = dmL, cut = dmL$doins, timescale = "per", new.state = "Ins", new.scale = "tfI", precursor.states = "DM" ) whc <- c(names(dmL)[1:8],"doins") # WHich Columns do we want to see? subset( dmC, lex.id %in% wh.id )[,whc] @ % (The \texttt{precursor.states=} argument is explained below). Note that the process of cutting time is simplified by having all types of events referred to the calendar time scale. This is a generally applicable advice in handling follow-up data: Get all event times as \emph{dates}, location of events and follow-up on other time scales can then easily be derived from this. Note that individual 52 has had his follow-up cut at 6.55 years from diabetes diagnosis and individual 484 at 5.70 years from diabetes diagnosis. This dataset could then be split along the time scales as we did before with \texttt{dmL}. The result of this can also be achieved by cutting the split dataset \texttt{dmS2} instead of \texttt{dmL}: <<>>= dmS2C <- cutLexis( data = dmS2, cut = dmS2$doins, timescale = "per", new.state = "Ins", new.scale = "tfI", precursor.states = "DM" ) subset( dmS2C, lex.id %in% wh.id )[,whc] @ % Thus it does not matter in which order we use \texttt{splitLexis} and \texttt{cutLexis}. Mathematicians would say that \texttt{splitLexis} and \texttt{cutLexis} are commutative. Note in \texttt{lex.id}=484, that follow-up subsequent to the event is classified as being in state \texttt{Ins}, but that the final transition to state \texttt{Dead} is preserved. This is the point of the \texttt{precursor.states=} argument. It names the states (in this case \texttt{DM}) that will be over-written by \texttt{new.state} (in this case \texttt{Ins}), while the state \texttt{Dead} should not be updated even if it is after the time where the persons moves to state \texttt{Ins}. In other words, only state \texttt{DM} is a precursor to state \texttt{Ins}, state \texttt{Dead} is always subsequent to state \texttt{Ins}. Note that we defined a new time scale, \texttt{tfI}, using the argument \texttt{new.scale=tfI}. This has a special status relative to the other three time scales, it is defined as time since entry into a state, namely \texttt{Ins}, this is noted in the time scale part of the summary of \texttt{Lexis} object --- the information sits in the attribute \texttt{time.since} of the \texttt{Lexis} object, which can be accessed by the function \texttt{timeSince()} or through the \texttt{summary()}: <<>>= summary( dmS2C, timeScales=TRUE ) @ % Finally we can get a quick overview of the states and transitions by using \texttt{boxes} --- \texttt{scale.R} scales transition rates to rates per 1000 PY: <>= boxes( dmC, boxpos=TRUE, scale.R=1000, show.BE=TRUE ) @ % \insfig{box1}{0.8}{States, person years, transitions and rates in the cut dataset. The numbers \emph{in} the boxes are person-years and the number of persons \texttt{B}eginning, resp. \texttt{E}nding their follow-up in each state (triggered by \textrm{\tt show.BE=TRUE}). The numbers at the arrows are the number of transitions and transition rates per 1000 (triggered by \textrm{\tt scale.R=1000}).} \chapter{Modeling rates from \texttt{Lexis} objects} \section{Covariates} In the dataset \texttt{dmS2C} there are three types of covariates that can be used to describe mortality rates: \begin{enumerate} \item time-dependent covariates \item time scales \item fixed covariates \end{enumerate} There is only one time-dependent covariate here, namely \texttt{lex.Cst}, the current state of the person's follow up; it takes the values \texttt{DM} and \texttt{Ins} according to whether the person has ever purchased insulin at a given time of follow-up. The time-scales are obvious candidates for explanatory variables for the rates, notably age and time from diagnosis (duration of diabetes) and insulin. \subsection{Time scales as covariates} If we want to model the effect of the time scale variables on occurrence rates, we will for each interval use either the value of the left endpoint in each interval or the middle. There is a function \texttt{timeBand} which returns either of these: <<>>= timeBand( dmS2C, "age", "middle" )[1:10] # For nice printing and column labelling we use the data.frame() function: data.frame( dmS2C[,c("per","age","tfD","lex.dur")], mid.age=timeBand( dmS2C, "age", "middle" ), mid.t=timeBand( dmS2C, "tfD", "middle" ), left.t=timeBand( dmS2C, "tfD", "left" ), right.t=timeBand( dmS2C, "tfD", "right" ), fact.t=timeBand( dmS2C, "tfD", "factor" ) )[1:15,] @ % Note that the values of these functions are characteristics of the intervals defined by \texttt{breaks=}, \emph{not} the midpoints nor left or right endpoints of the actual follow-up intervals (which would be \texttt{tfD} and \texttt{tfD+lex.dur}, respectively). These functions are intended for modeling time scale variables as factors (categorical variables) in which case the coding must be independent of the censoring and mortality pattern --- it should only depend on the chosen grouping of the time scale. Modeling time scales as \emph{quantitative} should not be based on these codings but directly on the values of the time-scale variables, notably the left endpoints of the intervals. \subsection{Differences between time scales} Apparently, the only fixed variable is \texttt{sex}, but formally the dates of birth (\texttt{dobth}), diagnosis (\texttt{dodm}) and first insulin purchase (\texttt{doins}) are fixed covariates too. They can be constructed as origins of time scales referred to the calendar time scale. Likewise, and possibly of greater interest, we can consider these origins on the age scale, calculated as the difference between age and another time scale. These would then be age at birth (hardly relevant since it is the same for all persons), age at diabetes diagnosis and age at insulin treatment. \subsection{Keeping the relation between time scales} The midpoint (as well as the right interval endpoint) should be used with caution if the variable age at diagnosis \texttt{dodm-dobth} is modeled too; the age at diabetes is logically equal to the difference between current age (\texttt{age}) and time since diabetes diagnosis (\texttt{tfD}): <<>>= summary( (dmS2$age-dmS2$tfD) - (dmS2$dodm-dmS2$dobth) ) @ % This calculation refers to the \emph{start} of each interval --- which are in the time scale variables in the \texttt{Lexis} object. But when using the middle of the intervals, this relationship is not preserved: <<>>= summary( timeBand( dmS2, "age", "middle" ) - timeBand( dmS2, "tfD", "middle" ) - (dmS2$dodm-dmS2$dobth) ) @ % If all three variables are to be included in a model, we must make sure that the \emph{substantial} relationship between the variables be maintained. One way is to recompute age at diabetes diagnosis from the two midpoint variables, but more straightforward would be to use the left endpoint of the intervals, that is the time scale variables in the \texttt{Lexis} object. If we dissolve the relationship between the variables \texttt{age}, \texttt{tfD} and age at diagnosis by grouping we may obtain identifiability of the three separate effects, but it will be at the price of an arbitrary allocation of a linear trend between them. For the sake of clarity, consider current age, $a$, duration of disease, $d$ and age at diagnosis $e$, where \[ \text{current age} = \text{age at diagnosis} + \text{disease duration}, \quad \text{\ie} \quad a=e+d \quad \Leftrightarrow \quad e+d-a=0 \] If we model the effect of the quantitative variables $a$, $e$ and $d$ on the log-rates by three functions $f$, $g$ and $h$: $ \log(\lambda)=f(a)+g(d)+h(e) $ then for any $\kappa$: \begin{align*} \log(\lambda) & = f(a)+g(d)+h(e)+\kappa(e+d-a)\\ & = \big(f(a)-\kappa a \big)+ \big(g(d)+\kappa d \big)+ \big(h(e)+\kappa e \big) \\ & = \tilde f(a)+ \tilde g(d)+ \tilde h(e) \end{align*} In practical modeling this will turn up as a singular model matrix with one parameter aliased, corresponding to some arbitrarily chosen value of $\kappa$ (depending on software conventions for singular models). This phenomenon is well known from age-period-cohort models. Thus we see that we can move any slope around between the three terms, so if we achieve identifiability by using grouping of one of the variables we will in reality have settled for a particular value of $\kappa$, without known why we chose just that. The solution is to resort to predictions which are independent of the particular parametrization or choose a particular parametrization with explicit constraints. \section{Modeling of rates} As mentioned, the purpose of subdividing follow-up data in smaller intervals is to be able to model effects of time scale variables as parametric functions. When we split along a time scale we can get intervals that are as small as we want; if they are sufficiently small, an assumption of constant rates in each interval becomes reasonable. In a model that assumes a constant occurrence rate in each of the intervals the likelihood contribution from each interval is the same as the likelihood contribution from a Poisson variate $D$, say, with mean $\lambda \ell$ where $\lambda$ is the rate and $\ell$ is the interval length, and where the value of the variate $D$ is 1 or 0 according to whether an event has occurred or not. Moreover, the likelihood contributions from all follow-up intervals from a single person are \emph{conditionally} independent (conditional on having survived till the start of the interval in question). This implies that the total contribution to the likelihood from a single person is a product of terms, and hence the same as the likelihood of a number of independent Poisson terms, one from each interval. Note that variables are neither Poisson distributed (\eg they can only ever assume values 0 or 1) nor independent --- it is only the likelihood for the follow-up data that happens to be the same as the likelihood from independent Poisson variates. Different models can have the same likelihood, a model cannot be inferred from the likelihood. Parametric modeling of the rates is obtained by using the \emph{values} of the time scales for each interval as \emph{quantitative} explanatory variables, using for example splines. And of course also the values of the fixed covariates and the time-dependent variables for each interval. Thus the model will be one where the rate is assumed constant in each (small) interval, but where a parametric form of the \emph{size} of the rate in each interval is imposed by the model, using the time scale as a quantitative covariate. \subsection{Interval length} In the first chapter we illustrated cutting and splitting by listing the results for a few individuals across a number of intervals. For illustrational purposes we used 5-year age bands to avoid excessive listings, but since the doubling time for mortality on the age scale is only slightly larger than 5 years, the assumption about constant rates in each interval would be pretty far fetched if we were to use 5 year intervals. Thus, for modeling purposes we split the follow-up in 3 month intervals. When we use intervals of 3 months length it is superfluous to split along multiple time scales --- the precise location of tightly spaced splits will be irrelevant from any practical point of view. \texttt{splitLexis} and \texttt{splitMulti} will allocate the actual split times for all of the time scale variables, so these can be used directly in modeling. So we split the cut dataset in 3 months intervals along the age scale: <<>>= dmCs <- splitMulti( dmC, age = seq(0,110,1/4) ) summary( dmCs, t=T ) @ % We see that we now have 228,748 records and 9996 persons, so about 23 records per person. The total risk time is 54,275 years, a bit less than 3 months on average per record as expected. \subsection{Practicalities for splines} In this study we want to look at how mortality depend on age (\texttt{age}) and time since start of insulin use (\texttt{tfI}). If we want to use splines in the description we must allocate knots for anchoring the splines at each of the time scales, either by some \textit{ad hoc} method or by using some sort of penalized splines as for example by \texttt{gam}; the latter will not be treated here; it belongs in the realm of the \texttt{mgcv} package. Here we shall use the former approach and allocate 5 knots on each of the time-scales. We allocate knots so that we have the events evenly distributed between the knots. Since the insulin state starts at 0 for all individuals we include 0 as the first knot, such that any set of natural splines with these knots will have the value 0 at 0 on the time scale. <<>>= ( a.kn <- with( subset( dmCs, lex.Xst=="Dead" ), quantile( age+lex.dur, (1:5-0.5)/5 ) ) ) ( i.kn <- c( 0, with( subset( dmCs, lex.Xst=="Dead" & lex.Cst=="Ins" ), quantile( tfI+lex.dur, (1:4)/5 ) ) ) ) @ % In the \texttt{Epi} package there is a convenience wrapper, \texttt{Ns}, for the \texttt{n}atural \texttt{s}pline generator \texttt{ns}, that takes the smallest and the largest of a set of supplied knots to be the boundary knots, so the explicit definition of the boundary knots becomes superfluous. Note that it is a feature of the \texttt{Ns} (via the features of \texttt{ns}) that any generated spline function is 0 at the leftmost knot. \subsection{Poisson models} A model that describes mortality rates as only a function of age would then be: <<>>= ma <- glm( (lex.Xst=="Dead") ~ Ns(age,knots=a.kn), family = poisson, offset = log(lex.dur), data = dmCs ) summary( ma ) @ % The offset, \texttt{log(lex.dur)} comes from the fact that the likelihood for the follow-up data during $\ell$ time is the same as that for independent Poisson variates with mean $\lambda \ell$, and that the default link function for the Poisson family is the log, so that we are using a linear model for the log-mean, $\log(\lambda) + \log(\ell)$. But when we want a model for the log-rate ($\log(\lambda)$), the term $\log(\ell)$ must still be included as a covariate, but with regression coefficient fixed to 1; a so-called \emph{offset}. This is however a technicality; it just exploits that the likelihood of a particular Poisson model and that of the rates model is the same. In the \texttt{Epi} package is a \texttt{glm} family, \texttt{poisreg} that has a more intuitive interface, where the response is a 2-column matrix of events and person-time, respectively. This is in concert with the fact that the outcome variable in follow-up studies is bivariate: (event, risk time). <<>>= Ma <- glm( cbind(lex.Xst=="Dead",lex.dur) ~ Ns(age,knots=a.kn), family = poisreg, data = dmCs ) summary( Ma ) @ % Exploiting the multistate structure in the \texttt{Lexis} object there is a multistate convenience wrapper for \texttt{glm} with the \texttt{poisreg} family, that just requires specification of the transitions in terms of \texttt{from} and \texttt{to}. Although it is called \texttt{glm.Lexis} it is \emph{not} an S3 method for \texttt{Lexis} objects: <<>>= Xa <- glm.Lexis( dmCs, from="DM", to="Dead", formula = ~ Ns(age,knots=a.kn) ) @ % The result is a \texttt{glm} object but with an extra attribute, \texttt{Lexis}: <<>>= attr( Xa, "Lexis" ) @ % There are similar wrappers for \texttt{gam} and \texttt{coxph} models, \texttt{gam.Lexis} and \texttt{coxph.Lexis}, but these will not be elaborated in detail. The \texttt{from=} and \texttt{to=} can even be omitted, in which case all possible transitions \emph{into} any of the absorbing states is modeled: <<>>= xa <- glm.Lexis( dmCs, formula = ~ Ns(age,knots=a.kn) ) @ We can check if the four models fitted are the same: <<>>= c( deviance(ma), deviance(Ma), deviance(Xa), deviance(xa) ) @ % Oops! the model \texttt{Xa} is apparently not the same as the other three? This is because the explicit specification \verb|from="DM", to="Dead"|, omits modeling contributions from the $\mathtt{Ins}\rightarrow\mathtt{Dead}$ transition --- the output actually said so --- see also figure \ref{fig:box1} on p. \pageref{fig:box1}. The other three models all use both transitions --- and assume that the two transition rates are the same, \ie that start of insulin has no effect on mortality. We shall relax this assumption later. The parameters from the model do not have any direct interpretation \textit{per se}, but we can compute the estimated mortality rates for a range of ages using \texttt{ci.pred} with a suitably defined prediction data frame. Note that if we use the \texttt{poisson} family of models, we must specify all covariates in the model, including the variable in the offset, \texttt{lex.dur} (remember that this was a covariate with coefficient fixed at 1). We set the latter to 1000, because we want the mortality rates per 1000 person-years. Using the \texttt{poisreg} family, the prediction will ignore any value of \texttt{lex.dur} specified in the prediction data frame, the returned rates will be per unit in which \texttt{lex.dur} is recorded. <>= nd <- data.frame( age=40:85, lex.dur=1000 ) pr.0 <- ci.pred( ma, newdata = nd ) # mortality per 100 PY pr.a <- ci.pred( Ma, newdata = nd )*1000 # mortality per 100 PY summary(pr.0/pr.a) matshade( nd$age, pr.a, plot=TRUE, type="l", lty=1, log="y", xlab="Age (years)", ylab="DM mortality per 1000 PY") @ % \insfig{pr-a}{0.8}{Mortality among Danish diabetes patients by age with 95\% CI as shaded area. We see that the rates increase linearly on the log-scale, that is exponentially by age.} \section{Time dependent covariate} A Poisson model approach to mortality by insulin status, would be to assume that the rate-ratio between patients on insulin and not on insulin is a fixed quantity, independent of time since start of insulin, independent of age. This is commonly termed a proportional hazards assumption, because the rates (hazards) in the two groups are proportional along the age (baseline time) scale. <<>>= pm <- glm( cbind(lex.Xst=="Dead",lex.dur) ~ Ns(age,knots=a.kn) + lex.Cst + sex, family=poisreg, data = dmCs ) round( ci.exp( pm ), 3 ) @ % So we see that persons on insulin have about twice the mortality of persons not on insulin and that women have 2/3 the mortality of men. \subsection{Time since insulin start} If we want to test whether the excess mortality depends on the time since start if insulin treatment, we can add a spline terms in \texttt{tfI}. But since \texttt{tfI} is a time scale defined as time since entry into a new state (\texttt{Ins}), the variable \texttt{tfI} will be missing for those in the \texttt{DM} state, so before modeling we must set the \texttt{NA}s to 0, which we do with \texttt{tsNA20} (acronym for \texttt{t}ime\texttt{s}cale \texttt{NA}s to zero): <<>>= pm <- glm( cbind(lex.Xst=="Dead",lex.dur) ~ Ns(age,knots=a.kn) + Ns(tfI,knots=i.kn) + lex.Cst + sex, family=poisreg, data = tsNA20(dmCs) ) @ % As noted before we could do this simpler with \texttt{glm.Lexis}, even without the \texttt{from=} and \texttt{to=} arguments, because we are modeling all transitions \emph{into} the absorbing state (\texttt{Dead}): <<>>= Pm <- glm.Lexis( tsNA20(dmCs), form = ~ Ns(age,knots=a.kn) + Ns(tfI,knots=i.kn) + lex.Cst + sex ) c( deviance(Pm), deviance(pm) ) identical( model.matrix(Pm), model.matrix(pm) ) @ % The coding of the effect of \texttt{tfI} is so that the value is 0 at 0, so the meaning of the estimate of the effect of \texttt{lex.Cst} is the RR between persons with and without insulin, immediately after start of insulin: <<>>= round( ci.exp( Pm, subset="ex" ), 3 ) @ % We see that the effect of sex is pretty much the same as before, but the effect of \texttt{lex.Cst} is much larger, it now refers to a different quantity, namely the RR at \texttt{tfI}=0. If we want to see the effect of time since insulin, it is best viewed jointly with the effect of age: <>= ndI <- data.frame( expand.grid( tfI=c(NA,seq(0,15,0.1)), ai=seq(40,80,10) ), sex="M", lex.Cst="Ins" ) ndI <- transform( ndI, age=ai+tfI ) head( ndI ) ndA <- data.frame( age= seq(40,100,0.1), tfI=0, lex.Cst="DM", sex="M" ) pri <- ci.pred( Pm, ndI ) * 1000 pra <- ci.pred( Pm, ndA ) * 1000 matshade( ndI$age, pri, plot=TRUE, las=1, xlab="Age (years)", ylab="DM mortality per 1000 PY", log="y", lty=1, col="blue" ) matshade( ndA$age, pra ) @ % \insfig{ins-time}{0.8}{Mortality rates of persons on insulin, starting insulin at ages 40,50,\ldots,80 (blue), compared with persons not on insulin (black curve). Shaded areas are 95\% CI.} In figure \ref{fig:ins-time}, p. \pageref{fig:ins-time}, we see that mortality is high just after insulin start, but falls by almost a factor 3 during the first year. Also we see that there is a tendency that mortality in a given age is smallest for those with the longest duration of insulin use. \section{The Cox model} Note that in the Cox-model the age is used as response variable, slightly counter-intuitive. Hence the age part of the linear predictors is not in that model: <<>>= library( survival ) cm <- coxph( Surv(age,age+lex.dur,lex.Xst=="Dead") ~ Ns(tfI,knots=i.kn) + lex.Cst + sex, data = tsNA20(dmCs) ) @ % There is also a multistate wrapper for Cox models, requiring a l.h.s. side for the \texttt{formula=} argument: <<>>= Cm <- coxph.Lexis( tsNA20(dmCs), form= age ~ Ns(tfI,knots=i.kn) + lex.Cst + sex ) cbind( ci.exp( cm ), ci.exp( Cm ) ) @ % We can compare the estimates from the Cox model with those from the Poisson model --- we must add \texttt{NA}s because the Cox-model does not give the parameters for the baseline time scale (\texttt{age}), but also remove one of the parameters, because \texttt{coxph} parametrizes factors (in this case \texttt{lex.Cst}) by all defined levels and not only by the levels present in the dataset at hand (note the line of \texttt{1.0000000}s in the print above): <<>>= round( cbind( ci.exp( Pm ), rbind( matrix(NA,5,3), ci.exp( cm )[-6,] ) ), 3 ) @ % Thus we see that the Poisson and Cox gives pretty much the same results. You may argue that Cox requires a smaller dataset, because there is no need to subdivide data in small intervals \emph{before} insulin use. But certainly the time \emph{after} insulin inception need to be if the effect of this time should be modeled. The drawback of the Cox-modeling is that it is not possible to show the absolute rates as we did in figure \ref{fig:ins-time} on \pageref{fig:ins-time}. \section{Marginal effect of time since insulin} When we plot the marginal effect of \texttt{tfI} from the two models we get pretty much the same; here we plot the RR relative to \texttt{tfI}=2 years. Note that we are deriving the RR as the ratio of two sets of predictions, from the data frames \texttt{nd} and \texttt{nr} --- for further details consult the help page for \texttt{ci.lin}, specifically the use of a list as the \texttt{ctr.mat} argument: <>= nd <- data.frame( tfI=seq(0,15,,151), lex.Cst="Ins", sex="M" ) nr <- data.frame( tfI= 2 , lex.Cst="Ins", sex="M" ) ppr <- ci.exp( pm, list(nd,nr), xvars="age" ) cpr <- ci.exp( cm, list(nd,nr) ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( nd$tfI, cbind(ppr,cpr), plot=T, lty=c(1,2), log="y", xlab="Time since insulin (years)", ylab="Rate ratio") abline( h=1, lty=3 ) @ % \insfig{Ieff}{0.8}{The naked duration effects relative to 2 years of duration, black from Poisson model, red from Cox model. The two sets of estimates are identical, and so are the standard errors, so the two shaded areas overlap almost perfectly.} In figure \ref{fig:Ieff}, p. \pageref{fig:Ieff}, we see that the duration effect is exactly the same from the two modeling approaches. We will also want the RR relative to the non-insulin users --- recall these are coded 0 on the \texttt{tfI} variable: <>= nd <- data.frame( tfI=seq(0,15,,151), lex.Cst="Ins", sex="M" ) nr <- data.frame( tfI= 0 , lex.Cst="DM" , sex="M" ) ppr <- ci.exp( pm, list(nd,nr), xvars="age" ) cpr <- ci.exp( cm, list(nd,nr) ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( nd$tfI, cbind(ppr,cpr), xlab="Time since insulin (years)", ylab="Rate ratio relative to non-Insulin", lty=c(1,2), log="y", plot=T ) @ % \insfig{IeffR}{0.8}{Insulin duration effect (state \textrm{\tt Ins}) relative to no insulin (state \textrm{\tt DM}), black from Poisson model, red from Cox model. The \emph{shape} is the same as the previous figure, but the RR is now relative to non-insulin, instead of relative to insulin users at 2 years duration. The two sets of estimates are identical, and so are the standard errors, so the two shaded areas overlap almost perfectly.} In figure \ref{fig:IeffR}, p. \pageref{fig:IeffR}, we see the effect of increasing duration of insulin use \emph{for a fixed age} which is a bit artificial, so we would like to see the \emph{joint} effects of age and insulin duration. What we cannot see is how the duration affects mortality relative to \texttt{current} age (at the age attained at the same time as the attained \texttt{tfI}). Another way of interpreting this curve is as the rate ratio relative to a person not on insulin, so we see that the RR (or hazard ratio, HR as some call it) is over 5 at the start of insulin (the \texttt{lex.Cst} estimate), and decreases to about 1.5 in the long term. Both figure \ref{fig:Ieff} and \ref{fig:IeffR} indicate a declining RR by insulin duration, but only from figure \ref{fig:ins-time} it is visible that mortality actually is \emph{in}creasing by age after some 2 years after insulin start. This point would not be available if we had only fitted a Cox model where we did not have access to the baseline hazard as a function of age. \section{Age$\times$duration interaction} The model we fitted assumes that the RR is the same regardless of the age at start of insulin --- the hazards are multiplicative. Sometimes this is termed the proportional hazards assumption: For \emph{any} fixed age the HR is the same as a function of time since insulin, and vice versa. A more correct term would be ``main effects model'' --- there is no interaction between age (the baseline time scale) and other covariates. So there is really no need for the term ``proportional hazards''; well defined and precise statistical terms for it has existed for aeons. \subsection{Age at insulin start} In order to check the consistency of the multiplicativity assumption across the spectrum of age at insulin inception, we can fit an interaction model. One approach to this would be using a non-linear effect of age at insulin use (for convenience we use the same knots as for age) --- note that the prediction data frames are the same as we used above, because we do not compute age at insulin use as a separate variable, but rather enter it as the difference between current age (\texttt{age}) and insulin duration (\texttt{tfI}). At first glance we might think of doing: <<>>= imx <- glm.Lexis( tsNA20(dmCs), formula = ~ Ns(age ,knots=a.kn) + Ns( tfI,knots=i.kn) + Ns(age-tfI,knots=a.kn) + lex.Cst + sex ) @ % But this will fit a model with a rate-ratio between persons with and without insulin that depends only on age at insulin start for the time \emph{after} insulin start, the RR at \texttt{tfI}=0 will be the same at any age, which really is not the type of interaction we wanted. We want the \texttt{age-tfI} term to be specific for the insulin exposed so we may use one of two other approaches, that are conceptually alike but mathematically different: <<>>= Im <- glm.Lexis( tsNA20(dmCs), formula = ~ Ns(age ,knots=a.kn) + Ns( tfI,knots=i.kn) + Ns((age-tfI)*(lex.Cst=="Ins"),knots=a.kn) + lex.Cst + sex ) im <- glm.Lexis( tsNA20(dmCs), formula = ~ Ns(age ,knots=a.kn) + Ns( tfI,knots=i.kn) + lex.Cst:Ns(age-tfI,knots=a.kn) + lex.Cst + sex ) @ % The first model (\texttt{Im}) has a common age-effect (\texttt{Ns(age,...}) for persons with and without diabetes and a RR depending on insulin duration \texttt{tfI} and age at insulin (\texttt{age-tfI}). Since the linear effect of these two terms are in the model as well, a linear trend in the RR by current age (\texttt{age}) is accommodated as well. The second model allows age-effects that differ non-linearly between person with and without insulin, because the interaction term \texttt{lex.Cst:Ns(age-tfI...} for persons not on insulin is merely an age term (since \texttt{tfI} is coded 0 for all follow-up not on insulin). We can compare the models fitted: <<>>= anova( imx, Im, im, test='Chisq') @ so we see that the models indeed are different, and moreover that the last model does not provide substantial further improvement, by allowing non-linear RR along the age-scale. We can illustrate the different estimated rates from the three models in figure \ref{fig:dur-int}, p. \pageref{fig:dur-int}: <>= pxi <- ci.pred( imx, ndI ) pxa <- ci.pred( imx, ndA ) pIi <- ci.pred( Im , ndI ) pIa <- ci.pred( Im , ndA ) pii <- ci.pred( im , ndI ) pia <- ci.pred( im , ndA ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( ndI$age, cbind( pxi, pIi, pii)*1000, plot=T, log="y", xlab="Age", ylab="Mortality per 1000 PY", lty=1, lwd=2, col=c("blue","forestgreen","red"), alpha=0.1 ) matshade( ndA$age, cbind( pxa, pIa, pia)*1000, lty=1, lwd=2, col=c("blue","forestgreen","red"), alpha=0.1 ) @ % \insfig{dur-int}{0.8}{Age at insulin as interaction between age and duration. Blue curves are from the naive interaction model \textrm{\tt imx} with identical $\RR$ at \textrm{\tt tfI}=0 at any age; green curves are from the interaction model with age at insulin, from the model \textrm{\tt Im} with only linear differences by age, and red lines from the full interaction model \textrm{\tt im}.} We can also plot the RRs only from these models (figure \ref{fig:dur-int-RR}, p. \pageref{fig:dur-int-RR}); for this we need the reference frames, and the machinery from \texttt{ci.exp} allowing a list of two data frames: <>= ndR <- transform( ndI, tfI=0, lex.Cst="DM" ) cbind( head(ndI), head(ndR) ) Rxi <- ci.exp( imx, list(ndI,ndR) ) Rii <- ci.exp( im , list(ndI,ndR) ) RIi <- ci.exp( Im , list(ndI,ndR) ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( ndI$age, cbind( Rxi, RIi, Rii), plot=T, log="y", xlab="Age (years)", ylab="Rate ratio vs, non-Insulin", lty=1, lwd=2, col=c("blue","forestgreen","red"), alpha=0.1 ) abline( h=1 ) abline( h=ci.exp(imx,subset="lex.Cst")[,1], lty="25", col="blue" ) @ % \insfig{dur-int-RR}{0.9}{RR from three different interaction models. The horizontal dotted line is at the estimated effect of \textrm{\tt lex.Cst}, to illustrate that the first model (blue) constrains this initial HR to be constant across age. The green curves are the extended interaction model, and the red the full one.} \clearpage \subsection{General interaction} As a final illustration we may want to explore a different kind of interaction, not defined from the duration --- here we simplify the interaction by not using the second-last knot in the interaction terms --- figure \ref{fig:splint}, p. \pageref{fig:splint}. Note again that the prediction code is the same: <>= gm <- glm.Lexis( tsNA20(dmCs), formula = ~ Ns(age,knots=a.kn) + Ns(tfI,knots=i.kn) + lex.Cst:Ns(age,knots=a.kn):Ns(tfI,knots=i.kn) + lex.Cst + sex ) pgi <- ci.pred( gm, ndI ) pga <- ci.pred( gm, ndA ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( ndI$age, cbind( pgi, pii )*1000, plot=T, lty=c("solid","21"), lend="butt", lwd=2, log="y", xlab="Age (years)", ylab="Mortality rates per 1000 PY", alpha=c(0.2,0.1), col=c("black","red") ) matshade( ndA$age, cbind( pga, pia )*1000, lty=c("solid","21"), lend="butt", lwd=2, alpha=c(0.2,0.1), col=c("black","red") ) @ % \insfig{splint}{0.8}{Spline-by-spline interaction between age and duration (model \textrm{\tt gm}, black), and the interaction using a non-linear effect of age at entry (model \textrm{\tt im}, red), corresponding to the red curves in figure \ref{fig:dur-int}.} This is in figure \ref{fig:splint}, p. \pageref{fig:splint}. \subsection{Evaluating interactions} Here we see that the interaction effect is such that in the older ages the length of insulin use has an increasing effect on mortality. Even though there is no statistically significant interaction between age and time since start of insulin, it would be illustrative to show the RR as a function of age at insulin and age at follow-up: <>= ndR <- transform( ndI, lex.Cst="DM", tfI=0 ) iRR <- ci.exp( im, ctr.mat=list(ndI,ndR) ) gRR <- ci.exp( gm, ctr.mat=list(ndI,ndR) ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( ndI$age, cbind(gRR,iRR), lty=1, log="y", plot=TRUE, xlab="Age (years)", ylab="Rate ratio: Ins vs. non-Ins", col=c("black","red") ) abline( h=1 ) @ % $ \insfig{RR-int}{0.8}{The effect of duration of insulin use at different ages of follow-up (and age at insulin start). Estimates are from the model with an interaction term using a non-linear effect of age at insulin start (model \textrm{\tt im}, red) and using a general spline interactions (model \textrm{\tt gm}, black). It appears that the general interaction over-models a bit.} This is in figure \ref{fig:RR-int}, p. \pageref{fig:RR-int}. The advantage of the parametric modeling (be that with age at insulin or general spline interaction) is that it is straight-forward to \emph{test} whether we have an interaction. \section{Separate models} In the above we insisted on making a joint model for the \texttt{DM}$\rightarrow$\texttt{Dead} and the \texttt{Ins}$\rightarrow$\texttt{Dead} transitions, but with the complications demonstrated it would actually have been more sensible to model the two transitions separately: <<>>= dmd <- glm.Lexis( dmCs, from="DM", to="Dead", formula = ~ Ns(age,knots=a.kn) + sex ) ind <- glm.Lexis( dmCs, from="Ins", to="Dead", formula = ~ Ns(age,knots=a.kn) + Ns(tfI,knots=i.kn) + Ns(age-tfI,knots=a.kn) + sex ) ini <- ci.pred( ind, ndI ) dmi <- ci.pred( dmd, ndI ) dma <- ci.pred( dmd, ndA ) @ % The estimated mortality rates are shown in figure \ref{fig:sep-mort}, p. \pageref{fig:sep-mort}, using: <>= par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") matshade( ndI$age, ini*1000, plot=TRUE, log="y", xlab="Age (years)", ylab="Mortality rates per 1000 PY", lwd=2, col="red" ) matshade( ndA$age, dma*1000, lwd=2, col="black" ) @ % The estimated RRs are computed using that the estimates from the two models are uncorrelated, and hence qualify for \texttt{ci.ratio} (this and the previous graph appear in figure \ref{fig:Ins-noIns}, p. \pageref{fig:Ins-noIns}) <>= par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") matshade( ndI$age, ci.ratio(ini,dmi), plot=TRUE, log="y", xlab="Age (years)", ylab="RR insulin vs. no insulin", lwd=2, col="red" ) abline( h=1 ) @ % \begin{figure}[tb] \centering \includegraphics[width=0.49\textwidth]{flup-sep-mort} \includegraphics[width=0.49\textwidth]{flup-sep-HR} \caption{\it Left panel: Mortality rates from separate models for the two mortality transitions; the \textrm{\tt DM}$\rightarrow$\textrm{\tt Dead} transition modeled by age alone; \textrm{\tt Ins}$\rightarrow$\textrm{\tt Dead} transition modeled with spline effects of current age, time since insulin and and age at insulin. \newline Right panel: Mortality HR of insulin vs. no insulin.} \label{fig:Ins-noIns} \end{figure} \chapter{More states} \section{Subdividing states} It may be of interest to subdivide the states following the intermediate event according to whether the event has occurred or not. This will enable us to address the question of the fraction of the patients that ever go on insulin. This is done by the argument \texttt{split.states=TRUE}. <<>>= dmCs <- cutLexis( data = dmS2, cut = dmS2$doins, timescale = "per", new.state = "Ins", new.scale = "tfI", precursor.states = "DM", split.states = TRUE ) summary( dmCs ) @ % We can illustrate the numbers and the transitions (figure \ref{fig:box4}, p. \pageref{fig:box4}) <>= boxes( dmCs, boxpos=list(x=c(15,15,85,85), y=c(85,15,85,15)), scale.R=1000, show.BE=TRUE ) @ % $ \insfig{box4}{0.7}{Transitions between 4 states: the numbers \emph{in} the boxes are person-years (middle), and below the number of persons who start, respectively end their follow-up in each of the states.} Note that it is only the mortality rates that we have been modeling, namely the transitions \texttt{DM}$\rightarrow$\texttt{Dead} and \texttt{Ins}$\rightarrow$\texttt{Dead(Ins)}. If we were to model the cumulative risk of using insulin we would also need a model for the DM$\rightarrow$Ins transition. Subsequent to that we would then compute the probability of being in each state conditional on suitable starting conditions. With models where transition rates depend on several time scales this is not a trivial task. This is treated in more detail in the vignette on \texttt{simLexis}. \section{Multiple intermediate events} We may be interested in starting either insulin or OAD (oral anti-diabetic drugs), thus giving rise to more states and more time scales. This can be accomplished by the \texttt{mcutLexis} function, that generalizes \texttt{cutLexis}: <<>>= dmM <- mcutLexis( dmL, timescale = "per", wh = c("doins","dooad"), new.states = c("Ins","OAD"), new.scales = c("tfI","tfO"), precursor.states = "DM", ties.resolve = TRUE ) summary( dmM, t=T ) @ We see that we now have two time scales defined as entry since into states. <<>>= wh <- c(subset(dmM,lex.Cst=="Ins-OAD")$lex.id[1:2], subset(dmM,lex.Cst=="OAD-Ins")$lex.id[1:2]) options( width=110 ) print( subset( dmM, lex.id %in% wh )[,c('lex.id',names(dmM[1:8]),c("doins","dooad"))], digits=6, row.names=FALSE ) @ % We can also illustrate the transitions to the different states, as in figure \ref{fig:mbox}: <>= boxes( dmM, boxpos=list(x=c(15,80,40,40,85,85), y=c(50,50,90,10,90,10)), scale.R=1000, show.BE=TRUE ) @ % \insfig{mbox}{1.0}{Boxes for the \textrm{\tt dmM} object. The numbers \emph{in} the boxes are person-years (middle), and below the number of persons who start, respectively end their follow-up in each of the states.} We may not be interested in whether persons were prescribed insulin before OAD or vice versa, in which case we would combine the levels with both insulin and OAD to one, regardless of order (figure \ref{fig:mboxr}): <>= summary( dmMr <- Relevel( dmM, list('OAD+Ins'=5:6), first=FALSE) ) boxes( dmMr, boxpos=list(x=c(15,50,15,85,85), y=c(85,50,15,85,15)), scale.R=1000, show.BE=TRUE ) @ % \insfig{mboxr}{1.0}{Boxes for the \textrm{\tt dmMr} object with collapsed states. The numbers \emph{in} the boxes are person-years (middle), and below the number of persons who start, respectively end their follow-up in each of the states.} Diagrams as those in figures \ref{fig:mbox} and \ref{fig:mboxr} gives an overview of the possible transitions, which states it might be relevant to collapse, and which transitions to model and how. The actual modeling of the transition rates is straightforward; split the data along some timescale and then use \texttt{glm.Lexis} or \texttt{gam.Lexis}, where it is possible to select the transitions modelled. This is also possible with the \texttt{coxph.Lexis} function, but it requires that a single time scale be selected as the baseline time scale, and the effect of this will not be accessible. \chapter{\texttt{Lexis} functions} The \texttt{Lexis} machinery has evolved over time since it was first introduced in a workable version in \texttt{Epi\_1.0.5} in August 2008. Over the years there have been additions of tools for handling multistate data. Here is a list of the current functions relating to \texttt{Lexis} objects with a very brief description; it does not replace the documentation. Unless otherwise stated, functions named \texttt{something.Lexis} (with a ``\texttt{.}'') are S3 methods for \texttt{Lexis} objects, so you can skip the ``\texttt{.Lexis}'' in daily use. \setlist{noitemsep} \begin{description} \item[Define]\ \\ \begin{description} \item[\texttt{Lexis}] defines a \texttt{Lexis} object \end{description} \item[Cut and split]\ \\ \begin{description} \item[\texttt{cutLexis}] cut follow-up at intermediate event \item[\texttt{mcutLexis}] cut follow-up at several intermediate events \item[\texttt{countLexis}] cut follow-up at intermediate event count the no. events so far \item[\texttt{splitLexis}] split follow up along a time scale \item[\texttt{splitMulti}] split follow up along a time scale --- from the \texttt{popEpi} package, faster and has simpler syntax than \texttt{splitLexis} \item[\texttt{addCov.Lexis}] add clinical measurements at a given date to a \texttt{Lexis} object \end{description} \item[Boxes and plots]\ \\ \begin{description} \item[\texttt{boxes.Lexis}] draw a diagram of states and transitions \item[\texttt{plot.Lexis}] draw a standard Lexis diagram \item[\texttt{points.Lexis}] add points to a Lexis diagram \item[\texttt{lines.Lexis}] add lines to a Lexis diagram \item[\texttt{PY.ann.Lexis}] annotate life lines in a Lexis diagram \end{description} \item[Summarize and query]\ \\ \begin{description} \item[\texttt{summary.Lexis}] overview of transitions, risk time etc. \item[\texttt{levels.Lexis}] what are the states in the \texttt{Lexis} object \item[\texttt{nid.Lexis}] number of persons in the \texttt{Lexis} object --- how many unique values of \texttt{lex.id} are present \item[\texttt{entry}] entry time \item[\texttt{exit}] exit time \item[\texttt{status}] status at entry or exit \item[\texttt{timeBand}] factor of time bands \item[\texttt{timeScales}] what time scales are in the \texttt{Lexis} object \item[\texttt{timeSince}] what time scales are defined as time since a given state \item[\texttt{breaks}] what breaks are currently defined \item[\texttt{absorbing}] what are the absorbing states \item[\texttt{transient}] what are the transient states \item[\texttt{preceding}, \texttt{before}] which states precede this \item[\texttt{succeeding}, \texttt{after}] which states can follow this \item[\texttt{tmat.Lexis}] transition matrix for the \texttt{Lexis} object \end{description} \item[Manipulate]\ \\ \begin{description} \item[\texttt{subset.Lexis}, \texttt{[}] subset of a \texttt{Lexis} object \item[\texttt{merge.Lexis}] merges a \texttt{Lexis} objects with a \texttt{data.frame} \item[\texttt{cbind.Lexis}] bind a \texttt{data.frame} to a \texttt{Lexis} object \item[\texttt{rbind.Lexis}] put two \texttt{Lexis} objects head-to-foot \item[\texttt{transform.Lexis}] transform and add variables \item[\texttt{tsNA20}] turn \texttt{NA}s to 0s for time scales \item[\texttt{Relevel.Lexis}, \texttt{factorize.Lexis}] reorder and combine states \item[\texttt{rm.tr}] remove transitions from a \texttt{Lexis} object \item[\texttt{bootLexis}] bootstrap sample of \emph{persons} (\texttt{lex.id}) in the \texttt{Lexis} object \end{description} \item[Simulate]\ \\ \begin{description} \item[\texttt{simLexis}] simulate a \texttt{Lexis} object from specified transition rate models \item[\texttt{nState}, \texttt{pState}] count state occupancy from a simulated \texttt{Lexis} object \item[\texttt{plot.pState}, \texttt{lines.pState}] plot state occupancy from a \texttt{pState} object \end{description} \item[Stack]\ \\ \begin{description} \item[\texttt{stack.Lexis}] make a stacked object for simultaneous analysis of transitions --- returns a \texttt{stacked.Lexis} object \item[\texttt{subset.stacked.Lexis}] subsets of a \texttt{stacked.Lexis} object \item[\texttt{transform.stacked.Lexis}] transform a \texttt{stacked.Lexis} object \end{description} \item[Interface to other packages]\ \\ \begin{description} \item[\texttt{msdata.Lexis}] interface to \texttt{mstate} package \item[\texttt{etm.Lexis}] interface to \texttt{etm} package \item[\texttt{crr.Lexis}] interface to \texttt{cmprsk} package \end{description} \item[Statistical models] --- these are \emph{not} S3 methods \begin{description} \item[\texttt{glm.Lexis}] fit a \texttt{glm} model using the \texttt{poisreg} family to (hopefully) time split data \item[\texttt{gam.Lexis}] fit a \texttt{gam} model (from the \texttt{mgcv} package) using the \texttt{poisreg} family to (hopefully) time split data \item[\texttt{coxph.Lexis}] fit a Cox model to follow-up in a \texttt{Lexis} object \end{description} \end{description} \renewcommand{\bibname}{References} \bibliographystyle{plain} \begin{thebibliography}{1} \bibitem{Carstensen.2011a} B~Carstensen and M~Plummer. \newblock Using {L}exis objects for multi-state models in {R}. \newblock {\em Journal of Statistical Software}, 38(6):1--18, 1 2011. %% \bibitem{Iacobelli.2013} %% S~Iacobelli and B~Carstensen. %% \newblock {Multiple time scales in multi-state models}. %% \newblock {\em Stat Med}, 32(30):5315--5327, Dec 2013. \bibitem{Plummer.2011} M~Plummer and B~Carstensen. \newblock Lexis: An {R} class for epidemiological studies with long-term follow-up. \newblock {\em Journal of Statistical Software}, 38(5):1--12, 1 2011. \end{thebibliography} \addcontentsline{toc}{chapter}{\bibname} \end{document} Epi/vignettes/crisk.tex0000644000176200001440000007404014003730256014641 0ustar liggesusers%\VignetteIndexEntry{Parametric competing risks with simulation based confidence intervals} \documentclass[a4paper,dvipsnames,twoside,12pt]{report} % ---------------------------------------------------------------------- % General information for the title page and the page headings \newcommand{\Title}{Parametric competing risks with simulation based confidence intervals} \newcommand{\Tit}{ParCmpRSim} \newcommand{\Version}{Version 3} \newcommand{\Dates}{January 2021} \newcommand{\Where}{SDCC} \newcommand{\Homepage}{\url{http://bendixcarstensen.com/}} \newcommand{\Faculty}{\begin{tabular}{rl} Bendix Carstensen & Steno Diabetes Center Copenhagen, Gentofte, Denmark\\ & {\small \& Department of Biostatistics, University of Copenhagen} \\ & \href{mailto:b@bxc.dk}{\tt b@bxc.dk} \\ & \url{http://BendixCarstensen.com} \\[1em] \end{tabular}} \input{topreport} \renewcommand{\rwpre}{./crisk} \chapter{Competing risks in practice} The concept of competing risks is one where persons in a given state, 'alive', say, er subject to a number of different causes of deaths, 'cause1', 'cause2' etc. Causes of death are required to be exhaustive and mutually exclusive. In situations where the causes are not causes of death but other events, it is implicit that we only consider the first occurrence of an event from the state 'alive', and ignore what occurs after. The likelihood for observations from a competing risk scenario is a function of the cause-specific transition rates, and is \emph{product} of the likelihoods that would emerge if we considered each cause the only one. Thus analysis is in principle straight forward; just estimate a model for each of the cause-specific rates. These will together form a complete model for the competing risks problem. If the cause-specific rates are all we want to assess then we will be done. But most often we would like to have estimates of the cumulative risks, that is the probability of dying from a specific cause before a given time as function of time. Each of these are functions of \emph{all} rates. Specifically, if the cause-specific rates are $\lambda_c(t)$, then: \[ R_c(t) = \int_0^t \lambda_c(s) \exp\left(-\int_0^s \sum_j \lambda_j(u) \dif u \right) \dif s \] Even if we from the modeling of the $\lambda$s have standard errors of $\log(\lambda_c)$ the standard errors of $R_c$s will be analytically intractable from these. The only viable way to get confidence intervals for the cumulative risks, $R_c$, is by calculation of the rates $\lambda(t)$ by sampling from the posterior distribution of the parameters in the models for $\log(\lambda(s))$, and computing the integrals numerically for each simulated sample. The simulation approach also allows calculation of confidence intervals for sums of the cumulative risks, $R_1(t)+R_2(t)$, for example, which will be needed if we want to show stacked cumulative risks. Finally, it will also allow calculation of standard errors of sojourn times in each of the states 'alive' and 'cause1', 'cause2'. While the latter two may not be of direct interest, then \texttt{differences} between such sojourn times between different groups can be interpreted as years of life lost to each cause between groups. \section{Example data} As an illustrative data example we use the (fake) diabetes register data; we set up the Lexis object, cut the follow-up time at dates of OAD, resp Ins: \begin{Schunk} \begin{Sinput} > library(Epi) > library(popEpi) > data(DMlate) > Ldm <- Lexis(entry = list( per = dodm, + age = dodm-dobth, + tfd = 0 ), + exit = list( per = dox ), + exit.status = factor( !is.na(dodth), labels = c("DM","Dead") ), + data = DMlate ) \end{Sinput} \begin{Soutput} NOTE: entry.status has been set to "DM" for all. NOTE: Dropping 4 rows with duration of follow up < tol \end{Soutput} \begin{Sinput} > summary(Ldm, t = T) \end{Sinput} \begin{Soutput} Transitions: To From DM Dead Records: Events: Risk time: Persons: DM 7497 2499 9996 2499 54273.27 9996 Timescales: per age tfd "" "" "" \end{Soutput} \begin{Sinput} > Mdm <- mcutLexis( Ldm, + wh = c('dooad','doins'), + new.states = c('OAD','Ins'), + precursor = 'DM', + seq.states = FALSE, + ties = TRUE ) \end{Sinput} \begin{Soutput} NOTE: 15 records with tied events times resolved (adding 0.01 random uniform), so results are only reproducible if the random number seed was set. \end{Soutput} \begin{Sinput} > summary( Mdm ) \end{Sinput} \begin{Soutput} Transitions: To From DM Dead OAD Ins Ins+OAD Records: Events: Risk time: Persons: DM 2830 1056 2957 689 0 7532 4702 22920.32 7532 OAD 0 992 3327 0 1005 5324 1997 22965.25 5324 Ins 0 152 0 462 172 786 324 3883.07 786 Ins+OAD 0 299 0 0 878 1177 299 4504.62 1177 Sum 2830 2499 6284 1151 2055 14819 7322 54273.27 9996 \end{Soutput} \end{Schunk} We initially split the FU before drug inception in intervals of 1/12 year, creating a \texttt{Lexis} object for a competing risks situation with three possible event types: \begin{Schunk} \begin{Sinput} > Sdm <- splitMulti(factorize(subset(Mdm, lex.Cst == "DM")), + tfd = seq(0, 20, 1/12)) \end{Sinput} \begin{Soutput} NOTE: lex.Cst and lex.Xst now have levels: DM Dead OAD Ins \end{Soutput} \end{Schunk} We can illustrate the follow-up in the full data set and in the restricted \begin{Schunk} \begin{Sinput} > boxes(Mdm, boxpos = list(x = c(15, 50, 15, 85, 85), + y = c(85, 50, 15, 85, 15)), + scale.R = 100, + show.BE = TRUE) \end{Sinput} \end{Schunk} \insfig{boxes5}{1.0}{The transitions in the multistate model, where follow-up is extended also after beginning of first drug exposure. Rates in brackets are per 100 PY.}% \begin{Schunk} \begin{Sinput} > boxes( Relevel(Sdm, c(1, 4, 2, 3)), + boxpos = list(x = c(15, 85, 80, 15), + y = c(85, 85, 20, 15)), + scale.R = 100, + show.BE = TRUE ) \end{Sinput} \end{Schunk} \insfig{boxes4}{1.0}{The transitions in the competing risks model, where follow-up is stopped at drug exposure. By that token only the \texttt{DM} state has person-years; a characteristic of a competing risks situation.} \section{Models for rates} Now that we have set up a dataset with three competing events, we can model the cause-specific rates separately by time from diagnosis as the only underlying time scale. Note that we only need to specify the \texttt{to=} argument because there is only one possible \texttt{from} for each \texttt{to} (incidentally the same for all \texttt{to} states, namely \texttt{DM}): \begin{Schunk} \begin{Sinput} > mD <- gam.Lexis(Sdm, ~ s(tfd, k = 5), to = 'Dead') \end{Sinput} \begin{Soutput} mgcv::gam Poisson analysis of Lexis object Sdm with log link: Rates for the transition: DM->Dead \end{Soutput} \begin{Sinput} > mO <- gam.Lexis(Sdm, ~ s(tfd, k = 5), to = 'OAD' ) \end{Sinput} \begin{Soutput} mgcv::gam Poisson analysis of Lexis object Sdm with log link: Rates for the transition: DM->OAD \end{Soutput} \begin{Sinput} > mI <- gam.Lexis(Sdm, ~ s(tfd, k = 5), to = 'Ins' ) \end{Sinput} \begin{Soutput} mgcv::gam Poisson analysis of Lexis object Sdm with log link: Rates for the transition: DM->Ins \end{Soutput} \end{Schunk} With these models fitted we can compute the rates, cumulative rates and the cumulative risks an sojourn times in states using the usual formulae. First we compute the rates in intervals of length 1/100 years. Note that these models only have time since diagnosis as covariates, so they are the counterpart of Nelson-Aalen estimates, albeit in a biologically more meaningful guise. The points where we compute the predicted rates are midpoints of intervals of length 1/100 year. These points are unrelated to the follow-up intervals in which we split the data---they were 1 month intervals, here we use 1/100 year (about 3.7 days): \begin{Schunk} \begin{Sinput} > int <- 1/100 > nd <- data.frame( tfd = seq(int,10,int)-int/2 ) # not the same as the split, > # and totally unrelated to it > rownames(nd) <- nd$tfd > str(nd) \end{Sinput} \begin{Soutput} 'data.frame': 1000 obs. of 1 variable: $ tfd: num 0.005 0.015 0.025 0.035 0.045 0.055 0.065 0.075 0.085 0.095 ... \end{Soutput} \end{Schunk} With this we can show the rates as a function of the time since diagnosis: \begin{Schunk} \begin{Sinput} > matshade(nd$tfd, cbind(ci.pred(mD, nd), + ci.pred(mI, nd), + ci.pred(mO, nd))*1000, + ylim = c(0.02,500), yaxt = "n", + ylab = "Rates per 1000 PY", + xlab = "Time since DM diagnosis (years)", + col = c("black","red","blue"), log = "y", lwd = 3, plot = TRUE) > axis(side = 2, at = ll<-outer(c(1,2,5),-2:3,function(x,y) x*10^y), + labels = formatC(ll,digits = 4), las = 1) > axis(side = 2, at = ll<-outer(c(1.5,2:9),-2:3,function(x,y) x*10^y), + labels = NA, tcl = -0.3) > text(0, 0.5*0.6^c(1,2,0), + c("Dead","Ins","OAD"), + col = c("black","red","blue"), adj = 0) \end{Sinput} \end{Schunk} \insfig{rates}{0.8}{Estimated rates from the \textrm{\tt DM} state, estimates are from \textrm{\tt gam} models fitted to data split in 1 month intervals (1/12 year, that is). Rates of \textrm{\tt OAD} is in the vicinity of 0.1/year, and mortality about half of this. Rates of insulin start among persons on no other drug are beginning high decreasing to about 4 year and then have a peak at 8 years.} Note that the graph in figure \ref{fig:rates} is not normally shown in analyses of competing risks; the competing cause-specific rates are hardly ever shown. I suspect that this is frequently because they are often modeled by a Cox model and so are buried in the model. \section{Cumulative rates and risks} For the calculation of the cumulative rates and state probabilities, we need just the rates without CIs: \begin{Schunk} \begin{Sinput} > # rates at midpoints > lD <- ci.pred( mD, nd )[,1] > lI <- ci.pred( mI, nd )[,1] > lO <- ci.pred( mO, nd )[,1] > # cumulative rates and survival fuction at right border of the intervals > LD <- cumsum(lD) * int > LI <- cumsum(lI) * int > LO <- cumsum(lO) * int > Sv <- exp( -LD - LI - LO ) > # but when integrating to get the cumulative risks we use the average > # of the survival function at the two endpoints (adding 1 as the first) > mp <- function(x) x - diff(c(1, x)) / 2 > rD <- cumsum(lD * mp(Sv)) * int > rI <- cumsum(lI * mp(Sv)) * int > rO <- cumsum(lO * mp(Sv)) * int \end{Sinput} \end{Schunk} Now we have the cumulative risks for the three causes and the survival, computed at the end of each of the intervals, at any time point the sum of the 3 cumulative risks and the survival should be 1: \begin{Schunk} \begin{Sinput} > summary(rD + rI +rO + Sv) \end{Sinput} \begin{Soutput} Min. 1st Qu. Median Mean 3rd Qu. Max. 1 1 1 1 1 1 \end{Soutput} \begin{Sinput} > oo <- options(digits = 20) > cbind(summary(Sv + rD + rI + rO)) \end{Sinput} \begin{Soutput} [,1] Min. 1.0000000534682520481 1st Qu. 1.0000010095665299303 Median 1.0000010154411886898 Mean 1.0000009973166215094 3rd Qu. 1.0000010316432050850 Max. 1.0000010385709348082 \end{Soutput} \begin{Sinput} > options(oo) \end{Sinput} \end{Schunk} We can then plot the 3 cumulative risk functions together: \begin{Schunk} \begin{Sinput} > zz <- mat2pol(cbind(rD,rI,rO,Sv), x = nd$tfd, + xlim = c(0,10), xaxs = "i", yaxs = "i", las = 1, + xlab = "Time since DM diagnosis (years)", + ylab = "Probability", + col = c("black","red","blue","forestgreen") ) > mm <- t(apply(zz,1,mid<-function(x) x[-1]-diff(x)/2)) > text( 9, mm[900,], c("Dead","Ins","OAD","DM"), col = "white" ) > box(col = "white",lwd = 3) \end{Sinput} \end{Schunk} \insfig{stack}{1.0}{Probabilities of being in the 4 different states as a function of time since diagnosis. Note that \texttt{OAD} means that OAD was initiated first, and similarly for \texttt{Ins}. We are not concerned about what occur after these events. \texttt{Dead} means dead without being on any drug.} \chapter{Confidence intervals} We want confidence intervals for each of the 4 cumulative risks, but we may also be interested in confidence intervals for \emph{sums} of any subset of the cumulative risks, corresponding to the borders between the colours in figure \ref{fig:stack}. If we only had two competing risks (and hence three states) the latter would not be an issue, because the sum of any two cumulative risks will be 1 minus the cumulative risk of the remainder, so we could get away with the confidence intervals for the single cumulative risks. This is the reason we have chosen an example with 3 competing risks and not just 2; we then have 4 probabilities to sum in different order. A short look at the formulae for cumulative risks will reveal that analytic approximation to the standard error of these probabilities (or some transform of them) is not really a viable way to go. Particularly if we also want confidence intervals of sums of the state probabilities as those shown in stacked plots. So in practice, if we want confidence intervals not only for the state probabilities, but also for any sum of subsets of them we would want a large number of simulated copies of the cumulative risks, each copy of the same structure as the one we just extracted from the model. Moreover, we might also want confidence intervals for sojourn times (i.e. time spent) in each state up to a given time, which would come almost for free from the simulation approach. This means that we must devise a method to make a prediction not from the estimated model, but where we instead of the model parameters use a sample from the posterior distribution of the estimated parameters. Here the posterior distribution of the parameters is taken to be the multivariate normal distribution with mean equal to the vector of parameter estimates and variance-covariance matrix equal to the estimated variance-covariance matrix of the parameters. Precisely this approach is implemented in \texttt{ci.lin} via the \texttt{sample} argument; we can get a predicted value from a given prediction data frame just as from \texttt{ci.pred} resp. \texttt{ci.exp}; here is an indication of different ways of getting predicted values of the cause-specific rates: \begin{Schunk} \begin{Sinput} > head(cbind(ci.pred(mI,nd), ci.exp(mI,nd) )) \end{Sinput} \begin{Soutput} Estimate 2.5% 97.5% exp(Est.) 2.5% 97.5% 0.005 0.3355221 0.3050046 0.3690931 0.3355221 0.3050046 0.3690931 0.015 0.3240042 0.2950104 0.3558474 0.3240042 0.2950104 0.3558474 0.025 0.3128817 0.2853291 0.3430948 0.3128817 0.2853291 0.3430948 0.035 0.3021411 0.2759506 0.3308172 0.3021411 0.2759506 0.3308172 0.045 0.2917693 0.2668654 0.3189974 0.2917693 0.2668654 0.3189974 0.055 0.2817538 0.2580639 0.3076184 0.2817538 0.2580639 0.3076184 \end{Soutput} \begin{Sinput} > head(cbind(ci.pred(mI,nd), exp(ci.lin(mI,nd)[,c(1,5:6)]))) \end{Sinput} \begin{Soutput} Estimate 2.5% 97.5% Estimate 2.5% 97.5% 0.005 0.3355221 0.3050046 0.3690931 0.3355221 0.3050046 0.3690931 0.015 0.3240042 0.2950104 0.3558474 0.3240042 0.2950104 0.3558474 0.025 0.3128817 0.2853291 0.3430948 0.3128817 0.2853291 0.3430948 0.035 0.3021411 0.2759506 0.3308172 0.3021411 0.2759506 0.3308172 0.045 0.2917693 0.2668654 0.3189974 0.2917693 0.2668654 0.3189974 0.055 0.2817538 0.2580639 0.3076184 0.2817538 0.2580639 0.3076184 \end{Soutput} \end{Schunk} Here is an illustration of the prediction with model based confidence intervals for the rates, alongside predictions based on samples from the posterior distribution of the parameters in the model: \begin{Schunk} \begin{Sinput} > str(ci.lin(mI, nd, sample = 4)) \end{Sinput} \begin{Soutput} num [1:1000, 1:4] -1.14 -1.18 -1.21 -1.24 -1.28 ... - attr(*, "dimnames")=List of 2 ..$ : chr [1:1000] "0.005" "0.015" "0.025" "0.035" ... ..$ : NULL \end{Soutput} \begin{Sinput} > head(cbind(ci.pred(mI,nd), exp(ci.lin(mI, nd, sample = 4)))) \end{Sinput} \begin{Soutput} Estimate 2.5% 97.5% 0.005 0.3355221 0.3050046 0.3690931 0.3767340 0.3368546 0.3618715 0.3346903 0.015 0.3240042 0.2950104 0.3558474 0.3633041 0.3245842 0.3484644 0.3233786 0.025 0.3128817 0.2853291 0.3430948 0.3503529 0.3127608 0.3355540 0.3124492 0.035 0.3021411 0.2759506 0.3308172 0.3378636 0.3013682 0.3231222 0.3018893 0.045 0.2917693 0.2668654 0.3189974 0.3258196 0.2903907 0.3111510 0.2916864 0.055 0.2817538 0.2580639 0.3076184 0.3142052 0.2798133 0.2996236 0.2818285 \end{Soutput} \end{Schunk} The simulation is taking place at the parameter level and the transformation to survival and cumulative risks is simply a function applied to every simulated set of rates. \section{Joint models for several transitions} Note that we are implicitly assuming that the transitions are being modeled separately. If some transitions are modeled jointly---for example assuming that the rates of \texttt{OAD} and \texttt{Ins} are proportional as functions of time since entry, using one model---we are in trouble, because we then need one sample from the posterior generating two predictions, one for each of the transitions modeled together. Moreover the model will have to be a model fitted to a \texttt{stack.Lexis} object, so a little more complicated to work with. A simple way to program would be to reset the seed to the same value before simulating with different values of \texttt{nd}, this is what is intended to be implemented, but is not yet. This is mainly the complication of having different prediction frames for different risks in this case. Finally, it is not a very urgent need, since the situation where you want common parameters for different rates out of a common state is quite rare. \section{Simulation based confidence intervals} These ideas have been implemented in the function \texttt{ci.Crisk} (\texttt{c}onfidence \texttt{i}ntervals for \texttt{C}umulative \texttt{risk}s) in the \texttt{Epi} package: We can now run the function using the model objects for the three competing events, using a common prediction data frame, \texttt{nd} for the rates: \begin{Schunk} \begin{Sinput} > system.time( + res <- ci.Crisk(list(OAD = mO, + Ins = mI, + Dead = mD), + nd = data.frame(tfd = (1:1000-0.5)/100), + nB = 1000, + perm = 4:1)) \end{Sinput} \begin{Soutput} Times are assumed to be in the column tfd at equal distances of 0.01 user system elapsed 12.326 0.669 12.477 \end{Soutput} \begin{Sinput} > str(res) \end{Sinput} \begin{Soutput} List of 3 $ Crisk: num [1:1001, 1:4, 1:3] 1 0.991 0.983 0.975 0.967 ... ..- attr(*, "dimnames")=List of 3 .. ..$ time : chr [1:1001] "0" "1" "2" "3" ... .. ..$ cause: chr [1:4] "Surv" "OAD" "Ins" "Dead" .. ..$ : chr [1:3] "50%" "2.5%" "97.5%" $ Srisk: num [1:1001, 1:3, 1:3] 0 0.000696 0.001385 0.002065 0.002738 ... ..- attr(*, "dimnames")=List of 3 .. ..$ time : chr [1:1001] "0" "1" "2" "3" ... .. ..$ cause: chr [1:3] "Dead" "Dead+Ins" "Dead+Ins+OAD" .. ..$ : chr [1:3] "50%" "2.5%" "97.5%" $ Stime: num [1:1000, 1:4, 1:3] 0.00996 0.01983 0.02962 0.03933 0.04896 ... ..- attr(*, "dimnames")=List of 3 .. ..$ : chr [1:1000] "1" "2" "3" "4" ... .. ..$ cause: chr [1:4] "Surv" "OAD" "Ins" "Dead" .. ..$ : chr [1:3] "50%" "2.5%" "97.5%" - attr(*, "int")= num 0.01 \end{Soutput} \end{Schunk} As we see, the returned object (\texttt{res}) is a list of length 3, each element a 3-way arrays. The three components of \texttt{res} represent \begin{itemize} \item \texttt{Crisk} \texttt{C}umulative \texttt{risk}s for each state \item \texttt{Srisk} \texttt{S}tacked cumulative \texttt{risk}s across states \item \texttt{Stime} \texttt{S}ojourn \texttt{time} for each state, truncated at each point of the time dimension, hence there is no 0 in the time dimension \end{itemize} The first dimension of each is time as interval \emph{number}, starting with 0, and corresponding to endpoints of intervals of length \texttt{int}. The second dimension is states (or combinations thereof). The last dimension of the arrays is the type of statistic; \texttt{50\%} the median of the samples, and the bootstrap intervals as indicated. The argument \texttt{perm} governs in which order the state probabilities are stacked in the \texttt{Srisk} element of the returned list, the default is the states in the order given in the list of models in the first argument to \texttt{ci.Crisk} followed by the survival. If we want the bootstrap samples to make other calculations we can ask the function to return the bootstrap samples of the rates by using the argument \texttt{sim.res='rates'} (defaults to \texttt{'none'}): \begin{Schunk} \begin{Sinput} > system.time( + rsm <- ci.Crisk(list(OAD = mO, + Ins = mI, + Dead = mD), + nd = data.frame(tfd = (1:1000-0.5)/100), + nB = 2000, + sim.res = 'rates')) \end{Sinput} \begin{Soutput} Times are assumed to be in the column tfd at equal distances of 0.01 user system elapsed 0.461 0.500 0.320 \end{Soutput} \begin{Sinput} > str(rsm) \end{Sinput} \begin{Soutput} num [1:1000, 1:3, 1:2000] 0.453 0.449 0.444 0.44 0.436 ... - attr(*, "dimnames")=List of 3 ..$ time: chr [1:1000] "1" "2" "3" "4" ... ..$ mod : chr [1:3] "OAD" "Ins" "Dead" ..$ sim : chr [1:2000] "1" "2" "3" "4" ... - attr(*, "int")= num 0.01 \end{Soutput} \end{Schunk} This is bootstrap samples of the rates evaluated at the 1000 midpoints of intervals. Alternatively we can get the bootstrap samples of the cumulative risks by setting \texttt{sim.res='crisk'}: \begin{Schunk} \begin{Sinput} > system.time( + csm <- ci.Crisk(list(OAD = mO, + Ins = mI, + Dead = mD), + nd = data.frame(tfd = (1:1000-0.5)/100), + nB = 2000, + sim.res = 'crisk')) \end{Sinput} \begin{Soutput} Times are assumed to be in the column tfd at equal distances of 0.01 user system elapsed 6.192 0.554 6.109 \end{Soutput} \begin{Sinput} > str(csm) \end{Sinput} \begin{Soutput} num [1:1001, 1:4, 1:2000] 1 0.991 0.982 0.974 0.966 ... - attr(*, "dimnames")=List of 3 ..$ time : chr [1:1001] "0" "1" "2" "3" ... ..$ cause: chr [1:4] "Surv" "OAD" "Ins" "Dead" ..$ sim : chr [1:2000] "1" "2" "3" "4" ... - attr(*, "int")= num 0.01 \end{Soutput} \end{Schunk} This is the cumulative risks evaluated at the 1001 endpoints of the 1000 intervals, and also includes the survival probability in the first slot of the \nth{1} dimension of \texttt{rsm}. In both cases, the first slot of the \nth{3} dimension, \texttt{sim}, is the rates, resp. cumulative risks from the model. \section{Simulated confidence intervals for rates} In figure \ref{fig:rates} we showed the rates with confidence intervals from the model. But in \texttt{rsm} we have 2000 (parametric) bootstrap samples of the occurrence rates, so we can derive the bootstrap medians and the bootstrap c.i.---remember that the first slice of the \nth{3} dimension is the model estimates that should not enter the calculations. We use the function \texttt{mnqt} to compute the model estimate and the mean, median and quantiles of the simulated values. \begin{Schunk} \begin{Sinput} > Brates <- aperm(apply(rsm, 1:2, Epi:::mnqt), c(2,3,1)) > str(Brates) \end{Sinput} \begin{Soutput} num [1:1000, 1:3, 1:3] 0.458 0.454 0.449 0.445 0.441 ... - attr(*, "dimnames")=List of 3 ..$ time: chr [1:1000] "1" "2" "3" "4" ... ..$ mod : chr [1:3] "OAD" "Ins" "Dead" ..$ : chr [1:3] "50%" "2.5%" "97.5%" \end{Soutput} \end{Schunk} Then we can plot the bootstrap estimates on top of the estimates based on the normal approximation to distribution of the parameters. They are not surprisingly in close agreement since they are both based on an assumption of normality of the parameters on the log-rate scale: \begin{Schunk} \begin{Sinput} > matshade(nd$tfd, cbind(ci.pred(mD, nd), + ci.pred(mI, nd), + ci.pred(mO, nd))*1000, + ylim = c(0.1,500), yaxt = "n", + ylab = "Rates per 1000 PY", + xlab = "Time since DM diagnosis (years)", + col = c("black","red","blue"), log = "y", lwd = 3, plot = TRUE) > matlines(nd$tfd, cbind(Brates[,"Dead",], + Brates[,"Ins" ,], + Brates[,"OAD" ,])*1000, + col = c("white","black","black"), lty = 3, lwd=c(3,1,1)) > axis(side = 2, at = ll<-outer(c(1,2,5),-2:3,function(x,y) x*10^y), + labels = formatC(ll,digits = 4), las = 1) > axis(side = 2, at = ll<-outer(c(1.5,2:9),-2:3,function(x,y) x*10^y), + labels = NA, tcl = -0.3) > text(0, 0.5*0.6^c(1,2,0), + c("Dead","Ins","OAD"), + col = c("black","red","blue"), adj = 0) \end{Sinput} \end{Schunk} \insfig{rates-ci}{0.8}{Estimated rates from the \textrm{\tt DM} state, estimates are from \textrm{\tt gam} models fitted to data split in 1 month intervals (1/12 year, that is). The white dotted curves are the bootstrap medians, black dotted curves are the bootstrap 95\% c.i.s.} \section{Confidence intervals for cumulative risks} In the \texttt{Crisk} component of \texttt{res} we have the cumulative risks as functions of of time, with bootstrap confidence intervals, so we can immediately plot the three cumulative risks: \begin{Schunk} \begin{Sinput} > matshade(c(0,nd$tfd+1/200), + cbind(res$Crisk[,"Dead",], + res$Crisk[,"Ins" ,], + res$Crisk[,"OAD" ,]), plot = TRUE, + xlim = c(0,10), xaxs = "i", yaxs = "i", las = 1, + xlab = "Time since DM diagnosis (years)", + ylab = "Cumulative probability", + col = c("black","red","blue")) > text(8, 0.3 + c(1,0,2)/25, + c("Dead","Ins","OAD"), + col = c("black","red","blue"), adj = 0) \end{Sinput} \end{Schunk} \insfig{crates}{0.9}{Cumulative risks for the three types of events, with 95\% bootstrap-based confidence intervals as shades.} \section{Confidence intervals for stacked cumulative risks} Unlike the single cumulative risks where we have a confidence interval for each cumulative risk, when we want to show the stacked probabilities we must deliver the confidence intervals for the relevant sums, they are in the \texttt{Srisk} component of \texttt{res}. \begin{Schunk} \begin{Sinput} > str(res$Crisk) \end{Sinput} \begin{Soutput} num [1:1001, 1:4, 1:3] 1 0.991 0.983 0.975 0.967 ... - attr(*, "dimnames")=List of 3 ..$ time : chr [1:1001] "0" "1" "2" "3" ... ..$ cause: chr [1:4] "Surv" "OAD" "Ins" "Dead" ..$ : chr [1:3] "50%" "2.5%" "97.5%" \end{Soutput} \begin{Sinput} > str(res$Srisk) \end{Sinput} \begin{Soutput} num [1:1001, 1:3, 1:3] 0 0.000696 0.001385 0.002065 0.002738 ... - attr(*, "dimnames")=List of 3 ..$ time : chr [1:1001] "0" "1" "2" "3" ... ..$ cause: chr [1:3] "Dead" "Dead+Ins" "Dead+Ins+OAD" ..$ : chr [1:3] "50%" "2.5%" "97.5%" \end{Soutput} \end{Schunk} But we start out by plotting the stacked probabilities using \texttt{mat2pol} (\texttt{mat}rix to \texttt{pol}ygon), the input required is the single components from the \texttt{Crisk} component. Then we can add the confidence intervals \begin{Schunk} \begin{Sinput} > zz <- mat2pol(res$Crisk[,c("Dead","Ins","OAD","Surv"),1], + x = as.numeric(dimnames(res$Crisk)[[1]])/100, + xlim = c(0,10), xaxs = "i", yaxs = "i", las = 1, + xlab = "Time since DM diagnosis (years)", + ylab = "Probability", + col = c("black","red","blue","forestgreen") ) > mm <- t(apply(zz, 1, mid<-function(x) x[-1] - diff(x) / 2)) > text( 9, mm[900,], c("Dead","Ins","OAD","DM"), col = "white" ) > matshade(as.numeric(dimnames(res$Srisk)[[1]])/100, + cbind(res$Srisk[,1,], + res$Srisk[,2,], + res$Srisk[,3,]), + col = 'transparent', col.shade = "white", alpha = 0.3) \end{Sinput} \end{Schunk} \insfig{stack-ci}{1.0}{Probabilities of being in the 4 different states as a function of time since diagnosis. Note that \texttt{OAD} means that OAD was initiated first, and similarly for \texttt{Ins}. We are not concerned about what occurs \emph{after} these events. \texttt{Dead} means dead without being on any drug.\newline The white shadings around the borders between coloured areas represent the 95\% confidence intervals for the (sum of) probabilities.} \section{Sojourn times} From the \texttt{Stime} component of the \texttt{res} we can derive the estimated time spent in each state during the first, say, 5 or 10 years: \begin{Schunk} \begin{Sinput} > str(res$Stime) \end{Sinput} \begin{Soutput} num [1:1000, 1:4, 1:3] 0.00996 0.01983 0.02962 0.03933 0.04896 ... - attr(*, "dimnames")=List of 3 ..$ : chr [1:1000] "1" "2" "3" "4" ... ..$ cause: chr [1:4] "Surv" "OAD" "Ins" "Dead" ..$ : chr [1:3] "50%" "2.5%" "97.5%" \end{Soutput} \end{Schunk} We extract the 5 and 10 years components: \begin{Schunk} \begin{Sinput} > s510 <- res$Stime[1:2*500,,] > dimnames(s510)[[1]] <- c(" 5 yr","10 yr") > round(ftable(s510, row.vars=1:2), 2) \end{Sinput} \begin{Soutput} 50% 2.5% 97.5% cause 5 yr Surv 2.77 2.72 2.82 OAD 1.44 1.40 1.49 Ins 0.40 0.37 0.43 Dead 0.39 0.36 0.42 10 yr Surv 4.31 4.22 4.41 OAD 3.64 3.54 3.75 Ins 0.84 0.78 0.90 Dead 1.20 1.14 1.27 \end{Soutput} \end{Schunk} So we see that the expected life lived without pharmaceutical treatment during the first 10 years after DM diagnosis is 4.31 years with a 95\% CI of (4.21;4.42), and during the first 5 years 2.77 (2.72;2.82). The quantity \texttt{OAD} is the years lived without medication that has been terminated by OAD inception, and similarly for \texttt{Ins} and \texttt{Dead}. \end{document} Epi/vignettes/simLexis.rnw0000644000176200001440000014376714003562304015343 0ustar liggesusers%\VignetteIndexEntry{Simulation of multistate models with multiple timescales: simLexis} \SweaveOpts{results=verbatim,keep.source=TRUE,include=FALSE,eps=FALSE} \documentclass[a4paper,dvipsnames,twoside,12pt]{report} \newcommand{\Title}{Simulation of\\ multistate models with\\ multiple timescales:\\ \texttt{simLexis} in the \texttt{Epi} package} \newcommand{\Tit}{Multistate models with multiple timescales} \newcommand{\Version}{Version 2.5} \newcommand{\Dates}{\today} \newcommand{\Where}{SDCC} \newcommand{\Homepage}{\url{http://BendixCarstensen.com/Epi/simLexis.pdf}} \newcommand{\Faculty}{\begin{tabular}{rl} Bendix Carstensen & Steno Diabetes Center Copenhagen, Gentofte, Denmark\\ & {\small \& Department of Biostatistics, University of Copenhagen} \\ & \texttt{b@bxc.dk}\\ & \url{http://BendixCarstensen.com} \\[1em] \end{tabular}} \input{topreport} \renewcommand{\rwpre}{./simLexis} <>= options( width=90, SweaveHooks=list( fig=function() par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") ) ) @ % \chapter{Using \texttt{simLexis}} \section{Introduction} This vignette explains the machinery behind simulation of life histories through multistate models implemented in \texttt{simLexis}. In \texttt{simLexis} transition rates are allowed to depend on multiple time scales, including timescales defined as time since entry to a particular state (duration). This therefore also covers the case where time \emph{at} entry into a state is an explanatory variable for the rates, since time at entry is merely time minus duration. Thus, the set-up here goes beyond Markov- and semi-Markov-models, and brings simulation based estimation of state-occupancy probabilities into the realm of realistic multistate models. The basic idea is to simulate a new \texttt{Lexis} object \cite{Plummer.2011,Carstensen.2011a} as defined in the \texttt{Epi} package for \R, based on 1) a multistate model defined by its states and the transition rates between them and 2) an initial population of individuals. Thus the output will be a \texttt{Lexis} object describing the transitions of a predefined set of persons through a multistate model. Therefore, if persons are defined to be identical at start, then calculation of the probability of being in a particular state at a given time boils down to a simple enumeration of the fraction of the persons in the particular state at the given time. Bar of course the (binomial) simulation error, but this can be brought down by simulation a sufficiently large number of persons. An observed \texttt{Lexis} object with follow-up of persons through a number of states will normally be the basis for estimation of transition rates between states, and thus will contain all information about covariates determining the occurrence rates, in particular the \emph{timescales} \cite{Iacobelli.2013}. Hence, the natural input to simulation from an estimated multistate model will typically be an object of the same structure as the originally observed. Since transitions and times are what is simulated, any values of \texttt{lex.Xst} and \texttt{lex.dur} in the input object will of course be ignored. This first chapter of this vignette shows by an example how to use the function \texttt{simLexis} and display the results. The second chapter discusses in more detail how the simulation machinery is implemented and is not needed for the practical use of \texttt{simLexis}. \section{\texttt{simLexis} in practice} This section is largely a commented walk-trough of the example from the help-page of \texttt{simLexis}, with a larger number of simulated persons in order to minimize the pure simulation variation. When we want to simulate transition times through a multistate model where transition rates may depend on time since entry to the current or a previous state, it is essential that we have a machinery to keep track of the transition time on \emph{all} time scales, as well as a mechanism that can initiate a new time scale to 0 when a transition occurs to a state where we shall use time since entry as determinant of exit rates from that state. This is provided by \texttt{simLexis}. \subsection{Input for the simulation} Input for simulation of a single trajectory through a multistate model requires a representation of the \emph{current status} of a person; the starting conditions. The object that we supply to the simulation function must contain information about all covariates and all timescales upon which transitions depend, and in particular which one(s) of the timescales that are defined as time since entry into a particular state. Hence, starting conditions should be represented as a \texttt{Lexis} object (where \texttt{lex.dur} and \texttt{lex.Xst} are ignored, since there is no follow-up yet), where the time scale information is in the attributes \texttt{time.scales} and \texttt{time.since} respectively. Note that \texttt{time.scales} attribute is a vector of names of variables in the \texttt{Lexis} object, so all of these variables should be present even if they are not used in the models for the transitions, and they should be set to 0; if they are not in the initial dataset, \texttt{simLexis} will crash, if they are \texttt{NA}, the \texttt{simLexis} will produce an object with 0 rows. Thus there are two main arguments to a function to simulate from a multistate model: \begin{enumerate} \item A \texttt{Lexis} object representing the initial states and covariates of the population to be simulated. This has to have the same structure as the original \texttt{Lexis} object representing the multistate model from which transition rates in the model were estimated. As noted above, the values for \texttt{lex.Xst} and \texttt{lex.dur} are not required (since these are the quantities that will be simulated). \item A transition object, representing the transition intensities between states, which should be a list of lists of intensity representations. As an intensity representation we mean a function that for a given \texttt{Lexis} object can be used to produce estimates of the transition intensities at a set of supplied time points. The names of the elements of the transition object (which are lists) will be names of the \emph{transient} states, that is the states \emph{from} which a transition can occur. The names of the elements of each of these lists are the names of states \emph{to} which transitions can occur (which may be either transient or absorbing states). Hence, if the transition object is called \texttt{Tr} then \verb+TR$A$B+ (or \verb+Tr[["A"]][["B"]]+) will represent the transition intensity from state \texttt{A} to the state \texttt{B}. The entries in the transition object can be either \texttt{glm} objects (either with \texttt{poisson} or \texttt{poisreg} family), representing Poisson models for the transitions, \texttt{coxph} objects representing an intensity model along one time scale, or simply a function that takes a \texttt{Lexis} object as input and returns an estimated intensity for each row. \end{enumerate} In addition to these two input items, there will be a couple of tuning parameters. The output of the function will simply be a \texttt{Lexis} object with simulated transitions between states. This will be the basis for deriving sensible statistics from the \texttt{Lexis} object --- see next section. \section{Setting up a \texttt{Lexis} object} As an example we will use the \texttt{DMlate} dataset from the \texttt{Epi} package; it is a dataset simulated to resemble a random sample of 10,000 patients from the Danish National Diabetes Register. We start by loading the \texttt{Epi} package: <>= options( width=90 ) library( Epi ) print( sessionInfo(), l=F ) @ % First we load the diabetes data and set up a simple illness-death model: <>= data(DMlate) dml <- Lexis( entry = list(Per=dodm, Age=dodm-dobth, DMdur=0 ), exit = list(Per=dox), exit.status = factor(!is.na(dodth),labels=c("DM","Dead")), data = DMlate ) @ % This is just data for a simple survival model with states \texttt{DM} and \texttt{Dead}. Now we cut the follow-up at insulin start, which for the majority of patients (T2D) is a clinical indicator of deterioration of disease regulation. We therefore also introduce a new timescale, and split the non-precursor states, so that we can address the question of ever having been on insulin: <>= dmi <- cutLexis( dml, cut = dml$doins, pre = "DM", new.state = "Ins", new.scale = "t.Ins", split.states = TRUE ) summary( dmi, timeScales=T ) @ % $ Note that we show the time scales in the \texttt{Lexis} object, and that it is indicated that the time scale \texttt{t.Ins} is defined as time since entry into stat state \texttt{Ins.} We can show how many person-years we have and show the number of transitions and transition rates (per 1000), using the \texttt{boxes.Lexis} function to display the states and the number of transitions between them: <>= boxes( dmi, boxpos = list(x=c(20,20,80,80), y=c(80,20,80,20)), scale.R = 1000, show.BE = TRUE ) @ % \insfig{boxes}{0.8}{Data overview for the \textrm{\tt dmi} dataset. Numbers in the boxes are person-years and the number of persons who begin, resp. end their follow-up in each state, and numbers on the arrows are no. of transitions and rates (transition intensities) per 1000 PY.} \section{Analysis of rates} In the \texttt{Lexis} object (which is just a data frame) each person is represented by one record for each transient state occupied, thus in this case either 1 or 2 records; those who have a recorded time both without and with insulin have two records. In order to be able to fit Poisson models with occurrence rates varying by the different time-scales, we split the follow-up in 3-month intervals for modeling: <>= Si <- splitLexis( dmi, seq(0,20,1/4), "DMdur" ) summary( Si ) print( subset( Si, lex.id==97 )[,1:10], digits=6 ) @ % Note that when we split the follow-up, each person's follow up now consists of many records, each with the \emph{current} values of the timescales at the start of the interval represented by the record. In the modeling we shall assume that the rates are constant within each 6-month interval, but the \emph{size} of these rates we model as smooth functions of the time scales (that is the values at the beginning of each interval). The approach often used in epidemiology where one parameter is attached to each interval of time (or age) is not feasible when more than one time scale is used, because intervals are not classified the same way on all timescales. We shall use natural splines (restricted cubic splines) for the analysis of rates, and hence we must allocate knots for the splines. This is done for each of the time-scales, and separately for the transition out of states \texttt{DM} and \texttt{Ins}. For age, we place the knots so that the number of events is the same between each pair of knots, but only half of this beyond each of the boundary knots, whereas for the timescales \texttt{DMdur} and \texttt{tIns} where we have observation from a well-defined 0, we put knots at 0 and place the remaining knots so that the number of events is the same between each pair of knots as well as outside the boundary knots. <>= nk <- 5 ( ai.kn <- with( subset(Si,lex.Xst=="Ins" & lex.Cst!=lex.Xst ), quantile( Age+lex.dur , probs=(1:nk-0.5)/nk ) ) ) ( ad.kn <- with( subset(Si,lex.Xst=="Dead"), quantile( Age+lex.dur , probs=(1:nk-0.5)/nk ) ) ) ( di.kn <- with( subset(Si,lex.Xst=="Ins" & lex.Cst!=lex.Xst ), c(0,quantile( DMdur+lex.dur, probs=(1:(nk-1))/nk ) )) ) ( dd.kn <- with( subset(Si,lex.Xst=="Dead"), c(0,quantile( DMdur+lex.dur, probs=(1:(nk-1))/nk ) )) ) ( ti.kn <- with( subset(Si,lex.Xst=="Dead(Ins)"), c(0,quantile( t.Ins+lex.dur, probs=(1:(nk-1))/nk ) )) ) @ % Note that when we tease out the event records for transition to \emph{transient} states (in this case \texttt{Ins}, that is \verb|lex.Xst=="Ins"|), we should add \verb|lex.Cst!=lex.Xst|, to include only transition records and avoiding including records of sojourn time in the transient state. We then fit Poisson models to transition rates, using the wrapper \texttt{Ns} from the \texttt{Epi} package to simplify the specification of the rates: <>= library( splines ) DM.Ins <- glm( (lex.Xst=="Ins") ~ Ns( Age , knots=ai.kn ) + Ns( DMdur, knots=di.kn ) + I(Per-2000) + sex, family=poisson, offset=log(lex.dur), data = subset(Si,lex.Cst=="DM") ) ci.exp( DM.Ins ) class( DM.Ins ) @ % We can also fit this model with a slightly simpler syntax using the \texttt{glm.Lexis} function: <<>>= DM.Ins <- glm.Lexis( Si, from = "DM", to = "Ins", formula = ~ Ns( Age , knots=ai.kn ) + Ns( DMdur, knots=di.kn ) + I(Per-2000) + sex ) ci.exp( DM.Ins ) class( DM.Ins ) @ % So we have a slightly simpler syntax, and we get an informative message of which transition(s) we are modeling. However we do not have \texttt{update} method for these objects. <<>>= DM.Dead <- glm.Lexis( Si, from = "DM", to = "Dead", formula = ~ Ns( Age , knots=ad.kn ) + Ns( DMdur, knots=dd.kn ) + I(Per-2000) + sex ) Ins.Dead <- glm.Lexis( Si, from = "Ins", formula = ~ Ns( Age , knots=ad.kn ) + Ns( DMdur, knots=dd.kn ) + Ns( t.Ins, knots=ti.kn ) + I(Per-2000) + sex ) @ % Note the similarity of the code used to fit the three models, is is mainly redefining the response variable (\texttt{to} state) and the subset of the data used (\texttt{from} state). Also note that the last model need no specification of \texttt{to}, the default is to model all transitions from the \texttt{from} state, and his case there is only one. \section{The mortality rates} This section discusses in some detail how to extract ad display the mortality rates from the models fitted. But it is not necessary for understanding how to use \texttt{simLexis} in practice. \subsection{Proportionality of mortality rates} Note that we have fitted separate models for the three transitions, there is no assumption of proportionality between the mortality rates from \texttt{DM} and \texttt{Ins}. However, there is nothing that prevents us from testing this assumption; we can just fit a model for the mortality rates in the entire data frame \texttt{Si}, and compare the deviance from this with the sum of the deviances from the separate models using the \texttt{glm.Lexis} function: <>= All.Dead <- glm.Lexis( Si, to = c("Dead(Ins)","Dead"), formula = ~ Ns( Age , knots=ad.kn ) + Ns( DMdur, knots=dd.kn ) + lex.Cst + I(Per-2000) + sex ) round( ci.exp( All.Dead ), 3 ) @ % Incidentally we could have dispensed with the \texttt{to=} argument too, because the default is to take \texttt{to} to be all absorbing states in the model. From the parameter values we would in a simple setting just claim that start of insulin-treatment was associated with a slightly more than doubling of mortality. The model \texttt{All.dead} assumes that the age- and DM-duration effects on mortality in the \texttt{DM} and \texttt{Ins} states are the same, and moreover that there is no effect of insulin duration, but merely a mortality that is larger by a multiplicative constant not depending on insulin duration. The model \texttt{DM.Dead} has 8 parameters to describe the dependency on age and DM duration, the model \texttt{Ins.Dead} has 12 for the same plus the insulin duration (a natural spline with $k$ knots gives $k-1$ parameters, and we chose $k=5$ above). We can compare the fit of the simple proportional hazards model with the fit of the separate models for the two mortality rates, by adding up the deviances and d.f. from these: <>= what <- c("null.deviance","df.null","deviance","df.residual") ( rD <- unlist( DM.Dead[what] ) ) ( rI <- unlist( Ins.Dead[what] ) ) ( rA <- unlist( All.Dead[what] ) ) round( c( dd <- rA-(rI+rD), "pVal"=1-pchisq(dd[3],dd[4]+1) ), 3 ) @ % Thus we see there is a substantial non-proportionality of mortality rates from the two states; but a test provides no clue whatsoever to the particular \emph{shape} of the non-proportionality. To this end, we shall explore the predicted mortalities under the two models quantitatively in more detail. Note that the reason that there is a difference in the null deviances (and a difference of 1 in the null d.f.) is that the null deviance of \texttt{All.Dead} refer to a model with a single intercept, that is a model with constant and \emph{identical} mortality rates from the states \texttt{DM} and \texttt{Ins}, whereas the null models for \texttt{DM.Dead} and \texttt{Ins.Dead} have constant but \emph{different} mortality rates from the states \texttt{DM} and \texttt{Ins}. This is however irrelevant for the comparison of the \emph{residual} deviances. \subsection{How the mortality rates look} If we want to see how the mortality rates are modelled in \texttt{DM.Dead} and \texttt{Ins.Dead} in relation to \texttt{All.Dead}, we make a prediction of rates for say men diagnosed in different ages and going on insulin at different times after this. So we consider men diagnosed in ages 40, 50, 60 and 70, and who either never enter insulin treatment or do it 0, 2 or 5 years after diagnosis of DM. To this end we create a prediction data frame where we have observation times from diagnosis and 12 years on (longer would not make sense as this is the extent of the data). But we start by setting up an array to hold the predicted mortality rates, classified by diabetes duration, age at diabetes onset, time of insulin onset, and of course type of model. What we want to do is to plot the age-specific mortality rates for persons not on insulin, and for persons starting insulin at different times after DM. The mortality curves start at the age where the person gets diabetes and continues 12 years; for persons on insulin they start at the age when they initiate insulin. <>= pr.rates <- NArray( list( DMdur = seq(0,12,0.1), DMage = 4:7*10, r.Ins = c(NA,0,2,5), model = c("DM/Ins","All"), what = c("rate","lo","hi") ) ) str( pr.rates ) @ % For convenience the \texttt{Epi} package contains a function that computes predicted (log-)rates with c.i. --- it is merely a wrapper for \texttt{predict.glm}. So we set up the prediction data frame and modify it in loops over ages at onset and insulin onset in order to collect the predicted rates in different scenarios: <>= nd <- data.frame( DMdur = as.numeric( dimnames(pr.rates)[[1]] ), lex.Cst = factor( 1, levels=1:4, labels=levels(Si$lex.Cst) ), sex = factor( 1, levels=1:2, labels=c("M","F")) ) @ % $ Note that we did \emph{not} insert \texttt{lex.dur} as covariate in the prediction frame. This would be required if we used the \texttt{poisson} family with the \texttt{glm}, but the wrapper \texttt{glm.Lexis} uses the \texttt{poisreg} family, so \texttt{lex.dur} is ignored and predictions always comes in the (inverse) units of \texttt{lex.dur}. So we get rates per 1 person-year in the predictions. <>= for( ia in dimnames(pr.rates)[[2]] ) { dnew <- transform( nd, Age = as.numeric(ia)+DMdur, Per = 1998+DMdur ) pr.rates[,ia,1,"DM/Ins",] <- ci.pred( DM.Dead, newdata = dnew ) pr.rates[,ia,1,"All" ,] <- ci.pred( All.Dead, newdata = dnew ) for( ii in dimnames(pr.rates)[[3]][-1] ) { dnew = transform( dnew, lex.Cst = factor( 2, levels=1:4, labels=levels(Si$lex.Cst) ), t.Ins = ifelse( (DMdur-as.numeric(ii)) >= 0, DMdur-as.numeric(ii), NA ) ) pr.rates[,ia, ii ,"DM/Ins",] <- ci.pred( Ins.Dead, newdata = dnew ) pr.rates[,ia, ii ,"All" ,] <- ci.pred( All.Dead, newdata = dnew ) } } @ % $ So for each age at DM onset we make a plot of the mortality as function of current age both for those with no insulin treatment and those that start insulin treatment 0, 2 and 5 years after diabetes diagnosis, thus 4 curves (with c.i.). These curves are replicated with a different color for the simplified model. <>= par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1 ) plot( NA, xlim=c(40,82), ylim=c(5,300), bty="n", log="y", xlab="Age", ylab="Mortality rate per 1000 PY" ) abline( v=seq(40,80,5), h=outer(1:9,10^(0:2),"*"), col=gray(0.8) ) for( aa in 4:7*10 ) for( ii in 1:4 ) matshade( aa+as.numeric(dimnames(pr.rates)[[1]]), cbind( pr.rates[,paste(aa),ii,"DM/Ins",], pr.rates[,paste(aa),ii,"All" ,] )*1000, type="l", lty=1, lwd=2, col=c("red","limegreen") ) @ % \insfig{mort-int}{0.9}{Estimated mortality rates for male diabetes patients with no insulin (lower sets of curves) and insulin (upper curves), with DM onset in age 40, 50, 60 and 70. The red curves are from the models with separate age effects for persons with and without insulin, and a separate effect of insulin duration. The green curves are from the model with common age-effects and only a time-dependent effect of insulin, assuming no effect of insulin duration (the classical time-dependent variable approach). Hence the upper green curve is common for any time of insulin inception.} From figure \ref{fig:mort-int} we see that there is a substantial insulin-duration effect which is not accommodated by the simple model with only one time-dependent variable to describe the insulin effect. Note that the simple model (green curves) for those on insulin does not depend in insulin duration, and hence the mortality curves for those on insulin are just parallel to the mortality curves for those not on insulin, regardless of diabetes duration (or age) at the time of insulin initiation. This is the proportional hazards assumption. Thus the effect of insulin initiation is under-estimated for short duration of insulin and over-estimated for long duration of insulin. This is the major discrepancy between the two models, and illustrates the importance of being able to accommodate different time scales, but there is also a declining overall insulin effect by age which is not accommodated by the proportional hazards approach. Finally, this plot illustrates an important feature in reporting models with multiple timescales; all timescales must be represented in the predicted rates, only reporting the effect of one timescale, conditional on a fixed value of other timescales is misleading since all timescales by definition advance at the same pace. For example, the age-effect for a fixed value of insulin duration really is a misnomer since it does not correspond to any real person's follow-up, but to the mortality of persons in different ages but with the same duration of insulin use. \section{Input to the \texttt{simLexis} function} We want to estimate the cumulative probability of being in each of the 4 states, so that we can assess the fraction of diabetes pateints that go on insulin In order to simulate from the multistate model with the estimated transition rates, and get the follow-up of a hypothetical cohort, we must supply \emph{both} the transition rates and the structure of the model \emph{as well as} the initial cohort status to \texttt{simLexis}. \subsection{The transition object} We first put the models into an object representing the transitions; note this is a list of lists, the latter having \texttt{glm} objects as elements: <>= Tr <- list( "DM" = list( "Ins" = DM.Ins, "Dead" = DM.Dead ), "Ins" = list( "Dead(Ins)" = Ins.Dead ) ) @ % Now we have the description of the rates and of the structure of the model. The \texttt{Tr} object defines the states and models for all transitions between them; the object \verb|Tr$A$B| is the model for the transition intensity from state \texttt{A} to state \texttt{B}. \subsection{The initial cohort} We now define an initial \texttt{Lexis} object of persons with all relevant covariates defined. Note that we use \texttt{NULL} as row indicator in the \texttt{Lexis} object we used for modeling; this conserves the \texttt{time.scale} and \texttt{time.since} attributes which are needed for the simulation: <>= str( ini <- Si[NULL,1:9] ) @ % We now have an empty \texttt{Lexis} object with attributes reflecting the timescales in the multistate model we want to simulate from. But we must enter some data to represent the initial state of the persons whose follow-up we want to simulate through the model; so fill in data for one man and one woman: <>= ini[1:2,"lex.id"] <- 1:2 ini[1:2,"lex.Cst"] <- "DM" ini[1:2,"Per"] <- 1995 ini[1:2,"Age"] <- 60 ini[1:2,"DMdur"] <- 5 ini[1:2,"sex"] <- c("M","F") ini @ % So the persons starts in age 60 in 1995 with 5 years of diabetes duration. Note that the \texttt{t.Ins} is \texttt{NA}, because this is a timescale that first comes alive if a transtion to \texttt{Ins} is simulated. \section{Simulation of the follow-up} Now we simulate life-courses of a 1000 of each of these persons using the estimated model. The \texttt{t.range} argument gives the times range where the integrated intensities (cumulative rates) are evaluated and where linear interpolation is used when simulating transition times. Note that this must be given in the same units as \texttt{lex.dur} in the \texttt{Lexis} object used for fitting the models for the transitions. It is not a parameter that can be easily determined from the \texttt{TR} object, hence it must be supplied by the user. <>= set.seed( 52381764 ) Nsim <- 5000 system.time( simL <- simLexis( Tr, ini, t.range = 12, N = Nsim ) ) @ % The result is a \texttt{Lexis} object --- a data frame representing the simulated follow-up of \Sexpr{2*Nsim} persons (\Sexpr{Nsim} identical men and \Sexpr{Nsim} identical women) according to the rates we estimated from the original dataset. <>= summary( simL, by="sex" ) @ % \subsection{Using other models for simulation} \subsubsection{Proportional hazards Poisson model} We fitted a proportional mortality model \texttt{All.Dead} (which fitted worse than the other two), this is a model for \emph{both} the transition from \texttt{DM} to \texttt{Death} \emph{and} from \texttt{Ins} to \texttt{Dead(Ins)}, assuming that they are proportional. But it can easily be used in the simulation set-up, because the state is embedded in the model via the term \texttt{lex.Cst}, which is updated during the simulation. Simulation using this instead just requires that we supply a different transition object: <>= Tr.p <- list( "DM" = list( "Ins" = DM.Ins, "Dead" = All.Dead ), "Ins" = list( "Dead(Ins)" = All.Dead ) ) system.time( simP <- simLexis( Tr.p, ini, t.range = 12, N = Nsim ) ) summary( simP, by="sex" ) @ % \subsubsection{Proportional hazards Cox model} A third possibility would be to replace the two-time scale proportional mortality model by a one-time-scale Cox-model, using diabetes duration as time scale, and age at diagnosis of DM as (fixed) covariate: <>= library( survival ) Cox.Dead <- coxph( Surv( DMdur, DMdur+lex.dur, lex.Xst %in% c("Dead(Ins)","Dead")) ~ Ns( Age-DMdur, knots=ad.kn ) + I(lex.Cst=="Ins") + I(Per-2000) + sex, data = Si ) round( ci.exp( Cox.Dead ), 3 ) @ % Note that in order for this model to be usable for simulation, it is necessary that we use the components of the \texttt{Lexis} object to specify the survival. Each record in the data frame \texttt{Si} represents follow up from \texttt{DMdur} to \texttt{DMdur+lex.dur}, so the model is a Cox model with diabetes duration as underlying timescale and age at diagnosis, \texttt{Age-DMdur}, as covariate. Also note that we used \texttt{I(lex.Cst=="Ins")} instead of just \texttt{lex.Cst}, because \texttt{coxph} assigns design matrix columns to all levels of \texttt{lex.Cst}, also those not present in data, which would give \texttt{NA}s among the parameter estimates and \texttt{NA}s as mortality outcomes. We see that the effect of insulin and the other covariates are pretty much the same as in the two-time-scale model. We can simulate from this model too; there is no restrictions on what type of model can be used for different transitions <>= Tr.c <- list( "DM" = list( "Ins" = Tr$DM$Ins, "Dead" = Cox.Dead ), "Ins" = list( "Dead(Ins)" = Cox.Dead ) ) system.time( simC <- simLexis( Tr.c, ini, t.range = 12, N = Nsim ) ) summary( simC, by="sex" ) @ \section{Reporting the simulation results} We can now tabulate the number of persons in each state at a predefined set of times on a given time scale. Note that in order for this to be sensible, the \texttt{from} argument would normally be equal to the starting time for the simulated individuals. <>= system.time( nSt <- nState( subset(simL,sex=="M"), at=seq(0,11,0.2), from=1995, time.scale="Per" ) ) nSt[1:10,] @ % We see that as time goes by, the 5000 men slowly move away from the starting state (\texttt{DM}). Based on this table (\texttt{nSt} is a table) we can now compute the fractions in each state, or, rather more relevant, the cumulative fraction across the states in some specified order, so that a plot of the stacked probabilities can be made, using either the default rather colorful layout, or a more minimalist version (both in figure \ref{fig:pstate0}): <>= pM <- pState( nSt, perm=c(1,2,4,3) ) head( pM ) par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) plot( pM ) plot( pM, border="black", col="transparent", lwd=3 ) text( rep(as.numeric(rownames(pM)[nrow(pM)-1]),ncol(pM)), pM[nrow(pM),]-diff(c(0,pM[nrow(pM),]))/5, colnames( pM ), adj=1 ) box( col="white", lwd=3 ) box() @ % \insfig{pstate0}{1.0}{Default layout of the \textrm{\tt plot.pState} graph (left), and a version with the state probabilities as lines and annotation of states.} A more useful set-up of the graph would include a more through annotation and sensible choice of colors, as seen in figure \ref{fig:pstatex}: <>= clr <- c("limegreen","orange") # expand with a lighter version of the two chosen colors clx <- c( clr, rgb( t( col2rgb( clr[2:1] )*2 + rep(255,3) ) / 3, max=255 ) ) par( mfrow=c(1,2), las=1, mar=c(3,3,4,2), mgp=c(3,1,0)/1.6 ) # Men plot( pM, col=clx, xlab="Date of FU" ) lines( as.numeric(rownames(pM)), pM[,2], lwd=3 ) mtext( "60 year old male, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) mtext( "Survival curve", side=3, line=1.5, adj=0 ) mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) axis( side=4 ) axis( side=4, at=1:19/20, labels=FALSE ) axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) # Women pF <- pState( nState( subset(simL,sex=="F"), at=seq(0,11,0.2), from=1995, time.scale="Per" ), perm=c(1,2,4,3) ) plot( pF, col=clx, xlab="Date of FU" ) lines( as.numeric(rownames(pF)), pF[,2], lwd=3 ) mtext( "60 year old female, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) mtext( "Survival curve", side=3, line=1.5, adj=0 ) mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) axis( side=4 ) axis( side=4, at=1:19/20, labels=FALSE ) axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) @ % \insfig{pstatex}{1.0}{\textrm{\tt plot.pState} graphs where persons ever on insulin are given in orange and persons never on insulin in green, and the overall survival (dead over the line) as a black line.} If we instead wanted to show the results on the age-scale, we would use age as timescale when constructing the probabilities; otherwise the code is pretty much the same as before (Figure \ref{fig:pstatey}): <>= par( mfrow=c(1,2), las=1, mar=c(3,3,4,2), mgp=c(3,1,0)/1.6 ) # Men pM <- pState( nState( subset(simL,sex=="M"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) plot( pM, col=clx, xlab="Age" ) lines( as.numeric(rownames(pM)), pM[,2], lwd=3 ) mtext( "60 year old male, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) mtext( "Survival curve", side=3, line=1.5, adj=0 ) mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) axis( side=4 ) axis( side=4, at=1:19/20, labels=FALSE ) axis( side=4, at=1:19/20, labels=FALSE, tcl=-0.4 ) axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) # Women pF <- pState( nState( subset(simL,sex=="F"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) plot( pF, col=clx, xlab="Age" ) lines( as.numeric(rownames(pF)), pF[,2], lwd=3 ) mtext( "60 year old female, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) mtext( "Survival curve", side=3, line=1.5, adj=0 ) mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) axis( side=4 ) axis( side=4, at=1:9/10, labels=FALSE ) axis( side=4, at=1:19/20, labels=FALSE, tcl=-0.4 ) axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) @ % Note the several statements with \texttt{axis(side=4,...}; they are necessary to get the fine tick-marks in the right hand side of the plots that you will need in order to read off the probabilities at 2006 (or 71 years). \insfig{pstatey}{1.0}{\textrm{\tt plot.pState} graphs where persons ever on insulin are given in orange and persons never on insulin in green, and the overall survival (dead over the line) as a black line.} \subsection{Comparing predictions from different models} We have actually fitted different models for the transitions, and we have simulated Lexis objects from all three approaches, so we can plot these predictions on top of each other: <>= PrM <- pState( nState( subset(simP,sex=="M"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) PrF <- pState( nState( subset(simP,sex=="F"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) CoxM <- pState( nState( subset(simC,sex=="M"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) CoxF <- pState( nState( subset(simC,sex=="F"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) plot( pM, border="black", col="transparent", lwd=3 ) lines( PrM, border="blue" , col="transparent", lwd=3 ) lines( CoxM, border="red" , col="transparent", lwd=3 ) text( 60.5, 0.05, "M" ) box( lwd=5, col="white" ) ; box( lwd=2, col="black" ) plot( pF, border="black", col="transparent", lwd=3 ) lines( PrF, border="blue" , col="transparent", lwd=3 ) lines( CoxF, border="red" , col="transparent", lwd=3 ) text( 60.5, 0.05, "F" ) box( lwd=5, col="white" ) ; box( lwd=2, col="black" ) @ % \insfig{comp-0}{1.0}{Comparison of the simulated state occupancy probabilities using separate Poisson models for the mortality rates with and without insulin (black) and using proportional hazards Poisson models (blue) and Cox-models with diabetes duration as timescale and age at diabetes diagnosis as covariate (red).} From figure \ref{fig:comp-0} it is clear that the two proportional hazards models (blue and red curves) produce pretty much the same estimates of the state occupancy probabilities over time, but also that they relative to the model with separately estimated transition intensities overestimates the probability of being alive without insulin and underestimates the probabilities of being dead without insulin. However both the overall survival, and the fraction of persons on insulin are quite well in agreement with the more elaborate model. Thus the proportional hazards models overestimate the relative mortality of the insulin treated diabetes patients relative to the non-insulin treated. Interestingly, we also see a bump in the estimated probabilities from the Cox-model based model, but this is entirely an artifact that comes from the estimation method for the baseline hazard of the Cox-model that lets the (cumulative) hazard have large jumps at event times where the risk set is small. So also here it shows up that an assumption of continuous underlying hazards leads to more credible estimates. \chapter{Simulation of transitions in multistate models} \section{Theory} Suppose that the rate functions for the transitions out of the current state to, say, 3 different states are $\lambda_1$, $\lambda_2$ and $\lambda_3$, and the corresponding cumulative rates are $\Lambda_1$, $\Lambda_2$ and $\Lambda_3$, and we want to simulate an exit time and an exit state (that is either 1, 2 or 3). This can be done in two slightly different ways: \begin{enumerate} \item First time, then state: \begin{enumerate} \item Compute the survival function, $S(t) = \exp\bigl(-\Lambda_1(t)-\Lambda_2(t)-\Lambda_3(t)\bigr)$ \item Simulate a random U(0,1) variate, $u$, say. \item The simulated exit time is then the solution $t_u$ to the equation $S(t_u) = u \quad \Leftrightarrow \quad \sum_j\Lambda_j(t_u) = -\log(u)$. \item A simulated transition at $t_u$ is then found by simulating a random draw from the multinomial distribution with probabilities $p_i=\lambda_i(t_u) / \sum_j\lambda_j(t_u)$. \end{enumerate} \item Separate cumulative incidences: \begin{enumerate} \item Simulate 3 independent U(0,1) random variates $u_1$, $u_2$ and $u_3$. \item Solve the equations $\Lambda_i(t_i)=-\log(u_i), i=1,2,3$ and get $(t_1,t_2,t_3)$. \item The simulated survival time is then $\min(t_1,t_2,t_3)$, and the simulated transition is to the state corresponding to this, that is $k \in \{1,2,3\}$, where $t_k=\min(t_1,t_2,t_3)$ \end{enumerate} \end{enumerate} The intuitive argument is that with three possible transition there are 3 independent processes running, but only the first transition is observed. The latter approach is used in the implementation in \texttt{simLexis}. The formal argument for the equality of the two approaches goes as follows: \begin{enumerate} \item Equality of the transition times: \begin{enumerate} \item In the first approach we simulate from a distribution with cumulative rate $\Lambda_1(t)+\Lambda_2(t)+\Lambda_3(t)$, hence from a distribution with survival function: \begin{align*} S(t) & = \exp\bigl(-(\Lambda_1(t)+\Lambda_2(t)+\Lambda_3(t))\bigr) \\ & = \exp\bigl(-\Lambda_1(t)\bigr)\times \exp\bigl(-\Lambda_2(t)\bigr)\times \exp\bigl(-\Lambda_3(t)\bigr) \end{align*} \item In the second approach we choose the smallest of three independent survival times, with survival functions $\exp(-\Lambda_i), i=1,2,3$. Now, the survival function for the minimum of three independent survival times is: \begin{align*} S_\text{min}(t) & = \pmat{\min(t_1,t_2,t_3)>t} \\ & = \pmat{t_1>t} \times \pmat{t_2>t} \times \pmat{t_3>t} \\ & = \exp\bigl(-\Lambda_1(t)\bigr)\times \exp\bigl(-\Lambda_2(t)\bigr)\times \exp\bigl(-\Lambda_3(t)\bigr) \end{align*} which is the same survival function as derived above. \end{enumerate} \item Type of transition: \begin{enumerate} \item In the first instance the probability of a transition to state $i$, conditional on the transition time being $t$, is as known from standard probability theory: $\lambda_i(t)/\bigl(\lambda_1(t)+\lambda_2(t)+\lambda_3(t)\bigr)$. \item In the second approach we choose the transition corresponding to the the smallest of the transition times. So when we condition on the event that a transition takes place at time $t$, we have to show that the conditional probability that the smallest of the three simulated transition times was actually the $i$th, is as above. But conditional on \emph{survival} till $t$, the probabilities that events of type $1,2,3$ takes place in the interval $(t,t+\dif t)$ are $\lambda_1(t)\dif t$, $\lambda_2(t)\dif t$ and $\lambda_1(t)\dif t$, respectively (assuming that the probability of more than one event in the interval of length $\dif t$ is 0). Hence the conditional probabilities \emph{given a transition time} in $(t,t+\dif t)$ is: \[ \frac{\lambda_i(t)\dif t}{\lambda_1(t)\dif t+\lambda_2(t)\dif t+\lambda_3(t)\dif t}= \frac{\lambda_i(t)}{\lambda_1(t)+\lambda_2(t)+\lambda_3(t)} \] --- exactly as above. \end{enumerate} \end{enumerate} \section{Components of \texttt{simLexis}} This section explains the actually existing code for \texttt{simLexis}, as it is in the current version of \texttt{Epi}. % The following code sources the originally formatted code in % simLexis.R in order to make it printable with all the formatting and % comments in it. However the sourcing does not work when compiling % the vignettes in R CMD build. So when checking the code we comment % this out by putting eval=FALSE, and moreover, because it is only % simLexis that is exported, we also need to bring the functions simX, % sim1, lint, get.next and chop.lex into the workspace. So depending % on whether we actually construct the pdf for the inst/doc folder or % test (upload) the package, one of the following to chunks are run % with eval=FALSE and the other with eval=TRUE % When compiling the published vignette <>= source( "../R/simLexis.R", keep.source=TRUE ) @ % % When checking the package <>= simX <- Epi:::simX sim1 <- Epi:::sim1 lint <- Epi:::lint get.next <- Epi:::get.next chop.lex <- Epi:::chop.lex @ % The function \texttt{simLexis} takes a \texttt{Lexis} object as input. This defines the initial state(s) and times of the start for a number of persons. Since the purpose is to simulate a history through the estimated multistate model, the input values of the outcome variables \texttt{lex.Xst} and \texttt{lex.dur} are ignored --- the aim is to simulate values for them. Note however that the attribute \texttt{time.since} must be present in the object. This is used for initializing timescales defined as time since entry into a particular state, it is a character vector of the same length as the \texttt{time.scales} attribute, with value equal to a state name if the corresponding time scale is defined as time since entry into that state. In this example the 4th timescale is time since entry into the \texttt{Ins} state, and hence: <<>>= cbind( attr( ini, "time.scales" ), attr( ini, "time.since" ) ) @ % \texttt{Lexis} objects will have this attribute set for time scales created using \texttt{cutLexis}. The other necessary argument is a transition object \texttt{Tr}, which is a list of lists. The elements of the lists should be \texttt{glm} objects derived by fitting Poisson models to a \texttt{Lexis} object representing follow-up data in a multistate model. It is assumed (but not checked) that timescales enter in the model via the timescales of the \texttt{Lexis} object. Formally, there are no assumptions about how \texttt{lex.dur} enters in the model. Optional arguments are \texttt{t.range}, \texttt{n.int} or \texttt{time.pts}, specifying the times after entry at which the cumulative rates will be computed (the maximum of which will be taken as the censoring time), and \texttt{N} a scalar or numerical vector of the number of persons with a given initial state each record of the \texttt{init} object should represent. The central part of the functions uses a \texttt{do.call} / \texttt{lapply} / \texttt{split} construction to do simulations for different initial states. This is the construction in the middle that calls \texttt{simX}. \texttt{simLexis} also calls \texttt{get.next} which is further detailed below. <<>>= simLexis @ % \subsection{\texttt{simX}} \texttt{simX} is called by \texttt{simLexis} and simulates transition-times and -types for a set of patients assumed to be in the same state. It is called from \texttt{simLexis} with a data frame as argument, uses the state in \texttt{lex.Cst} to select the relevant component of \texttt{Tr} and compute predicted cumulative intensities for all states reachable from this state. Note that it is here the switch between \texttt{glm}, \texttt{coxph} and objects of class \texttt{function} is made. The dataset on which this prediction is done has \texttt{length(time.pts)} rows per person. <<>>= simX @ % As we see, \texttt{simX} calls \texttt{sim1} which simulates the transition for one person. \subsection{\texttt{sim1}} The predicted cumulative intensities are fed, person by person, to \texttt{sim1} --- again via a \texttt{do.call} / \texttt{lapply} / \texttt{split} construction --- and the resulting time and state is appended to the \texttt{nd} data frame. This way we have simulated \emph{one} transition (time and state) for each person: <<>>= sim1 @ % The \texttt{sim1} function uses \texttt{lint} to do linear interpolation. \subsection{\texttt{lint}} We do not use \texttt{approx} to do the linear interpolation, because this function does not do the right thing if the cumulative incidences (\texttt{ci}) are constant across a number of times. Therefore we have a custom made linear interpolator that does the interpolation exploiting the fact the the \texttt{ci} is non-decreasing and \texttt{tt} is strictly monotonously increasing: <<>>= lint @ \subsection{\texttt{get.next}} We must repeat the simulation operation on those that have a simulated entry to a transient state, and also make sure that any time scales defined as time since entry to one of these states be initialized to 0 before a call to \texttt{simX} is made for these persons. This accomplished by the function \texttt{get.next}: <<>>= get.next @ \subsection{\texttt{chop.lex}} The operation so far has censored individuals \texttt{max(time.pts)} after \emph{each} new entry to a transient state. In order to groom the output data we use \texttt{chop.lex} to censor all persons at the same designated time after \emph{initial} entry. <<>>= chop.lex @ \section{Probabilities from simulated \texttt{Lexis} objects} Once we have simulated a Lexis object we will of course want to use it for estimating probabilities, so basically we will want to enumerate the number of persons in each state at a pre-specified set of time points. \subsection{\texttt{nState}} Since we are dealing with multistate model with potentially multiple time scales, it is necessary to define the timescale (\texttt{time.scale}), the starting point on this timescale (\texttt{from}) and the points after this where we compute the number of occupants in each state, (\texttt{at}). <<>>= nState @ % \subsection{\texttt{pState}, \texttt{plot.pState} and \texttt{lines.pState}} In order to plot probabilities of state-occupancy it is useful to compute cumulative probabilities across states in any given order; this is done by the function \texttt{pState}, which returns a matrix of class \texttt{pState}: <<>>= pState @ % There is also a \texttt{plot} and \texttt{lines} method for the resulting \texttt{pState} objects: <<>>= plot.pState lines.pState @ % \bibliographystyle{plain} \begin{thebibliography}{1} \bibitem{Carstensen.2011a} B~Carstensen and M~Plummer. \newblock Using {L}exis objects for multi-state models in {R}. \newblock {\em Journal of Statistical Software}, 38(6):1--18, 1 2011. \bibitem{Iacobelli.2013} S~Iacobelli and B~Carstensen. \newblock {Multiple time scales in multi-state models}. \newblock {\em Stat Med}, 32(30):5315--5327, Dec 2013. \bibitem{Plummer.2011} M~Plummer and B~Carstensen. \newblock Lexis: An {R} class for epidemiological studies with long-term follow-up. \newblock {\em Journal of Statistical Software}, 38(5):1--12, 1 2011. \end{thebibliography} \addcontentsline{toc}{chapter}{References} \end{document} Epi/R/0000755000176200001440000000000014016520013011160 5ustar liggesusersEpi/R/N2Y.r0000644000176200001440000000425413245401062011765 0ustar liggesusersN2Y <- function( A, P, N, data=NULL, return.dfr=TRUE ) { # Make local versions of variables if a dataframe is supplied if( !is.null(data) ) { A <- if( !missing(A) ) eval( substitute(A), data, parent.frame() ) else data$A P <- if( !missing(P) ) eval( substitute(P), data, parent.frame() ) else data$P N <- if( !missing(N) ) eval( substitute(N), data, parent.frame() ) else data$N } # Derive the interval lengths from supplied data A.int <- unique( diff(sort(unique(A))) ) P.int <- unique( diff(sort(unique(P))) ) # Check if something is fishy if( length(A.int)!=1 ) stop( "Non-uniform age interval lengths:\n", A.int ) if( length(P.int)!=1 ) stop( "Non-uniform period interval lengths:\n", P.int ) if( A.int!=P.int ) stop( "Unequal age and period interval lengths:\n", "age: ", A.int, ", period: ", P.int ) # Put population prevalence data in a table Ntab <- xtabs( N ~ A + P ) # Devise a table for the risk times Ydim <- c(dimnames(Ntab),list(wh=c("lo","up"))) # Note: one less period category Ytab <- NArray( Ydim )[,-dim(Ntab)[2],] # How many age and period classes na <- nrow(Ytab) np <- ncol(Ytab) for(a in 1:na) for(p in 1:np) { if( a < na ) Ytab[a,p,"up"] <- Ntab[a ,p]/3 + Ntab[a+1,p+1]/6 if( a > 1 ) Ytab[a,p,"lo"] <- Ntab[a-1,p]/6 + Ntab[a ,p+1]/3 if( a == 1 ) Ytab[a,p,"lo"] <- Ntab[a ,p]/2 + Ntab[a ,p+1]/2 - Ytab[a,p,"up"] if( a ==na ) Ytab[a,p,"up"] <- Ntab[a ,p]/2 + Ntab[a ,p+1]/2 - Ytab[a,p,"lo"] } # Remember to multiply to get the follow-up time Ytab <- Ytab * A.int # Convert to a data frame if required (the default) if( return.dfr ) { ## If a dataframe is required as return value Ytab <- data.frame(expand.grid(dimnames(Ytab)), Y=c(Ytab)) ## Retrieve the numerical values of left endpoints of intervals Ytab$A <- as.numeric(as.character(Ytab$A)) Ytab$P <- as.numeric(as.character(Ytab$P)) ## Compute the correct midpoints from the supplied data Ytab$A <- Ytab$A + A.int * (1 + (Ytab$wh == "up"))/3 Ytab$P <- Ytab$P + P.int * (1 + (Ytab$wh == "lo"))/3 Ytab <- Ytab[, c("A","P","Y")] } Ytab } Epi/R/lexis.R0000644000176200001440000006342414015164716012455 0ustar liggesusersLexis <- function(entry, exit, duration, entry.status=0, exit.status=0, id, data, merge=TRUE, states, notes=TRUE, tol=.Machine$double.eps^0.5, keep.dropped=FALSE ) { nmissing <- missing(entry) + missing(exit) + missing(duration) if (nmissing > 2) stop("At least one of the arguments exit and duration must be supplied") only.exit <- missing( entry.status ) && !missing( exit.status ) ## If data argument is supplied, use it to evaluate arguments if (!missing(data)) { if (!missing(entry)) { entry <- eval(substitute(entry), data, parent.frame()) } if (!missing(exit)) { exit <- eval(substitute(exit), data, parent.frame()) } if (!missing(duration)) { duration <- eval(substitute(duration), data, parent.frame()) } entry.status <- eval(substitute(entry.status), data, parent.frame()) exit.status <- eval(substitute(exit.status), data, parent.frame()) if (!missing(id)) { id <- eval(substitute(id), data, parent.frame()) } if (merge) { data <- as.data.frame(data) } } ## Check for missing values in status variables wh.miss <- any(is.na(entry.status)) + 2*any(is.na(exit.status)) if ( wh.miss > 0 ) stop("Missing values in ", switch( wh.miss, "entry status", "exit status", "entry AND exit status" ) ) ## Adjust entry status mode according to exit status if( only.exit ) { if( is.logical( exit.status ) ) { entry.status <- FALSE if( notes ) cat("NOTE: entry.status has been set to FALSE for all.\n" ) } if( is.character( exit.status ) ) { exit.status <- factor( exit.status ) } if( is.factor( exit.status ) ) { entry.status <- factor( rep( levels(exit.status)[1], length(exit.status)), levels=levels(exit.status), labels=levels(exit.status) ) if( notes ) cat("NOTE: entry.status has been set to", paste( '"', levels(exit.status)[1], '"', sep='' ), "for all.\n" ) } if( is.numeric( exit.status ) ) { if( notes ) entry.status <- rep( 0, length( exit.status ) ) cat("NOTE: entry.status has been set to 0 for all.\n" ) } } ## Convert character states to factors if( is.character(entry.status) ) entry.status <- factor(entry.status) if( is.character( exit.status) ) exit.status <- factor( exit.status) ## Check compatibility of entry and exit status if (is.factor(entry.status) || is.factor(exit.status)) { if (is.factor(entry.status) && is.factor(exit.status)) { if (!identical(levels(entry.status),levels(exit.status))) { all.levels = union(levels(entry.status),levels(exit.status)) entry.status <- factor( entry.status, levels=all.levels ) exit.status <- factor( exit.status, levels=all.levels ) if( notes ) cat("Incompatible factor levels in entry.status and exit.status:\n", "both lex.Cst and lex.Xst now have levels:\n", all.levels, "\n") } } else { stop("Incompatible classes for entry and exit status") } } else { if (mode(entry.status) != mode(exit.status)) { stop("Incompatible mode for entry and exit status") } } ## If entry is missing and one of the others is given as a list of length ## one, entry is assumed to be 0 on this only timescale. if( nmissing==2 ) { if( !missing(exit) ) { if( length(exit)>1 ) stop("If 'entry' is omitted, only one timescale can be specified.") else { entry <- exit entry[[1]] <- 0*entry[[1]] if( notes ) cat( "NOTE: entry is assumed to be 0 on the",names(exit),"timescale.\n") } } else if( !missing(duration) ) { if( length(duration)>1 ) stop("If 'entry' is omitted, only one timescale can be specified") else { entry <- duration entry[[1]] <- 0*entry[[1]] if( notes ) cat( "NOTE: entry is assumed to be 0 on the",names(duration),"timescale.\n") } } else stop("Either exit or duration must be supplied.") } ## Coerce entry and exit lists to data frames if(!missing(entry)) { entry <- as.data.frame(entry) if (is.null(names(entry))) stop("entry times have no names") if (any(substr(names(entry),1,4) == "lex.")) stop("names starting with \"lex.\" cannot be used for time scales") } if(!missing(exit)) { exit <- as.data.frame(exit) if (is.null(names(exit))) stop("exit times have no names") if (any(substr(names(exit),1,4) == "lex.")) stop("names starting with \"lex.\" cannot be used for time scales") } if(!missing(duration)) { duration <- as.data.frame(duration) if (is.null(names(duration))) stop("duration have no names") if (any(substr(names(duration),1,4) == "lex.")) stop("names starting with \"lex.\" cannot be used for time scales") } if (missing(entry)) { ## Impute entry entry <- exit - duration } if (missing(duration)) { ## Impute duration full.time.scales <- intersect(names(entry), names(exit)) if (length(full.time.scales) == 0) { stop("Cannot calculate duration from entry and exit times") } duration <- exit[,full.time.scales[1]] - entry[,full.time.scales[1]] } if (missing(exit)) { all.time.scales <- names(entry) } else { ## We dont need the exit times but, if they are supplied, we must ## make sure they are consistent with the entry and duration. all.time.scales <- unique(c(names(entry), names(exit))) ## Fill in any missing entry times entry.missing <- setdiff(all.time.scales, names(entry)) if (length(entry.missing) > 0) { entry <- cbind(entry, exit[,entry.missing, drop=FALSE] - duration) } ## Check that duration is the same on all time scales dura <- exit - entry[,names(exit),drop=FALSE] if (missing(duration)) { duration <- dura[,1] #BxC# apply( dura, 1, mean, na.rm=TRUE ) # Allows for timescales with missing values } ok <- sapply(lapply(dura, all.equal, duration), isTRUE) # ok <- sapply(lapply(dura, all.equal, duration), # function(x) identical(FALSE,x) ) if (!all(ok)) { stop("Duration is not the same on all time scales") } } # Taken care of by the code that detects whether lex.du <= tol # ## Check that duration is positive # if (any(duration<0)) { # stop("Duration must be non-negative") # } ## Make sure id values - if supplied - are valid. Otherwise supply default id if (missing(id)) { id <- 1:nrow(entry) } else if (any(duplicated(id))) { ##Fixme: check for overlapping intervals ##stop("Duplicate values in id") } ## Return a data frame with the entry times, duration, and status ## variables Use the prefix "lex." for the names of reserved ## variables. if( is.data.frame( duration ) ) duration <- duration[,1] lex <- data.frame( entry, "lex.dur" = duration, "lex.Cst" = entry.status, "lex.Xst" = exit.status, "lex.id" = id ) #### Addition by BxC --- support for states as factors # Convert states to factors if states are given if( !missing( states ) ) #is.character( states ) ) { # This as.character-business is necessary because we cannot assume # that the values of states are 1,2, etc. st.lev <- sort( unique( as.character( c(lex$lex.Cst,lex$lex.Xst) ) ) ) lex$lex.Cst <- factor( as.character(lex$lex.Cst), levels=st.lev, labels=states ) lex$lex.Xst <- factor( as.character(lex$lex.Xst), levels=st.lev, labels=states ) } if (!missing(data) && merge) { duplicate.names <- intersect(names(lex), names(data)) if (length(duplicate.names) > 0) { stop( "Cannot merge data with duplicate names:", paste(duplicate.names,collapse=" ") ) } lex <- cbind(lex, data) } ## Drop rows with short or negative duration for consistency with splitLexis short.dur <- lex$lex.dur <= tol if ( any(short.dur) ) { if( notes ) cat("NOTE: Dropping ", sum(short.dur), " rows with duration of follow up < tol\n", if( keep.dropped ) " The dropped rows are in the attribute 'dropped'\n", if( keep.dropped ) " To see them type attr(Obj,'dropped'),\n", if( keep.dropped ) " to get rid of them type: attr(Obj,'dropped') <- NULL\n", if( keep.dropped ) " - where 'Obj' is the name of your Lexis object" ) lex <- subset(lex, !short.dur) if( keep.dropped ) attr(lex,"dropped") <- subset(data, short.dur) } ## Return Lexis object attr(lex,"time.scales") <- all.time.scales attr(lex,"time.since") <- rep( "", length(all.time.scales) ) breaks <- vector("list", length(all.time.scales)) names(breaks) <- all.time.scales attr(lex,"breaks") <- breaks class(lex) <- c("Lexis", class(lex)) return(lex) } is.Lexis <- function(x) { inherits(x, "Lexis") } check.time.scale <- function(lex, time.scale=NULL) { ## Utility function, returns the names of the time scales in a Lexis object ## lex - a Lexis object ## time.scale - a numeric or character vector. The function checks that ## these are valid time scales for the Lexis object. ## Return value is a character vector containing the names of the requested ## time scales all.names <- timeScales(lex) if (is.null(time.scale)) return(all.names) nscale <- length(time.scale) scale.names <- character(nscale) if (is.character(time.scale)) { for (i in 1:nscale) { if (is.null(lex[[time.scale[i]]])) stop(time.scale[i], " is not a valid time scale name") } } else if (is.numeric(time.scale)) { if (any(time.scale > length(all.names)) || any(time.scale < 1)) stop(time.scale, " not valid time scale column number(s)") time.scale <- all.names[time.scale] } else { stop("invalid type for time scale") } return(time.scale) } valid.times <- function(x, time.scale=1) { # A utility function that returns a data.frame / Lexis object with # rows with missing timescales removed x[complete.cases(x[,check.time.scale(x,time.scale)]),] } plot.Lexis.1D <- function(x, time.scale=1, breaks="lightgray", type="l", col="darkgray", xlim, ylim, xlab, ylab, ...) { ## x Lexis object ## time.scale name of time scale to plot if (length(time.scale) != 1) stop("Only one time scale allowed") x <- valid.times(x,time.scale) time.entry <- x[,time.scale] time.exit <- x[,time.scale] + x$lex.dur id <- x$lex.id if (missing(xlim)) xlim <- c(min(time.entry), max(time.exit)) if (missing(ylim)) ylim <- range(id) if (missing(xlab)) xlab <- time.scale if (missing(ylab)) ylab <- "id number" plot(time.entry, id, type="n", xlab=xlab, ylab=ylab, xlim=xlim, ylim=ylim, ...) if (type=="b" || type=="l") { segments(time.entry, id, time.exit, id, col=col, ...) } if (type=="b" || type=="p") { points(time.exit, id, col=col, ...) } ## Plot break points brk <- attr(x,"breaks")[[time.scale]] abline(v=brk, col=breaks, ...) } points.Lexis.1D <- function(x, time.scale, ...) { x <- valid.times(x,time.scale) time.exit <- x[,time.scale] + x$lex.dur points(time.exit, x$lex.id, ...) } lines.Lexis.1D <- function(x, time.scale, type="l", col="darkgray", breaks="lightgray", ...) { x <- valid.times(x,time.scale) time.entry <- x[,time.scale] time.exit <- x[,time.scale] + x$lex.dur id <- x$lex.id segments(time.entry, id, time.exit, id, col=col, ...) ## Plot break points brk <- attr(x,"breaks")[[time.scale]] abline(v=brk, col=breaks, ...) } plot.Lexis.2D <- function(x, time.scale, breaks="lightgray", type="l", col="darkgray", xlim, ylim, xlab, ylab, grid=FALSE, col.grid="lightgray", lty.grid=2, coh.grid=FALSE, ...) { if (length(time.scale) != 2) stop("Two time scales are required") x <- valid.times(x,time.scale) time.entry <- time.exit <- vector("list",2) for (i in 1:2) { time.entry[[i]] <- x[,time.scale[i]] time.exit[[i]] <- x[,time.scale[i]] + x$lex.dur } if (missing(xlim) && missing(ylim)) { ## If no axis limits are given, set the plotting region to be ## square, and adjust the axis limits to cover the same time interval. ## All life lines will then be at 45 degrees. opar <- par(pty="s") on.exit(par(opar)) min.times <- sapply(time.entry, min) max.times <- sapply(time.exit, max) xywidth <- max(max.times - min.times) xlim <- min.times[1] + c(0, xywidth) ylim <- min.times[2] + c(0, xywidth) } else if (missing(xlim)) { xlim <- c(min(time.entry[[1]]), max(time.exit[[1]])) } else if (missing(ylim)) { ylim <- c(min(time.entry[[2]]), max(time.exit[[2]])) } if (missing(xlab)) xlab <- time.scale[1] if (missing(ylab)) ylab <- time.scale[2] plot(time.entry[[1]], time.entry[[2]], type="n", xlab=xlab, ylab=ylab, xlim=xlim, ylim=ylim, ...) # Set up the background grid(s): if (!missing(grid)) { if (is.logical(grid)) { if (grid) { vgrid <- pretty(xlim) hgrid <- pretty(ylim) } } else if (is.list(grid)) { vgrid <- grid[[1]] hgrid <- grid[[length(grid)]] } else if (is.numeric(grid)) { vgrid <- grid - min( grid ) + min( pretty( xlim )[pretty(xlim)>=par("usr")[1]] ) hgrid <- grid - min( grid ) + min( pretty( ylim )[pretty(ylim)>=par("usr")[3]] ) } else stop( "'grid' must be either logical, list or a numeric vector" ) # and plot the grid: abline( v=vgrid, h=hgrid, col=col.grid, lty=lty.grid ) box() } if (!missing(grid) & coh.grid) { # Make the 45-degree grids as fine as the finest grid on the axes for (yy in c(hgrid-diff(range(hgrid)),hgrid)) abline( yy-min(vgrid), 1, col=col.grid, lty=lty.grid ) for (yy in c(vgrid-diff(range(vgrid)),vgrid)) abline( min(hgrid)-yy, 1, col=col.grid, lty=lty.grid ) } # End of explicitly requested background grid(s) (PHEW!) if (type=="b" || type=="l") { segments(time.entry[[1]], time.entry[[2]], time.exit[[1]], time.exit[[2]], col=col, ...) } if (type=="b" || type=="p") { points(time.exit[[1]], time.exit[[2]], col = col, ...) } if (type != "n") { ## Plot break points brk <- attr(x,"breaks")[time.scale] abline(v=brk[[1]], h=brk[[2]], col=breaks, ...) } } points.Lexis.2D <- function(x, time.scale, ...) { x <- valid.times(x,time.scale) time.exit <- vector("list",2) for (i in 1:2) { time.exit[[i]] <- x[,time.scale[i]] + x$lex.dur } points( time.exit[[1]], time.exit[[2]], ...) } lines.Lexis.2D <- function(x, time.scale, col="darkgray", ...) { x <- valid.times(x,time.scale) time.entry <- time.exit <- vector("list",2) for (i in 1:2) { time.entry[[i]] <- x[,time.scale[i]] time.exit[[i]] <- x[,time.scale[i]] + x$lex.dur } segments(time.entry[[1]], time.entry[[2]], time.exit[[1]], time.exit[[2]], col=col, ...) } ### Plotting generic functions plot.Lexis <- function( x = Lexis( entry=list(Date=1900,Age=0), exit=list(Age=0) ), time.scale=NULL, type="l", breaks="lightgray", ...) { time.scale <- check.time.scale(x, time.scale) if (length(time.scale) > 2) time.scale <- time.scale[1:2] # Save the timescale(s) for use in subsequent calls options( Lexis.time.scale = time.scale ) if (length(time.scale) == 1) plot.Lexis.1D(x, time.scale=time.scale, type=type, breaks=breaks, ...) else if (length(time.scale) == 2) plot.Lexis.2D(x, time.scale=time.scale, type=type, breaks=breaks, ...) } lines.Lexis <- function(x, time.scale=options()[["Lexis.time.scale"]], ...) { time.scale <- check.time.scale(x, time.scale) if (length(time.scale) > 2) time.scale <- time.scale[1:2] if (length(time.scale) == 1) lines.Lexis.1D(x, time.scale=time.scale, ...) else if (length(time.scale) == 2) lines.Lexis.2D(x, time.scale=time.scale, ...) } points.Lexis <- function(x, time.scale=options()[["Lexis.time.scale"]], ...) { time.scale <- check.time.scale(x, time.scale) if (length(time.scale) > 2) time.scale <- time.scale[1:2] if (length(time.scale) == 1) points.Lexis.1D(x, time.scale=time.scale, ...) else if (length(time.scale) == 2) points.Lexis.2D(x, time.scale=time.scale, ...) } PY.ann <- function (x, ...) UseMethod("PY.ann") PY.ann.Lexis <- function( x, time.scale=options()[["Lexis.time.scale"]], digits=1, ... ) { if( !inherits(x,"Lexis") ) stop( "Only meaningful for Lexis objects not for objects of class ", class(x) ) wh.x <- x[,time.scale[1]] + x[,"lex.dur"]/2 if( two.scales <- length(time.scale)==2 ) wh.y <- x[,time.scale[2]] + x[,"lex.dur"]/2 else wh.y <- x[,"lex.id"] text( wh.x, wh.y, formatC(x$lex.dur,format="f",digits=digits), adj=c(0.5,-0.5), srt=if(two.scales) 45 else 0, ... ) } ### Generic functions ### Methods for data.frame drop Lexis attributes, so we need Lexis ### methods that retain them subset.Lexis <- function(x, ... ) { y <- subset.data.frame(x, ...) attr(y,"breaks") <- attr(x, "breaks") attr(y,"time.scales") <- attr(x, "time.scales") attr(y,"time.since") <- attr(x, "time.since") return(y) } `[.Lexis` <- function(x, ...) { y <- NextMethod(x) if (is.data.frame(y)) { for (a in c("class", "time.scales", "time.since", "breaks")) { data.table::setattr(y ,a, attr(x, a))} } y } merge.Lexis <- function(x, y, id, by, ...) { if (!missing(id)) { if (!is.character(id) || length(id) != 1 || !(id %in% names(y))) { stop("id must be the name of a single variable in y") } if (any(duplicated(y[[id]]))) { stop("values of the id variable must be unique in y") } y$lex.id <- y[[id]] } else if (missing(by)) { by <- intersect(names(x), names(y)) if (length(by)==0) { stop("x and y have no variable names in common") } } z <- base::merge.data.frame(x, y, ...) attr(z,"breaks") <- attr(x, "breaks") attr(z,"time.scales") <- attr(x, "time.scales") attr(z,"time.since") <- attr(x, "time.since") class(z) <- c("Lexis", "data.frame") return(z) } cbind.Lexis <- function( ... ) { allargs <- list( ... ) # Check that at least one argument is Lexis is.lex <- sapply( allargs, inherits, "Lexis" ) if( all(!is.lex) ) stop( "At least one argument nust be a Lexis object\n", "and none of the given are.\n") if( sum(is.lex)>1 ) stop( "It is meaningless to 'cbind' several Lexis objects:", " arguments ", paste( which(is.lex), collapse=","), " are Lexis objects.\n" ) is.lex <- which(is.lex) res <- do.call( base::cbind.data.frame, allargs ) attr( res, "class" ) <- attr( allargs[[is.lex]], "class" ) attr( res, "breaks" ) <- attr( allargs[[is.lex]], "breaks" ) attr( res, "time.scales" ) <- attr( allargs[[is.lex]], "time.scales" ) attr( res, "time.since" ) <- attr( allargs[[is.lex]], "time.since" ) res } rbind.Lexis <- function( ... ) { # A list of all Lexis objects allargs <- list( ... ) # Check if they are all Lexis # (or possibly NULL - often rbind-ing with NULL is very useful) is.lex <- sapply( allargs, inherits, "Lexis" ) is.nul <- sapply( allargs, is.null ) if( !all(is.lex[!is.nul]) ) stop( "All arguments must be Lexis objects,\n", "arguments number ", which(!is.lex & !is.null), " are not." ) # Put them all together allargs <- allargs[!is.nul] res <- plyr::rbind.fill( allargs ) # Get the union of time.scale names and the corresponding time.since tscl <- do.call( c, lapply( allargs, function(x) attr(x,"time.scales") ) ) tsin <- do.call( c, lapply( allargs, function(x) attr(x,"time.since" ) ) ) # but only one copy of each scls <- match( unique(tscl), tscl ) tscl <- tscl[scls] tsin <- tsin[scls] # Fish out the breaks on timescale in turn from all input objects and # - if all the non-NULL are identical use this # - if not, set the corresponding break to NULL newbrks <- list() # all the breaks attributes in a list brks <- lapply( allargs, function(x) attr(x,"breaks") ) # run through the timescales found for( scl in tscl ) { # breaks for this timescale in any of the objects brk <- lapply( brks, function(x) x[[scl]] ) # but only the non-null ones brk <- brk[!sapply( brk, is.null )] # if more than one occurrence, all non-NULL breaks should be identical if( ( length(brk)>1 & all( sapply( brk[-1], function(x) identical(brk[[1]],x) ) ) ) | length(brk) == 1 ) newbrks[scl] <- brk[1] else newbrks[scl] <- list(NULL) } # define attributes of the reulting object: attr( res, "class" ) <- c( "Lexis", "data.frame" ) attr( res, "breaks" ) <- newbrks attr( res, "time.scales" ) <- tscl attr( res, "time.since" ) <- tsin res } ## Extractor functions entry <- function(x, time.scale = NULL, by.id = FALSE ) { time.scale <- check.time.scale(x, time.scale) wh <- x[,time.scale[1]] == ave( x[,time.scale[1]], x$lex.id, FUN=if( by.id ) min else I ) if (length(time.scale) > 1) { res <- as.matrix(x[wh, time.scale]) if( by.id ) rownames( res ) <- x$lex.id[wh] return( res ) } else { res <- x[wh, time.scale] if( by.id ) names( res ) <- x$lex.id[wh] return( res ) } } exit <- function(x, time.scale = NULL, by.id = FALSE ) { time.scale <- check.time.scale(x, time.scale) wh <- x[,time.scale[1]] == ave( x[,time.scale[1]], x$lex.id, FUN=if( by.id ) max else I ) if (length(time.scale) > 1) { res <- as.matrix(x[wh, time.scale]) + x$lex.dur[wh] if( by.id ) rownames( res ) <- x$lex.id[wh] return( res ) } else { res <- x[wh, time.scale] + x$lex.dur[wh] if( by.id ) names( res ) <- x$lex.id[wh] return( res ) } } dur <- function(x, by.id=FALSE) { if( by.id ) return( tapply(x$lex.dur,x$lex.id,sum) ) else return( x$lex.dur ) } status <- function(x, at="exit", by.id = FALSE) { at <- match.arg(at, c("entry","exit")) wh <- x[,timeScales(x)[1]] == ave( x[,timeScales(x)[1]], x$lex.id, FUN=if(by.id) switch(at, "entry"=min, "exit"=max) else I ) res <- switch(at, "entry"=x$lex.Cst, "exit"=x$lex.Xst)[wh] if( by.id ) names( res ) <- x$lex.id[wh] res } transient <- function( x ) { if( !is.Lexis(x) ) stop( "Not a Lexis object" ) tc <- tapply( x$lex.dur, x$lex.Cst, sum ) nt <- names( tc[tc>0] ) nt[!is.na(nt)] } absorbing <- function( x ) { if( !is.Lexis(x) ) stop( "Not a Lexis object" ) tc <- table( x$lex.Xst ) setdiff( names( tc[tc>0] ), transient(x) ) } updn <- function( x, tt, states ) { if( any(is.na(match(states,levels(x)))) ) stop( "'states' must be among states: ", paste(levels(x),sep=',') ) tt <- tt[,states,drop=FALSE] setdiff( rownames( tt[apply(tt,1,sum)>0,,drop=FALSE] ), states ) } before <- preceding <- function( x, states ) updn( x, table(x$lex.Cst,x$lex.Xst), states ) after <- succeeding <- function( x, states ) updn( x, table(x$lex.Xst,x$lex.Cst), states ) timeScales <- function(x) { return (attr(x,"time.scales")) } timeSince <- function(x) { tt <- attr(x,"time.since") names(tt) <- attr(x,"time.scales") return( tt ) } timeBand <- function(lex, time.scale, type="integer") { time.scale <- check.time.scale(lex, time.scale)[1] breaks <- attr(lex, "breaks")[[time.scale]] time1 <- lex[[time.scale]] band <- findInterval(time1, breaks) ##Check that right hand side of interval falls in the same band abrk <- c(breaks, Inf) tol <- sqrt(.Machine$double.eps) if (any(time1 + lex$lex.dur > abrk[band+1] + tol)) { stop("Intervals spanning multiple time bands in Lexis object") } type <- match.arg(type, choices = c("integer","factor","left","middle", "right")) if (type=="integer") { return(band) } I1 <- c(-Inf, breaks) I2 <- c(breaks, Inf) labels <- switch(type, "factor" = paste("(", I1, ",", I2, "]", sep=""), "left" = I1, "right" = I2, "middle" = (I1 + I2)/2) if(type=="factor") { return(factor(band, levels=0:length(breaks), labels=labels)) } else { return(labels[band+1]) } } breaks <- function(lex, time.scale) { time.scale <- check.time.scale(lex, time.scale)[1] return(attr(lex, "breaks")[[time.scale]]) } transform.Lexis <- function(`_data`, ... ) { save.at <- attributes(`_data`) ## We can't use NextMethod here because of the special scoping rules ## used by transform.data.frame y <- base::transform.data.frame(`_data`, ...) save.at[["names"]] <- attr(y, "names") attributes(y) <- save.at y } # Two utility functions used to sort a Lexis object by (lex.id,time) order.Lexis <- orderLexis <- function( x ) { # Some time scales may contain missing values # So find one with minimal NAs so we can sort on it if (!inherits(x, "Lexis")) stop("Argument must be a Lexis object\n") # Fixing things if a data.table attr(x, "class") <- c("Lexis", "data.frame") nNA <- apply(x[, timeScales(x), drop=FALSE], 2, function(x) sum(is.na(x))) a.ts <- timeScales(x)[which( nNA == min(nNA))[1]] order(x$lex.id, x[,a.ts], na.last = FALSE) } sortLexis <- function( x ) x[orderLexis(x),] Epi/R/xgrep.R0000644000176200001440000000036013100324421012425 0ustar liggesusersfgrep <- function( pattern, x, ... ) x [grep( pattern, x , ... )] ngrep <- function( pattern, x, ... ) names(x)[grep( pattern, names(x), ... )] lgrep <- function( pattern, x, ... ) levels(x)[grep( pattern, levels(x), ... )] Epi/R/plotCIF.R0000644000176200001440000000217713564775677012655 0ustar liggesusersplotCIF <- function (x, event = 1, xlab = "Time", ylab = "Cumulative incidence", ylim = c(0, 1), lty = 1, col = "black", ... ) { ng <- length(x$n) co <- rep(col, ng)[1:ng] lt <- rep(lty, ng)[1:ng] ne <- dim(x$pstate)[2] - 1 if (event %in% 1:ne) { time <- x$time gr <- rep(1, length(time)) if (ng > 1) for (g in 2:ng) for (t in (cumsum(x$strata)[g - 1] + 1):cumsum(x$strata)[g]) gr[t] <- g CI <- x$pstate[, 2] for (e in 1:ne) if (event == e) CI <- x$pstate[, e+1] plot(c(0, time[gr == 1], max(time[gr == 1])), c(0, CI[gr == 1], max(CI[gr == 1])), type = "s", ylim = ylim, xlab = xlab, ylab = ylab, col = co[1], lty = lt[1], ...) if (ng > 1) for (g in 2:ng) lines(c(0, time[gr == g], max(time[gr == g])), c(0, CI[gr == g], max(CI[gr == g])), type = "s", lty = lt[g], col = co[g], ...) } else print(paste("Error: event must be an integer from 1 to", ne)) } Epi/R/plotEst.R0000644000176200001440000000726312531361077012762 0ustar liggesusersget.ests <- function( ests, ... ) { # If a model object is supplied, extract the parameters and the # standard errors # if( inherits( ests, c("glm","coxph","clogistic","gnlm","survreg") ) ) ests <- ci.exp( ests, ... ) else if( inherits( ests, c("lm","gls","lme","nls","polr", "mer","MIresult","mipo") ) ) ests <- ci.lin( ests, ... )[,-(2:4)] ests } plotEst <- function( ests, y = dim(ests)[1]:1, txt = rownames(ests), txtpos = y, ylim = range(y)-c(0.5,0), xlab = "", xtic = nice( ests[!is.na(ests)], log=xlog ), xlim = range( xtic ), xlog = FALSE, pch = 16, cex = 1, lwd = 2, col = "black", col.txt = "black", font.txt = 1, col.lines = col, col.points = col, vref = NULL, grid = FALSE, col.grid = gray(0.9), restore.par = TRUE, ... ) { # Function to plot estimates from a model. # Assumes that ests is a p by 3 matrix with estimate, lo and hi as # columns OR a model object. # Extract the estimates if necessary # ests <- get.ests( ests, ... ) # Is it likley that we want a log-axis for the parameters? # mult <- inherits( ests, c("glm","coxph","gnlm") ) if( missing(xlog) ) xlog <- mult # Create an empty plot in order to access the dimension so that # sufficient place can be made for the text in the margin # plot.new() mx <- max( strwidth( txt, units="in" ) ) oldpar <- par( mai=par("mai") + c(0,mx,0,0) ) if( restore.par ) on.exit( par( oldpar ) ) # Set up the coordinate system witout advancing a frame # plot.window( xlim = xlim, ylim = ylim, log = ifelse( xlog, "x", "") ) # Draw a grid if requested # if( !is.logical( grid ) ) abline( v = grid, col = col.grid ) if( is.logical( grid ) & grid[1] ) abline( v = xtic, col = col.grid ) # Draw a vertical reference line # if( !missing( vref ) ) abline( v = vref ) # Draw the estimates with c.i. s # linesEst( ests, y, pch=pch, cex=cex, lwd=lwd, col.points=col.points, col.lines=col.lines ) # Finally the x-axis and the annotation of the estimates # axis( side=1, at=xtic ) mtext( side=1, xlab, line=par("mgp")[1], cex=par("cex")*par("cex.lab") ) axis( side=2, at=txtpos, labels=txt, las=1, lty=0, col.axis=col.txt ) invisible( oldpar ) } pointsEst <- linesEst <- function( ests, y = dim(ests)[1]:1, pch = 16, cex = 1, lwd = 2, col = "black", col.lines = col, col.points = col, ... ) { # Function to add estimates from a model to a drawing. # Assumes that ests is a p by 3 matrix with estimate, lo and hi as # columns. # Extract the estimates if necessary # ests <- get.ests( ests, ... ) # Cut the confidence interval lines to fit inside the plot # before drawing them. # xrng <- if( par("xlog") ) 10^par("usr")[1:2] else par("usr")[1:2] segments( pmax(ests[, 2],xrng[1]), y, pmin(ests[, 3], xrng[2]), y, lwd = lwd, col=col.lines ) # Then the point estimates on top of the lines. # points( ests[, 1], y, pch = pch, cex = cex, col=col.points ) invisible() } nice <- function( x, log = F, lpos = c(1,2,5), ... ) { # Function to produce nice labels also for log-axes. # if( log ) { fc <- floor( log10( min( x ) ) ):ceiling( log10( max( x ) ) ) tick <- as.vector( outer( lpos, 10^fc, "*" ) ) ft <- max( tick[tickmax(x)] ) tick <- tick[tick>=ft & tick<=lt] if( length( tick ) < 4 & missing( lpos ) ) tick <- nice( x, log=T, lpos=c(1:9) ) if( length( tick ) > 10 & missing( lpos ) ) tick <- nice( x, log=T, lpos=1 ) tick } else pretty( x, ... ) } Epi/R/Relevel.R0000644000176200001440000001157313763627513012735 0ustar liggesusers# The Relevel method Relevel <- function (x, ...) UseMethod("Relevel") # Utility to group a factor from a 2-column table; # called from Relevel if second argument is a matrix or table tRelevel <- function( ff, # factor to be grouped gg, # 2-column matrix or table with levels resp. grouping xlevels = TRUE, # include also grouped levels not present in ff nogroup = TRUE ) # levels of ff not grouped are tranferred (if FALSE set to NA) { if( any( wh <- ( apply( table( gg[,1], gg[,2] )>0, 1, sum )>1 ) ) ) stop( "\nFactor level", if(sum(wh)>1) "s", ": \n", paste(names(wh)[wh],collapse=" / "), "\nis grouped to more than one group.\n" ) if( any( is.na( match( unique(as.character(ff)), unique(as.character(gg[,1])) ) ) ) ) cat( "Note: Some values of factor not among levels grouped.\n" ) if( any( wh <- ( apply( table( gg[,1], gg[,2] ), 1, sum )>1 ) ) ) warning( "Factor level", if(sum(wh)>1) "s", ": ", paste(names(wh)[wh],collapse=" / "), "\nappear more than once in the table of groupings." ) # indices and names of the original factor levels ixff <- as.integer( ff ) chff <- as.character( ff ) # where they are in the translation table ixg1 <- as.integer( factor( gg[,1], levels=levels(ff) ) ) # indices of the new levels in the translation table ixg2 <- as.integer( g2 <- factor(gg[,2]) ) # remove unwanted NAs (levels in g[,1] not present in ff) ixg2 <- ixg2[!is.na(ixg1)] ixg1 <- ixg1[!is.na(ixg1)] # where in ixg2 are the integers ixff - match(), choose those values grff <- levels(g2)[ixg2[match(ixff,ixg1)]] # transfer non-grouped levels of ff if( nogroup ) grff[is.na(grff)] <- chff[is.na(grff)] # a factor with the correct levels in the correct order grff <- factor( grff, levels=union(levels(g2),levels(factor(grff))) ) # keep all levels from second column or not? if( xlevels ) grff else factor(grff) } # The factor method is the default method Relevel.default <- Relevel.factor <- function( x, ref, first = TRUE, collapse = "+", xlevels = TRUE, nogroup = TRUE, ... ) { # Function that collapses multiple sets of levels of a factor # # If ref is a 2-dim structure if( is.matrix( ref) | is.table( ref) | is.array( ref) | is.data.frame(ref) ) { if( length(dim(ref)) !=2 ) stop("ref must be 2-dimensional\n") if( dim(ref)[2] < 2 ) stop("ref must have at least 2 colums\n") return( tRelevel( x, ref, xlevels, nogroup ) ) } else { # Otherwise use the old version # if( !is.factor(x) ) { argnam <- deparse( substitute(x) ) f <- factor( x ) cat( "WARNING: ", argnam, "has been converted to a factor with levels:\n", levels( f ) ) } else f <- x # This is a copy of the relevel function from the base package: # relev <- function (x, ref, ...) { lev <- levels(x) if ( is.character( ref ) ) ref <- match(ref, lev) if ( any( is.na( ref ) ) ) stop( "any values in ref must be an existing level\n" ) nlev <- length( lev ) if ( any( ref < 1 ) || any( ref > nlev ) ) stop( paste( "ref=", paste( ref, collapse="," ), ": All elements must be in 1:", nlev, sep="" ) ) factor(x, levels = lev[c(ref, seq(along = lev)[-ref])]) } # If called with a non-list argument assume reshuffling of levels # if( !is.list( ref ) ) fnew <- relev( f, ref ) # If called with a list collapse levels in each list element. # if( is.list( ref ) ) { fnew <- f newnames <- levels( f ) uninames <- character( length( ref ) ) for( s in 1:length(ref) ) if ( is.character( ref[[s]] ) ) ref[[s]] <- match( ref[[s]], levels(f) ) # Check for replicates in levels to be grouped if( any( (tt<-table(unlist(ref))) > 1 ) ) stop("Factor level(s) ", levels( f )[as.numeric(names(tt)[tt>1])], " has been allocated to more than one new level.") for( s in 1:length(ref) ) { uninames[s] <- if( is.null( names( ref ) ) ) { paste( levels( f )[ref[[s]]], collapse=collapse ) } else if( names( ref )[s]=="" ) { paste( levels( f )[ref[[s]]], collapse=collapse ) } else names( ref )[s] newnames[ref[[s]]] <- rep( uninames[s], length( ref[[s]] ) ) } levels( fnew ) <- newnames if( !is.null( first ) ) { if( !first ) fnew <- factor( fnew, c( levels( f )[-unlist( ref )], uninames ) ) if( first ) fnew <- factor( fnew, c( uninames, levels( f )[-unlist( ref )] ) ) } } # This is in order to merge levels with identical names # return( factor( fnew, levels=levels(fnew) ) ) } } Epi/R/mh.R0000644000176200001440000001034512531361077011727 0ustar liggesusers# Mantel-Haenszel estimate and test mh <- function(cases, denom, compare = 1, levels = c(1, 2), by = NULL, cohort = !is.integer(denom), confidence = 0.9) { ndim <- length(dim(cases)) edgin <- names(dimnames(cases)) edgen <- paste("Dimension", 1:ndim) if (is.null(edgin)) edges <- edgen else edges <- ifelse(edgin == "", edgen, edgin) if (is.null(edges)) edges <- rep("", ndim) if(length(dim(denom)) != ndim) { stop("Cases and Pyrs arrays of unequal dimension") } if(is.numeric(compare)) { comp <- as.integer(compare) if(comp < 1 || comp > ndim) { stop("Illegal argument: compare") } } else { comp <- (1:ndim)[edges == compare] if(length(comp) != 1) { stop("Illegal argument: compare") } } if(!is.null(by)) { if (!is.numeric(by)) { mtch <- match(by, edges) if (any(is.na(mtch))) { stop("Illegal argument: by") } by <- (1:ndim)[mtch] } if (any(by < 1 | by > ndim | by == comp)) { stop("Illegal argument: by") } } gtxt <- vector("character", 3) gtxt[1] <- edges[comp] gtxt[2] <- dimnames(cases)[[comp]][levels[1]] gtxt[3] <- dimnames(cases)[[comp]][levels[2]] ctxt <- edges[-c(comp, by)] if (length(ctxt) == 0) ctxt <- as.null() others <- (1:ndim)[ - comp] select <- function(a, el) { b <- a[el] ifelse(is.na(b), 0, b) } d1 <- apply(cases, others, select, el = levels[1]) d2 <- apply(cases, others, select, el = levels[2]) if(length(d1) == 0 || length(d2) == 0) { stop("Illegal argument: levels") } y1 <- apply(denom, others, select, el = levels[1]) y2 <- apply(denom, others, select, el = levels[2]) d <- d1 + d2 y <- y1 + y2 if (cohort) { qt <- ifelse(y>0, (d1 * y2)/y, 0) rt <- ifelse(y>0, (d2 * y1)/y, 0) ut <- ifelse(y>0, d1 - ((d * y1)/y), 0) vt <- ifelse(y>0, (d * y1 * y2)/(y^2), 0) } else { s1 <- d1 + y1 s2 <- d2 + y2 t <- s1 + s2 qt <- ifelse(t>1, (d1 * y2)/t, 0) rt <- ifelse(t>1, (d2 * y1)/t, 0) ut <- ifelse(t>1, d1 - ((d * s1)/t), 0) vt <- ifelse(t>1, (d * y * s1 * s2)/((t - 1) * (t^2)), 0) } if(!is.null(by)) { if(length(by) < ndim - 1) { nby <- match(by, others) q <- apply(qt, nby, sum) r <- apply(rt, nby, sum) u <- apply(ut, nby, sum) v <- apply(vt, nby, sum) } else { q <- qt r <- rt u <- ut v <- vt } } else { q <- sum(qt) r <- sum(rt) u <- sum(ut) v <- sum(vt) } rr <- q/r se <- sqrt(v/(q * r)) ch <- (u^2)/v ef <- exp( - qnorm((1 - confidence)/2) * se) if (cohort) ty <- "Rate ratio" else ty <- "Odds ratio" res <- list(groups = gtxt, control = ctxt, type=ty, q=q, r=r, u=u, v=v, ratio = rr, se.log.ratio = se, cl.lower = rr/ef, cl.upper = rr * ef, chisq = ch, p.value = 1 - pchisq( ch, 1)) class(res) <- "mh" res } print.mh <- function(m) { cat("\n") if (!is.null(m$control)) cat("\nMantel-Haenszel comparison for: ") else cat("Comparison for: ") cat(m$groups[1], " (", m$groups[2], "versus", m$groups[3], ")\n") if (!is.null(m$control)) cat("controlled for:", m$control, "\n") cols <- c(m$type, "CL (lower)", "CL (upper)", "Chisq (1 df)", "p-value") nr <- length(m$ratio) if (is.array(m$ratio)) { dnt <- dimnames(m$ratio) size <- dim(m$ratio) nw <- length(dnt) } else { rn <- names(m$ratio) if (length(rn) > 1) dnt <- list(names(m$ratio)) else dnt <- list("") size <- nr nw <- 1 } dno <- vector("list", nw+1) so <- vector("numeric", nw+1) dno[[1]] <- dnt[[1]] dno[[2]] <- cols so[1] <- size[1] so[2] <- 5 if (nw > 1) for (i in 2:nw) { dno[[i+1]] <- dnt[[i]] so[i+1] <- size[i] } s1 <- size[1] tab <- cbind(m$ratio, m$cl.lower, m$cl.upper, m$chisq, m$p.value) # as.matrix(m$ratio, nrow=s1), # as.matrix(m$cl.lower, nrow=s1), # as.matrix(m$cl.upper, nrow=s1), # as.matrix(m$chisq, nrow=s1), # as.matrix(m$p.value, nrow=s1) ) print(array(tab, dim=so, dimnames=dno)) if (nr > 1) { Q <- sum(m$q) R <- sum(m$r) cat("\nOverall Mantel-Haenszel estimate of", m$type, ":", format(Q/R)) h <- sum(((m$q*R-m$r*Q)^2)/m$v)/(Q*R) df <- sum(m$v>0)-1 cat("\nChi-squared test of heterogeneity:", format(h), "(",df," df), p =", format(1-pchisq(h, df)), "\n") } cat("\n") } # Power calculations mh.power <- function(mh, ratio, alpha=0.05) { n.se <- log(ratio)/mh$se.log.ratio pnorm(n.se - qnorm(1-alpha/2)) } Epi/R/mcutLexis.R0000644000176200001440000001333513761777063013316 0ustar liggesusersmcutLexis <- function( L0, # A Lexis object timescale = 1, # the time scale referred to by L0[,wh] wh, # indices/names of columns witha dates of state entries (events) new.states = NULL, # Names of the event types (states) precursor.states = transient(L0), # NULL, seq.states = TRUE, # Should state names reflect ordering of events new.scales = NULL, # Time-scales referring to time since ties.resolve = FALSE # Are tied event times accepted? ) { ### we rely on referring to the timescale and event time variables by name if( is.numeric(timescale) ) timescale <- timeScales(L0)[timescale] if( is.numeric(wh) ) wh <- names(L0)[wh] ### don't be silly if( length(wh)==1 ) # return( docut( L0, osv ) ) # old cutLexis should be absorbed here stop( "mcutLexis not needed for one type of event - use cutLexis\n" ) ### states if( is.null(new.states) ) { new.states <- wh cat( "NOTE: Name of new states set to\n", new.states ) } if( length(wh) != length(new.states) ) stop( "wh and new.states must have same length, but lengths are", "wh:", length(wh), "and new.states:", length(new.states), "\n" ) ### precursor state if(missing(precursor.states)) cat("NOTE: Precursor states set to", precursor.states, "\n") ### timescales # either all or none if( is.logical(new.scales) ) if( any( new.scales ) ) { new.scales <- paste( "tf", new.states, sep="" ) cat( "NOTE: new.scales set to: ", new.scales, "\n" ) } if( is.character(new.scales) & length(new.scales) != length(wh) ) { new.scales <- paste( "tf", new.states, sep="" ) warning( "new.scales not of same length as wh. Set to: ", new.scales, "\n" ) } if( is.character(new.scales) & length(intersect(new.scales,timeScales(L0))) ) stop( "Names of new time scales must be different from names of existing timescales:\n", timeScales(L0) ) ### Tied transition times untied has.ties <- any( wh.tied <- apply( L0[,wh], 1, function(x) any(diff(sort(x[!is.na(x)]))==0) ) ) if( has.ties & is.logical(ties.resolve) & !ties.resolve ) stop( "Tied event times not allowed with ties.resolve=FALSE:\n", "there were", length(wh.tied), "records with tied event times.") if( has.ties & is.logical(ties.resolve) & ties.resolve ) ties.resolve <- 1/100 if( has.ties & is.numeric(ties.resolve) ) { rnd <- L0[wh.tied,wh]*0 rnd[,] <- runif(rnd,-1,1) * ties.resolve L0[wh.tied,wh] <- L0[wh.tied,wh] + rnd cat("NOTE:", sum(wh.tied), "records with tied events times resolved (adding", ties.resolve, "random uniform),\n", " so results are only", "reproducible if the random number seed was set.\n") } # End of checks # The object to return initiated as NULL Lcut <- NULL # Utility function returning sequences of ocurrences as paste of numbers NAorder <- function (x) { oo <- order(x, na.last = T) on <- (1:length(oo))[oo] on[is.na(x[oo])] <- NA paste(on[!is.na(on)], collapse = "-") } # where do the different sequences of events actually occur in data L0$whseq <- apply( L0[,wh], 1, NAorder ) # Loop through the actually occurring orders of event occurrences for( sq in unique(L0$whseq) ) { # Persons with none of the events occurring transferred to result if( sq=="" ) Lcut <- rbind( Lcut, L0[L0$whseq=="",] ) else { # Extract the subset of persons with a given sequence of events Ltmp <- L0[L0$whseq==sq,] # The numerical sequence of states (refer to the elements of wh) ost <- as.numeric( strsplit( sq, "-" )[[1]] ) nxst <- "" prst <- precursor.states for( cs in ost ) { nxst <- ifelse( cs==ost[1], new.states[cs], paste( nxst, new.states[cs], sep="-" ) ) Ltmp <- cutLexis( Ltmp, cut = Ltmp[,wh[cs]], timescale = timescale, new.state = nxst, precursor.states = prst ) # include the created state among the precursor states for next cut prst <- c(prst,nxst) } # end of for loop through events in this sequence (cs) # Attach it to the end of the Lexis object Lcut <- rbind( Lcut, Ltmp ) } # end of the else clause } # end of for loop through sequences (sq) # Do we want the sequences, the unordered set of previous events or # just the current one: old.seq <- seq.states if( is.logical(seq.states) ) seq.states <- ifelse( seq.states, "s", "u" ) if( is.character(seq.states) ) seq.states <- tolower( substr(seq.states,1,1) ) if( !(seq.states %in% c("s","o","u","l","c")) ) stop( "What do you mean by seq.states=", old.seq, "? - it should abbreviate to one of s, o, u, l or c \n") # Unordered or last (current) states if( seq.states %in% c("u","l","c") ) { # Each list element is a vector of states visited slvl <- strsplit( levels( Lcut ), "-" ) # merge those that have the same elements or take the last rlvl <- if( seq.states=="u" ) { sapply( lapply( slvl, sort ), paste, collapse="+" ) } else sapply( slvl, function(x) x[length(x)] ) # Relevel the states levels( Lcut$lex.Cst ) <- levels( Lcut$lex.Xst ) <- rlvl } # Did we ask for timescales as time since events? if( !is.null(new.scales) ) { # insert columns for the new time scales Lcut <- Lcut[,c(rep("whseq",length(new.scales)),names(Lcut))] names( Lcut )[1:length(new.scales)] <- new.scales for( i in 1:length(wh) ) Lcut[,i] <- ifelse( Lcut[,timescale] - Lcut[,wh[i]] < 0, NA, Lcut[,timescale] - Lcut[,wh[i]] ) # set attributes attr( Lcut, "time.scales" ) <- c( attr( Lcut, "time.scales" ), new.scales ) attr( Lcut, "time.since" ) <- c( attr( Lcut, "time.since" ), new.states ) } # return the cut object without the auxilary variable rmcol <- grep( "whseq", names(Lcut) ) Lcut[,-rmcol] } Epi/R/NArray.R0000644000176200001440000000146212531361077012517 0ustar liggesusersNArray <- function( x, cells=NA ) { if( !is.list(x) ) stop("Argument must be a (named) list." ) array( cells, dimnames=x, dim=sapply( x, length ) ) } ZArray <- function( x, cells=0 ) NArray( x, cells=cells ) larray <- function( data=NA, dim, dimnames ) { if( is.list(data) ) return( array(data=NA,dim=sapply(data,length), dimnames=data) ) else if( is.list(dim) ) return( array(data=data,dim=sapply(dim,length), dimnames=dim) ) else if( is.list(dimnames) ) return( array(data=data,dim=sapply(dimnames,length), dimnames=dimnames) ) else if( !missing(dimnames) ) return( array(data=data,dim=length(data), dimnames=dimnames) ) else return( array(data=data,dim=length(data)) ) } Epi/R/stattable.R0000644000176200001440000003440412531361077013310 0ustar liggesusersstat.table <- function(index, contents=count(), data, margins=FALSE) { ## Get names of indices, using either user-supplied names, or by ## deparsing. Some of this code is stolen from the list.names() ## function in table() index.sub <- substitute(index) index <- if (missing(data)) eval(index) else eval(index.sub, data) deparse.name <- function(x) if(is.symbol(x)) as.character(x) else "" if (is.list(index)) { if (is.call(index.sub)) { ## List constructed in the call to stat.table index.names <- names(index.sub) fixup <- if (is.null(index.names)) seq(along = index.sub) else index.names == "" dep <- sapply(index.sub[fixup], deparse.name) if (is.null(index.names)) index.labels <- dep else { index.labels <- index.names index.labels[fixup] <- dep } index.labels <- index.labels[-1] } else { ## List constructed outside the call to stat.table index.labels <- if (!is.null(names(index))) { names(index) } else { rep("", length(index)) } } } else { ## A single vector index.labels <- deparse.name(index.sub) } ## Coerce index to list of factors if (!is.list(index)) index <- list(index) index <- lapply(index, as.factor) ## Coerce contents to an expression representing a list of function calls contents <- substitute(contents) if (!identical(deparse(contents[[1]]), "list")) { contents <- call("list", contents) } ## Check that functions in the contents list are valid valid.functions <- c("count","mean","weighted.mean","sum","quantile", "median","IQR","max","min","ratio","percent","sd") table.fun <- character(length(contents) - 1) for (i in 2:length(contents)) { if (!is.call(contents[[i]])) stop("contents must be a list of function calls") FUN <- deparse(contents[[i]][[1]]) if (!FUN %in% valid.functions) stop(paste("Function",FUN,"not permitted in stat.table")) else table.fun[i-1] <- FUN } ## Label the contents by default with the function call ## But if user has supplied a label use that instead. stat.labels <- sapply(contents, deparse)[-1] content.names <- names(contents) if (!is.null(content.names)) { for (i in 2:length(content.names)) { if (nchar(content.names[i]) > 0) stat.labels[i-1] <- content.names[i] } } ##Define the allowed tabulation functions count <- function(id){ if (missing(id)) { id <- seq(along=index[[1]]) } y <- tapply(id, INDEX=subindex, FUN=function(x) length(unique(x))) y[is.na(y)] <- 0 return(y) } mean <- function(x, trim=0, na.rm=TRUE) { tapply(x, INDEX=subindex, FUN = base::mean, trim=trim, na.rm=na.rm) } weighted.mean <- function(x,w,na.rm=TRUE) { tapply(x, INDEX=subindex, FUN=stats::weighted.mean, w=w, na.rm=na.rm) } sum <- function(...,na.rm=TRUE) { tapply(..., INDEX=subindex, FUN = base::sum, na.rm=na.rm) } quantile <- function(x, probs, na.rm=TRUE,names=TRUE,type=7,...) { if (length(probs) > 1) stop("The quantile function only accepts scalar prob values within stat.table") tapply(x, INDEX=subindex, FUN = stats::quantile, probs=probs, na.rm=na.rm,names=names,type=type,...) } median <- function(x, na.rm=TRUE) { tapply(x, INDEX=subindex, FUN = stats::median, na.rm=na.rm) } IQR <- function(x, na.rm=TRUE) { tapply(x, INDEX=subindex, FUN= stats::IQR, na.rm=na.rm) } max <- function(..., na.rm=TRUE) { tapply(..., INDEX=subindex, FUN = base::max, na.rm=na.rm) } min <- function(..., na.rm=TRUE) { tapply(..., INDEX=subindex, FUN = base::min, na.rm=na.rm) } ratio <- function(d,y,scale=1, na.rm=TRUE) { if (length(scale) != 1) stop("Scale parameter must be a scalar") if (na.rm) { w <- (!is.na(d) & !is.na(y)) tab1 <- tapply(d*w, INDEX=subindex, FUN=base::sum, na.rm=TRUE) tab2 <- tapply(y*w, INDEX=subindex, FUN=base::sum, na.rm=TRUE) } else { tab1 <- tapply(d, INDEX=subindex, FUN=base::sum, na.rm=FALSE) tab2 <- tapply(y, INDEX=subindex, FUN=base::sum, na.rm=FALSE) } return(scale*tab1/tab2) } percent <- function(...) { x <- list(...) if (length(x) == 0) stop("No variables to calculate percent") x <- lapply(x, as.factor) n <- count() ## Work out which indices to sweep out sweep.index <- logical(length(subindex)) for (i in seq(along=subindex)) { sweep.index[i] <- !any(sapply(x,identical,subindex[[i]])) } if (!any(sweep.index)) { return(100*n/base::sum(n, na.rm=TRUE)) } else { margin <- apply(n,which(sweep.index),base::sum, na.rm=TRUE) margin[margin==0] <- NA return(100*sweep(n, which(sweep.index), margin,"/")) } } sd <- function (..., na.rm = TRUE) { tapply(..., INDEX=subindex, FUN = stats::sd, na.rm=na.rm) } ##Calculate dimension of the main table, excluding margins n.dim <- length(index) tab.dim <- sapply(index, nlevels) ##Sort out margins if (length(margins) == 1) margins <- rep(margins, n.dim) else if(length(margins) != n.dim) stop("Incorrect length for margins argument") ##Create grid of all possible subtables. fac.list <- vector("list", n.dim) for (i in 1:n.dim) { fac.list[[i]] <- if (margins[i]) c(0,1) else 1 } subtable.grid <- as.matrix(expand.grid(fac.list)) ##Fill in the subtables ans.dim <- c(length(contents)-1, tab.dim + margins) ans <- numeric(prod(ans.dim)) for (i in 1:nrow(subtable.grid)) { ##in.subtable is a logical vector indicating which dimensions are ##in the subtable (i.e. which have not been marginalized out) in.subtable <- as.logical(subtable.grid[i,]) llim <- rep(1,n.dim) + ifelse(in.subtable,rep(0,n.dim),tab.dim) ulim <- tab.dim + ifelse(in.subtable,rep(0,n.dim),rep(1, n.dim)) subindex <- index[in.subtable] if (length(subindex) == 0) { ## Marginalizing out all dimensions subindex <- list(rep(1, length(index[[1]]))) } subtable.list <- if(missing(data)) ##eval(contents, parent.frame()) eval(contents) else eval(as.expression(contents), data) for (j in 1:length(subtable.list)) { ans[array.subset(ans.dim,c(j,llim),c(j,ulim))] <- subtable.list[[j]] } } ans <- array(ans, dim=ans.dim) ans.dimnames <- lapply(index, levels) names(ans.dimnames) <- index.labels for (i in 1:length(index)) { if (margins[i]) ans.dimnames[[i]] <- c(ans.dimnames[[i]], "Total") } dimnames(ans) <- c(list("contents"=stat.labels), ans.dimnames) attr(ans, "table.fun") <- table.fun class(ans) <- c("stat.table", class(ans)) return(ans) } array.subset <- function(dim,lower,upper) { ##Returns a logical array of dimension dim for which elements in the range ##[lower[1]:upper[1], lower[2]:upper[2],...] are TRUE and others FALSE ##Check validity of arguments (but assume everything is an integer) ndim <- length(dim) if (length(lower) != ndim || length(upper) != ndim) { stop("Length of lower and upper limits must match dimension") } if (any(lower > upper) || any(lower < 1) || any(upper > dim)) { stop("Invalid limits") } ##The math is easier if we index arrays from 0 rather than 1 lower <- lower - 1 upper <- upper - 1 N <- prod(dim) ans <- rep(TRUE, N) for (i in 1:N) { l <- i - 1 for (d in 1:ndim) { k <- l %% dim[d] #k is the index of the ith element in dimension d if (k < lower[d] || k > upper[d]) { ans[i] <- FALSE break } l <- l %/% dim[d] } } return(array(ans, dim)) } split.to.width <- function(x,width) { ## Splits a string into a vector so that each element has at most width ## characters. If width is smaller than the length of the shortest word ## then the latter is used instead x.split <- strsplit(x,split=" ")[[1]] width <- max(c(width,nchar(x.split))) y <- character(0) imin <- 1 n <- length(x.split) for (i in 1:n) { cum.width <- if(i==n) { Inf } else { sum(nchar(x.split[imin:(i+1)])) + (i - imin + 1) } if (cum.width > width) { y <- c(y,paste(x.split[imin:i], collapse=" ")) imin <- i + 1 } } return(y) } pretty.print.stattable.1d <- function(x, width, digits) { ##Pretty printing of 1-D stat.table if (length(dim(x)) != 2) stop("Cannot print stat.table") ncol <- nrow(x) col.width <- numeric(ncol+1) col.header <- vector("list",ncol+1) n.header <- integer(ncol+1) print.list <- vector("list",ncol+1) ##First column col.header[[1]] <- split.to.width(names(dimnames(x))[2], width) n.header[1] <- length(col.header[[1]]) col1 <- format(c(col.header[[1]],dimnames(x)[[2]]), justify="left") col.header[[1]] <- col1[1:n.header[1]] print.list[[1]] <- col1[-(1:n.header[1])] col.width[1] <- nchar(col.header[[1]][1]) ##Other columns for (i in 2:(ncol+1)) { col.header[[i]] <- split.to.width(dimnames(x)[[1]][i-1], width) n.header[i] <- length(col.header[[i]]) this.col <- formatC(x[i-1,],width=width, digits=digits[attr(x,"table.fun")[i-1]], "f") this.col <- format(c(col.header[[i]],this.col),justify="right") col.width[i] <- nchar(this.col[1]) col.header[[i]] <- this.col[1:n.header[i]] print.list[[i]] <- this.col[-(1:n.header[i])] } ## table.width <- sum(col.width) + ncol + 3 max.n.header <- max(n.header) cat(" ",rep("-",table.width)," \n",sep="") for(i in 1:max.n.header) { cat(" ") for(j in 1:length(print.list)) { if (i <= n.header[j]) { cat(col.header[[j]][i]) } else { cat(rep(" ", col.width[[j]]),sep="") } if (j==1) cat(" ") else cat(" ") } cat(" \n") } cat(" ",rep("-",table.width)," \n",sep="") for (i in 1:length(print.list[[1]])) { cat(" ") if (pmatch("Total",print.list[[1]][i],nomatch=0)) { ##Add a blank line before the total cat(rep(" ",col.width[1]+1)," ",rep(" ",sum(col.width[-1])+ncol), " \n ",sep="") } for (j in 1:length(print.list)) { cat(print.list[[j]][i]) if (j == 1) { cat(" " ) } else { cat(" ") } } cat(" \n") } cat(" ",rep("-",table.width)," \n",sep="") return(invisible(x)) } pretty.print.stattable.2d <- function(x, width, digits) { ##Pretty printing of 2-Dimensional stat.table if (length(dim(x)) != 3) stop("Cannot print stat.table") nstat <- dim(x)[1] ncol <- dim(x)[3] nrow <- dim(x)[2] col.width <- numeric(ncol+1) col.header <- vector("list",ncol+1) n.header <- integer(ncol+1) print.list <- vector("list",ncol+1) ##First column col.header[[1]] <- split.to.width(names(dimnames(x))[2], width) n.header[1] <- length(col.header[[1]]) col1 <- format(c(col.header[[1]],dimnames(x)[[2]]), justify="left") col.header[[1]] <- col1[1:n.header[1]] print.list[[1]] <- col1[-(1:n.header[1])] col.width[1] <- nchar(col.header[[1]][1]) ##Other columns for (i in 2:(ncol+1)) { col.header[[i]] <- split.to.width(dimnames(x)[[3]][i-1], width) n.header[i] <- length(col.header[[i]]) this.col <- matrix("", nrow=nstat,ncol=nrow) for (j in 1:nstat) { z <- x[j,,i-1] this.col[j,] <- formatC(z, width=width, format="f", digits=digits[attr(x,"table.fun")[j]]) ## this.col[j,] <- formatC(z, width=width, digits=digits, ## format=ifelse(identical(round(z),z),"d","f")) } this.col <- format(c(col.header[[i]],this.col),justify="right") col.width[i] <- nchar(this.col[1]) col.header[[i]] <- this.col[1:n.header[i]] print.list[[i]] <- this.col[-(1:n.header[i])] } ##Correct first column for multiple stats if (nstat > 1) { pl1 <- print.list[[1]] print.list[[1]] <- rep(paste(rep(" ",col.width[1]),collapse=""),nstat*nrow) print.list[[1]][1 + nstat*((1:nrow)-1)] <- pl1 } table.width <- sum(col.width) + ncol + 3 max.n.header <- max(n.header) cat(" ",rep("-",table.width)," \n",sep="") ## Supercolumn header super.header <- names(dimnames(x))[3] npad <- sum(col.width[-1]) + ncol + 1 - nchar(super.header) if (npad >= 0) { cat(" ",rep(" ",col.width[1])," ",sep="") cat(rep("-",floor(npad/2)),sep="") cat(super.header) cat(rep("-",ceiling(npad/2))," \n",sep="") } ## Headers for(i in 1:max.n.header) { cat(" ") for(j in 1:length(print.list)) { if (i <= n.header[j]) { cat(col.header[[j]][i]) } else { cat(rep(" ", col.width[[j]]),sep="") } if (j==1) cat(" ") else cat(" ") } cat(" \n") } cat(" ",rep("-",table.width)," \n",sep="") ## Body of table blank.line <- function() { cat(" ",rep(" ",col.width[1]+1)," ",rep(" ",sum(col.width[-1])+ncol), " \n",sep="") } for (i in 1:length(print.list[[1]])) { if (pmatch("Total",print.list[[1]][i],nomatch=0)) { ##Add a blank line before the total blank.line() } cat(" ") for (j in 1:length(print.list)) { cat(print.list[[j]][i]) if (j == 1) { cat(" " ) } else { cat(" ") } } cat(" \n") if (nstat > 1 && i %% nstat == 0 && i != length(print.list[[1]])) { ##Separate interleaved stats blank.line() } } cat(" ",rep("-",table.width)," \n",sep="") return(invisible(x)) } print.stat.table <- function(x, width=7,digits,...) { fun.digits <- c("count"=0,"mean"=2,"weighted.mean"=2,"sum"=2,"quantile"=2, "median"=2,"IQR"=2,"max"=2,"min"=2,"ratio"=2,"percent"=1, "sd"=2) if (!missing(digits)) { if (is.null(names(digits))) { if (length(digits) > 1) stop("digits must be a scalar or named vector") else fun.digits[1:length(fun.digits)] <- digits } else { fun.digits[names(digits)] <- digits } } if (length(dim(x)) == 2) pretty.print.stattable.1d(x, width, fun.digits) else if (length(dim(x)) == 3) pretty.print.stattable.2d(x, width, fun.digits) else NextMethod("print",...) } ## Satisfy QA checks by defining these functions. But if we never ## export them they can't be used directly. count <- function(id) { } ratio <- function(d, y, scale=1, na.rm=TRUE) { } percent <- function(...) { } Epi/R/mat2pol.R0000644000176200001440000000102313564245720012675 0ustar liggesusersmat2pol <- function( pm, perm = 1:ncol(pm), x = as.numeric(rownames(pm)), col = rainbow(ncol(pm)), yl = 0:1, append = FALSE, ... ) { if( missing(x) ) x <- as.numeric( rownames(pm) ) if( length(x)==0 ) x <- 1:nrow(pm) xm <- cbind( 0, pm[,perm] ) xm <- t( apply(xm,1,cumsum) ) if( !append ) plot( x, x, type="n", ylim=yl, ... ) for( j in 1:ncol(pm) ) polygon( c(x,rev(x)), c(xm[,j],rev(xm[,j+1])), col = col[j], border="transparent" ) invisible( xm ) } Epi/R/boxes.MS.R0000644000176200001440000003752713763222575013003 0ustar liggesuserstbox <- function( txt, x, y, wd, ht, font=2, lwd=2, col.txt=par("fg"), col.border=par("fg"), col.bg="transparent" ) { rect( x-wd/2, y-ht/2, x+wd/2, y+ht/2, lwd=lwd, border=col.border, col=col.bg ) text( x, y, txt, font=font, col=col.txt ) invisible( c( x, y, wd, ht ) ) } dbox <- function( x, y, wd, ht=wd, font=2, lwd=2, cwd=5, col.cross=par("fg"), col.border=par("fg"), col.bg="transparent" ) { rect( x-wd/2, y-ht/2, x+wd/2, y+ht/2, lwd=lwd, border=col.border, col=col.bg ) ch <- ht*2/3 segments( c(x , x-ch/3), c(y+ch/2, y+ch/6), c(x , x+ch/3), c(y-ch/2, y+ch/6), lwd=cwd, col=col.cross ) invisible( c( x, y, wd, ht ) ) } fillarr <- function( x1, y1, x2, y2, gap=2, fr=0.8, angle=17, lwd=2, length=par("pin")[1]/30, ... ) { fr <- 1-gap/sqrt((x1-x2)^2+(y1-y2)^2) if( !missing(fr) ) if( fr > 1 ) fr <- fr/100 for( a in 1:angle ) arrows( x1 + (x2-x1)*(1-fr)/2, y1 + (y2-y1)*(1-fr)/2, x2 - (x2-x1)*(1-fr)/2, y2 - (y2-y1)*(1-fr)/2, angle=a, lwd=lwd, ... ) } std.vec <- function( a, b ) { l <- sqrt(a^2+b^2) if( l==0 ) return( c(0,0) ) else return( c(a/l,b/l) ) } boxarr <- function (b1, b2, offset = FALSE, pos = 0.45, ...) { d <- std.vec(b2[1] - b1[1], b2[2] - b1[2]) dd <- d * offset x1 <- b1[1] - dd[2] y1 <- b1[2] + dd[1] w1 <- b1[3] h1 <- b1[4] x2 <- b2[1] - dd[2] y2 <- b2[2] + dd[1] w2 <- b2[3] h2 <- b2[4] hx1 <- x1 + ifelse((y2-y1) != 0, (x2-x1) * ((h1/2)/abs(y2-y1)), sign(x2-x1) * w1/2) vx1 <- x1 + ifelse((x2-x1) != 0, (x2-x1) * ((w1/2)/abs(x2-x1)), 0) hx2 <- x2 + ifelse((y1-y2) != 0, (x1-x2) * ((h2/2)/abs(y1-y2)), sign(x1-x2) * w2/2) vx2 <- x2 + ifelse((x1-x2) != 0, (x1-x2) * ((w2/2)/abs(x1-x2)), 0) hy1 <- y1 + ifelse((y2-y1) != 0, (y2-y1) * ((h1/2)/abs(y2-y1)), 0) vy1 <- y1 + ifelse((x2-x1) != 0, (y2-y1) * ((w1/2)/abs(x2-x1)), sign(y2-y1) * h1/2) hy2 <- y2 + ifelse((y1-y2) != 0, (y1-y2) * ((h2/2)/abs(y1-y2)), 0) vy2 <- y2 + ifelse((x1-x2) != 0, (y1-y2) * ((w2/2)/abs(x1-x2)), sign(y1-y2) * h2/2) if( abs(vy1-y1) < h1/2 ) { bx1 <- vx1 by1 <- vy1 } else { bx1 <- hx1 by1 <- hy1 } if( abs(vy2-y2) < h2/2 ) { bx2 <- vx2 by2 <- vy2 } else { bx2 <- hx2 by2 <- hy2 } fillarr( bx1, by1, bx2, by2, ... ) invisible( list( x = bx1*(1-pos)+bx2*pos, y = by1*(1-pos)+by2*pos, d = d ) ) } wh.no <- function( tt, i, j ) { ## Utility to count the number of non-NA off diagonal elements with ## rown.tr ) col.arr <- col.arr [1:n.tr] if( length(col.txt.arr)>n.tr ) col.txt.arr<- col.txt.arr[1:n.tr] if( length(lwd.arr )>n.tr ) lwd.arr <- lwd.arr [1:n.tr] if( length(font.arr )>n.tr ) font.arr <- font.arr [1:n.tr] if( length(pos.arr )>n.tr ) pos.arr <- pos.arr [1:n.tr] # Here comes the plot # First setting up the plot area, and restoring the plot parameters later opar <- par( mar=c(0,0,0,0), cex=cex ) on.exit( par(opar) ) plot( NA, bty="n", xlim=0:1*100, ylim=0:1*100, xaxt="n", yaxt="n", xlab="", ylab="" ) # String height and width only meaningful after a plot has been called if( missing(ht) ) { ht <- strheight( pl.nam ) * hmult if( eq.ht ) ht <- rep( max(ht), length(ht) ) } if( missing(wd) ) { wd <- strwidth( pl.nam ) * wmult if( eq.wd ) wd <- rep( max(wd), length(wd) ) } # If not supplied, ask for positions of boxes if( is.list(boxpos) ) { names(boxpos) <- tolower( names(boxpos) ) if( length(intersect(names(boxpos),c("x","y")))<2 ) stop( "The list given in 'boxpos=' must have components 'x' and 'y'" ) if( length(boxpos$x) != n.st | length(boxpos$y) != n.st ) stop( "The elements 'x' and 'y' of boxpos must both have length equal to no. states", n.st ) xx <- boxpos$x yy <- boxpos$y } if( is.logical(boxpos) ) if( boxpos ) { ang <- pi - 2*pi*((1:n.st-0.5)/n.st) xx <- cos( ang ) * 35 + 50 yy <- sin( ang ) * 35 + 50 } else { xx <- yy <- numeric(n.st) for( i in subset ) { cat( "\nClick for level ", st.nam[i] ) flush.console() pt <- locator(1) xx[i] <- pt$x yy[i] <- pt$y tbox( pl.nam[i], xx[i], yy[i], wd[i], ht[i], ... ) } cat( "\n" ) } # Plot the boxes and record position and size b <- list() for( i in subset ) b[[i]] <- tbox( pl.nam[i], xx[i], yy[i], wd[i], ht[i], font=font[i], lwd=lwd[i], col.txt=col.txt[i], col.border=col.border[i], col.bg=col.bg[i] ) # Arrows and text on them arrowtext <- character(0) for( i in subset ) for( j in subset ) { if( !is.na(tt[i,j]) & i!=j ) { # Which number of arrow is currently processed? a <- wh.no( tt, i, j ) arr <- boxarr( b[[i]], b[[j]], offset=(!is.na(tt[j,i]))*offset.arr, lwd=lwd.arr[a], col=col.arr[a], pos=pos.arr[a], ... ) if( show.D | show.R ) { if( show.D & D[i,j]>0 ) arrowtext[a] <- formatC( D[i,j], format="f", digits=0, big.mark="," ) else arrowtext[a] <- "" if( show.R & R[i,j]>0 ) arrowtext[a] <- paste( if( !is.null(arrowtext[a]) ) paste( arrowtext[a], DR.sep[1], sep="" ), formatC( R[i,j], format="f", digits=digits.R, big.mark="," ), if( length(DR.sep) > 1 ) DR.sep[2], sep="" ) } else if( !is.null(txt.arr) ) arrowtext[a] <- txt.arr[a] if( !is.null(arrowtext[a]) ) text( arr$x-arr$d[2], arr$y+arr$d[1], arrowtext[a], adj=as.numeric(c(arr$d[2]>0,arr$d[1]<0)), font=font.arr[a], col=col.txt.arr[a] ) } } # Redraw the boxes with white background to remove any arrows crossing for( i in subset ) tbox( pl.nam[i], xx[i], yy[i], wd[i], ht[i], font=font[i], lwd=lwd[i], col.bg=par("bg") ) # Then redraw the boxes again for( i in subset ) tbox( pl.nam[i], xx[i], yy[i], wd[i], ht[i], font=font[i], lwd=lwd[i], col.txt=col.txt[i], col.border=col.border[i], col.bg=col.bg[i] ) # Finally create an object with all information to re-draw the display MSboxes <- list( Boxes = data.frame( xx = xx, yy = yy, wd = wd, ht = ht, font = font, lwd = lwd, col.txt = col.txt, col.border = col.border, col.bg = col.bg, stringsAsFactors=FALSE ), State.names = pl.nam, Tmat = tt, Arrows = data.frame( lwd.arr = lwd.arr, col.arr = col.arr, pos.arr = pos.arr, col.txt.arr = col.txt.arr, font.arr = font.arr, offset.arr = offset.arr, stringsAsFactors=FALSE ), Arrowtext = arrowtext ) class( MSboxes ) <- "MS" invisible( MSboxes ) } boxes.MS <- function( obj, sub.st, sub.tr, cex=1.5, ... ) { if( !inherits(obj,"MS") ) stop( "You must supply an object of class 'MSboxes'" ) n.st <- nrow( obj$Boxes ) n.tr <- nrow( obj$Arrows ) if( missing(sub.st) ) sub.st <- 1:n.st if( missing(sub.tr) ) sub.tr <- 1:n.tr # First setting up the plot area, and restoring the plot parameters later opar <- par( mar=c(0,0,0,0), cex=cex ) on.exit( par(opar) ) plot( NA, bty="n", xlim=0:1*100, ylim=0:1*100, xaxt="n", yaxt="n", xlab="", ylab="" ) # Exercise the subsets by putting the relevant colors to "transparent" obj$Boxes[-sub.st,c("col.txt", "col.border", "col.bg")] <- "transparent" obj$Arrows[-sub.tr,c("col.arr", "col.txt.arr")] <- "transparent" # Then draw the boxes b <- list() for( i in 1:n.st ) b[[i]] <- with( obj$Boxes, tbox( obj$State.names[i], xx[i], yy[i], wd[i], ht[i], font=font[i], lwd=lwd[i], col.txt=col.txt[i], col.border=col.border[i], col.bg=col.bg[i] ) ) # and the arrows for( i in 1:n.st ) for( j in 1:n.st ) { if( !is.na(obj$Tmat[i,j]) & i!=j ) { a <- wh.no( obj$Tmat, i, j ) arr <- with( obj$Arrows, boxarr( b[[i]], b[[j]], offset=(!is.na(obj$Tmat[j,i]))*offset.arr, lwd=lwd.arr[a], col=col.arr[a], pos=pos.arr[a], ... ) ) with( obj$Arrows, text( arr$x-arr$d[2], arr$y+arr$d[1], obj$Arrowtext[a], adj=as.numeric(c(arr$d[2]>0,arr$d[1]<0)), font=font.arr[a], col=col.txt.arr[a] ) ) } } # Redraw the boxes with "bg" background to remove any arrows crossing for( i in sub.st ) with( obj$Boxes, tbox( obj$State.names[i], xx[i], yy[i], wd[i], ht[i], font=font[i], lwd=lwd[i], col.txt=par("bg"), col.border=par("bg"), col.bg=par("bg") ) ) # Then redraw the boxes again for( i in sub.st ) with( obj$Boxes, tbox( obj$State.names[i], xx[i], yy[i], wd[i], ht[i], font=font[i], lwd=lwd[i], col.txt=col.txt[i], col.border=col.border[i], col.bg=col.bg[i] ) ) # Done! invisible( NULL ) } Epi/R/cal.yr.R0000644000176200001440000000300312664034207012503 0ustar liggesuserscal.yr <- function( x, format = "%Y-%m-%d", wh = NULL ) { cl.typ <- c("Date","POSIXct","POSIXlt","date","dates","chron") # Check if the input is a data frame and convert if( inherits( x, "data.frame" ) & is.null(wh) & missing(format) ) { # Indicator of where a date-type variable is wh <- which( sapply( x, inherits, cl.typ ) ) } if( inherits( x, "data.frame" ) & is.null(wh) & !missing(format) ) { # Indicator of where the character variables are wh <- which( sapply( x, is.character ) ) } if( inherits( x, "data.frame" ) & is.vector(wh) ) { if( is.character(wh) ) wh <- match( wh, names(x) ) # Convert the dates or the character variables for( i in wh ) { if( is.character(x[,i]) ) x[,i] <- cal.yr( x[,i], format=format ) else x[,i] <- cal.yr( x[,i] ) } return( x ) } # Finally, down to business --- converting a vector to decimal years: # Check if the input is some kind of date or time object if( any( inherits( x, cl.typ ) ) ) x <- as.Date( as.POSIXct( x ) ) else if( is.character( x ) ) x <- as.Date( x, format = format ) else if( is.factor( x ) ) x <- as.Date( as.character( x ), format = format ) else stop( "\nInput should be a data frame, a character vector, a factor or ", "some kind of date or time object:\n", "Date, POSIXct, POSIXlt, date, dates or chron" ) res <- as.numeric( x ) / 365.25 + 1970 class( res ) <- c("cal.yr","numeric") return( res ) } Epi/R/ROC.R0000644000176200001440000002211313150633754011744 0ustar liggesuserssteplines <- function( x, y, left = TRUE, right = !left, order = TRUE, ... ) { # A function to plot step-functions # # Get the logic right if right is supplied... left <- !right # ... right! n <- length( x ) if( any( order ) ) ord <- order(x) else ord <- 1:n dbl <- rep( 1:n, rep( 2, n) ) xv <- c( !left, rep( T, 2*(n-1) ), left) yv <- c( left, rep( T, 2*(n-1) ), !left) lines( x[ord[dbl[xv]]], y[ord[dbl[yv]]], ... ) } interp <- function ( target, fv, res ) { # Linear interpolaton of the values in the N by 2 matrix res, # to the target value target on the N-vector fv. # Used for placing tickmarks on the ROC-curves. # where <- which( fv>target )[1] - 1:0 int <- fv[where] wt <- ( int[2] - target ) / diff( int ) wt[2] <- 1-wt t( res[where,] ) %*% wt } ROC.tic <- function ( tt, txt = formatC(tt,digits=2,format="f"), dist = 0.02, angle = +135, col = "black", cex = 1.0, fv, res ) { # Function for drawing tickmarks on a ROC-curve # for (i in 1:length(tt)) { pnt <- interp ( tt[i], fv, res ) x <- 1-pnt[2] y <- pnt[1] lines( c( x, x+dist*cos(pi*angle/180) ), c( y, y+dist*sin(pi*angle/180) ), col=col ) text( x+dist*cos(pi*angle/180), y+dist*sin(pi*angle/180), txt[i], col=col, adj=c( as.numeric(abs(angle)>=90), as.numeric( angle <= 0)), cex=cex ) } } ROC <- function ( test = NULL, stat = NULL, form = NULL, plot = c( "sp", "ROC" ), PS = is.null(test), # Curves on probability scale PV = TRUE, # sn, sp, PV printed at "optimality" point MX = TRUE, # tick at "optimality" point MI = TRUE, # Model fit printed AUC = TRUE, # Area under the curve printed grid = seq(0,100,10), # Background grid (%) col.grid = gray( 0.9 ), cuts = NULL, lwd = 2, data = parent.frame(), ... ) { # First all the computations # # Name of the response rnam <- if ( !missing( test ) ) deparse( substitute( test ) ) else "lr.eta" # Fit the model and get the info for the two possible types of input if( is.null( form ) ) { if( is.null( stat ) | is.null( test ) ) stop( "Either 'test' AND 'stat' OR 'formula' must be supplied!" ) lr <- glm( stat ~ test, family=binomial )#, data=data ) resp <- stat Model.inf <- paste("Model: ", deparse( substitute( stat ) ), "~", deparse( substitute( test ) ) ) } else { lr <- glm(form, family = binomial, data = data) resp <- eval( parse(text = deparse(form[[2]])), envir=lr$model ) Model.inf <- paste("Model: ",paste(paste(form)[c(2,1,3)], collapse=" ")) } # From the empirical distribution function for test for each of # the two categories of resp. # First a table of the test (continuous variable) vs. the response and # adding a row of 0s so that we have all points for the ROC curve m <- as.matrix( base::table( switch( PS+1, test, lr$fit ), resp ) ) m <- addmargins( rbind( 0, m ), 2 ) # What values of test/eta do the rows refer to fv <- c( -Inf, sort( unique( switch( PS+1, test, lr$fit ) ) ) ) # How many rows in this matrix nr <- nrow(m) # Calculate the empirical distribution functions (well, cumulative numbers): m <- apply( m, 2, cumsum ) # Then the relevant measures are computed. sns <- (m[nr,2]-m[,2]) / m[nr,2] spc <- m[,1] / m[nr,1] pvp <- m[,2] / m[,3] pvn <- (m[nr,1]-m[,1]) / ( m[nr,3]-m[,3] ) res <- data.frame( cbind( sns, spc, pvp, pvn, fv ) ) names( res ) <- c( "sens", "spec", "pvp", "pvn", rnam ) # AUC by triangulation auc <- sum( (res[-1,"sens"]+res[-nr,"sens"])/2 * abs(diff(1-res[,"spec"])) ) # Plot of sens, spec, PV+, PV-: if ( any( !is.na( match( c( "SP", "SNSP", "SPV" ), toupper( plot ) ) ) ) ) { # First for probability scale if ( PS ) { plot( 0:1, 0:1, xlim=0:1, xlab="Cutpoint for predicted probability", ylim=0:1, ylab=" ", type="n" ) if( is.numeric( grid ) ) abline( h=grid/100, v=grid/100, col=col.grid ) box() for ( j in 4:1 ){ steplines( fv, res[,j], lty=1, lwd=lwd, col=gray((j+1)/7)) } text( 0, 1.01, "Sensitivity", cex=0.7, adj=c(0,0), font=2 ) text( 1, 1.01, "Specificity", cex=0.7, adj=c(1,0), font=2 ) text( 0, m[nr,2]/m[nr,3]-0.01, "PV+", cex=0.7, adj=c(0,1), font=2 ) text( 0 + strwidth( "PV+", cex=0.7 ), m[nr,2]/m[nr,3]-0.01, paste( " (= ", m[nr,2],"/", m[nr,3], " =", formatC( 100*m[nr,2]/m[nr,3], digits=3 ), "%)", sep=""), adj=c(0,1), cex=0.7 ) text( 1, 1-m[nr,2]/m[nr,3]-0.01, "PV-", cex=0.7, adj=c(1,1), font=2 ) } # then for test-variable scale else { xl <- range( test ) plot( xl, 0:1, xlim=xl, xlab=paste( deparse( substitute( test ) ), "(quantiles)" ), ylim=0:1, ylab=" ", type="n" ) if( is.numeric( grid ) ) abline( h=grid/100, v=quantile( test, grid/100 ), col=col.grid ) box() for ( j in 4:1 ){ steplines( fv, res[,j], lty=1, lwd=lwd, col=gray((j+1)/7))} text( xl[1], 1.01, "Sensitivity", cex=0.7, adj=c(0,0), font=2 ) text( xl[2], 1.01, "Specificity", cex=0.7, adj=c(1,0), font=2 ) text( xl[1], m[nr,2]/m[nr,3]-0.01, "PV+", cex=0.7, adj=c(0,1), font=2 ) text( xl[1] + strwidth( "PV+", cex=0.7 ), m[nr,2]/m[nr,3]-0.01, paste( " (= ", m[nr,2],"/", m[nr,3], " =", formatC( 100*m[nr,2]/m[nr,3], digits=3 ), "%)", sep=""), adj=c(0,1), cex=0.7 ) text( xl[2], 1-m[nr,2]/m[nr,3]-0.01, "PV-", cex=0.7, adj=c(1,1), font=2 ) } } # Plot of ROC-curve: if ( any( !is.na( match( "ROC", toupper( plot ) ) ) ) ) { plot( 1-res[,2], res[,1], xlim=0:1, xlab="1-Specificity", ylim=0:1, ylab= "Sensitivity", type="n", ...) if( is.numeric( grid ) ) abline( h=grid/100, v=grid/100, col=gray( 0.9 ) ) abline( 0, 1, col=gray( 0.4 ) ) box() lines( 1-res[,"spec"], res[,"sens"], lwd=lwd ) # Tickmarks on the ROC-curve if ( !is.null(cuts) ) { ROC.tic( cuts, txt=formatC( cuts, digits=2, format="f" ), fv=fv, res=res, dist=0.03, cex=0.7) } # Plot of optimality point if (MX) { mx <- max( res[,1]+res[,2] ) mhv <- which( (res[,1]+res[,2])==mx )[1] mxf <- fv[mhv] abline( mx-1, 1, col=gray(0.4) ) ROC.tic( mxf, txt=paste( rnam, "=", formatC( mxf, format="f", digits=3 ) ), fv=fv, res=res, dist=0.03, cex=0.7, angle=135 ) } # Model information if (MI) { crn <- par()$usr text(0.95*crn[2]+0.05*crn[1], 0.07, Model.inf, adj=c(1,0.5),cex=0.7) cf <- summary(lr)$coef[,1:2] nf <- dimnames(cf)[[1]] text(0.95*crn[2]+0.05*crn[1], 0.10, paste("Variable\ \ \ \ \ \ est.\ \ \ \ \ (s.e.) \ \ \n", paste(rbind(nf, rep("\ \ \ \ ",length(nf)), formatC(cf[,1],digits=3,format="f"), rep("\ \ \ (",length(nf)), formatC(cf[,2],digits=3,format="f"), rep(")",length(nf)), rep("\n",length(nf))), collapse=""), collapse=""), adj=c(1,0), cex=0.7 ) } # Print the area under the curve if (AUC) { crn <- par()$usr text( 0.95*crn[2]+0.05*crn[1], 0.00, paste( "Area under the curve:", formatC( auc, format="f", digits=3, width=5 ) ), adj=c(1,0), cex=0.7 ) } # Predictive values at maximum if (PV) { if(!MX) { mx <- max(res[,1]+res[,2]) mhv <- which((res[,1]+res[,2])==mx) mxf <- fv[mhv] } ROC.tic(mxf, fv=fv, res=res, txt= paste( "Sens: ", formatC(100*res[mhv,1],digits=1,format="f"), "%\n", "Spec: ", formatC(100*res[mhv,2],digits=1,format="f"), "%\n", "PV+: ", formatC(100*res[mhv,3],digits=1,format="f"), "%\n", "PV-: ", formatC(100*res[mhv,4],digits=1,format="f"), "%", sep="" ), dist=0.1, cex=0.7, angle=-45 ) } } invisible( list( res=res, AUC=auc, lr=lr ) ) } Epi/R/ftrend.R0000644000176200001440000000520312531361077012602 0ustar liggesusers"ftrend" <- function(object, ...) { if(length(object$xlevels) == 0) { stop("No factors in model") } xname <- names(object$xlevels)[1] if (!identical(object$contrasts[[1]], "contr.treatment")) { stop(paste("Treatment contrasts must be used for variable", xname)) } xlevels <- object$xlevels[[1]] nlevels <- length(xlevels) coefnames <- paste(xname, xlevels, sep="") ncoef <- length(coef(object)) if (!all(coefnames %in% names(coef(object)))) { stop("The model must not have an intercept term") } index1 <- match(coefnames, names(coef(object))) index2 <- (1:ncoef)[-index1] m <- length(index1) ncov <- length(index2) ## Centre the covariates according to Greenland et al (weighted mean = 0) X0 <- model.matrix(object) if (!is.null(object$weights)) { mu <- -apply(X0, 2, weighted.mean, object$weights )[index2] } else { mu <- -apply(X0, 2, mean)[index2] } mu.full <- rep(0, ncoef) mu.full[index2] <- mu X <- sweep(X0, 2, mu.full, "+") ## Information matrix with centred covariates if (!is.null(object$weights)) { J <- crossprod(X, sweep(X, 1, object$weights, "*")) } else { ## linear models J <- crossprod(X,X) } J11 <- J[index1, index1] J12 <- J[index1, index2] J21 <- J[index2, index1] J22 <- J[index2, index2] ## Variance matrix V <- solve(J) V11 <- V[index1, index1] V12 <- V[index1, index2] V21 <- V[index2, index1] V22 <- V[index2, index2] cal.V <- function(mu) { one <- as.matrix(rep(1,m)) mu <- as.matrix(mu) return(V11 - one %*% t(mu) %*% V21 - V12 %*% mu %*% t(one) + matrix(1, m, m) * (t(mu) %*% V22 %*% mu)[1,1]) } f <- function(mu) { V.mu <- cal.V(mu) # lambda is current vector of floating variances D <- sum(diag(V.mu)/lambda) - c(determinant(V.mu)$modulus) + sum(log(lambda)) - m S <- (1/sum(diag(J11)) + t(mu) %*% solve(J22) %*% mu)[1,1] grad1 <- - t(1/lambda) %*% V12 grad2 <- + sum(1/lambda) * t(mu) %*% V22 grad3 <- - t(mu) %*% solve(J22)/S attr(D,"gradient") <- 2 * (grad1 + grad2 + grad3) H1 <- V22 * sum(1/lambda) H2 <- -solve(J22)/S b <- solve(J22) %*% mu/S H3 <- 2 * b %*% t(b) attr(D, "hessian") <- 2 * (H1 + H2 + H3) return(D) } ## Initial value of lambda lambda <- diag(V[index1,index1]) ## Do the minimization nlm.out <- nlm(f, rep(0,ncov), check.analyticals=TRUE, ...) mu2 <- nlm.out$estimate ## Calculate parameter values and their covariance matrix ## if the covariates are appropriately centred coef <- coef(object)[index1] - c(crossprod(mu + mu2, coef(object)[index2])) return(list(coef=coef, vcov=cal.V(mu2))) } Epi/R/Lexis.diagram.R0000644000176200001440000000742312531361077014015 0ustar liggesusersLexis.diagram <- function( age = c( 0, 60), alab = "Age", date = c( 1940, 2000 ), dlab = "Calendar time", int = 5, lab.int = 2*int, col.life = "black", lwd.life = 2, age.grid = TRUE, date.grid = TRUE, coh.grid = FALSE, col.grid = gray(0.7), lwd.grid = 1, las = 1, entry.date = NA, entry.age = NA, exit.date = NA, exit.age = NA, risk.time = NA, birth.date = NA, fail = NA, cex.fail = 1.1, pch.fail = c(NA,16), col.fail = rep( col.life, 2 ), data = NULL, ... ) { # Function to plot a Lexis-diagram # # BxC, 2002, revsions in 2005 ## Get variables from data argument, if supplied, or from parent ## frame if not. entry.date <- eval(substitute(entry.date), data) entry.age <- eval(substitute(entry.age ), data) exit.date <- eval(substitute(exit.date ), data) exit.age <- eval(substitute(exit.age ), data) risk.time <- eval(substitute(birth.date), data) birth.date <- eval(substitute(birth.date), data) fail <- eval(substitute(fail ), data) # First expand intervals to both dimensions # int[1:2] <- c( int, int)[1:2] lab.int[1:2] <- c(lab.int,lab.int)[1:2] # Plot the diagram # plot( NA, xlim=date, xaxt="n", xaxs="i", xlab=dlab, ylim=age, yaxt="n", yaxs="i", ylab=alab, ... ) axis( side=1, at=seq( date[1], date[2], lab.int[2] ), las=las ) axis( side=2, at=seq( age[1], age[2], lab.int[1] ), las=las ) box( col="white" ) # par("fg") ) # Then the required grids # if ( age.grid ) { abline( h = seq( age[1], age[2], int[1] ), col=col.grid, lwd=lwd.grid ) } if ( date.grid ) { abline( v = seq( date[1], date[2], int[2] ), col=col.grid, lwd=lwd.grid ) } ages <- seq( age[1], age[2], min( int ) ) dates <- seq( date[1], date[2], min( int ) ) if ( coh.grid ) { segments( rep( date[1], length( ages ) ), ages, pmin( date[1] + ( age[2] - ages ), date[2] ), pmin( ages + ( date[2] - date[1] ), age[2] ), col=col.grid, lwd=lwd.grid ) segments( dates, rep( age[1], length( dates ) ), pmin( dates + ( age[2] - age[1] ), date[2] ), pmin( age[1] + ( date[2] - dates ), age[2] ), col=col.grid, lwd=lwd.grid ) } # Check if data for lifelines is supplied and plot lifelines if so # if( sum( !is.na( list( entry.date, entry.age, exit.date, exit.age, birth.date, risk.time ) ) ) > 2 ) { LL <- Lexis.lines( entry.date = entry.date, exit.date = exit.date, birth.date = birth.date, entry.age = entry.age, exit.age = exit.age, risk.time = risk.time, col.life = col.life, lwd.life = lwd.life, fail = fail, cex.fail = cex.fail, pch.fail = pch.fail, col.fail = col.fail, data = data ) invisible( LL ) } } Epi/R/LCa.fit.R0000644000176200001440000005332013320763654012547 0ustar liggesusers###################################################################### ### estimation method LCa.fit <- function( data, A, P, D, Y, model = "APa", # or one of "ACa", "APaC", "APCa" or "APaCa" a.ref, # age reference for the interactions pi.ref = a.ref, # age reference for the period interaction ci.ref = a.ref, # age reference for the cohort interaction p.ref, # period reference for the intercation c.ref, # cohort reference for the interactions npar = c(a = 6, # no. knots for main age-effect p = 6, # no. knots for peroid-effect c = 6, # no. knots for cohort-effect pi = 6, # no. knots for age in the period interaction ci = 6), # no. knots for age in the cohort interaction VC = TRUE, # numerical calculation of the Hessia? alpha = 0.05, # 1 minus confidence level eps = 1e-6, # convergence criterion maxit = 100, # max. no iterations quiet = TRUE ) # cut the crap { # "model" must have values in c(APa/ACa/APaC/APCa/APaCa)? if( !(model %in% c("APa","ACa","APaC","APCa","APaCa")) ) stop( '"model" must be one of "APa","ACa","APaC","APCa","APaCa", but is', model,'\n' ) # Which main effects and interactions are in the model intP <- as.logical(length(grep("Pa",model))) intC <- as.logical(length(grep("Ca",model))) mainP <- as.logical(length(grep("P" ,model))) # Also includes the age-period interaction mainC <- as.logical(length(grep("C" ,model))) # Also includes the age-cohort product # if a dataframe is supplied, fish out data and put in the function's environment if( !missing(data) ) { if (length(match(c("A", "P", "D", "Y"), names(data))) != 4) stop("Data frame ", deparse(substitute(data)), " has columns:\n", names(data), "\nmust have variables:\n", "A (age), P (period), D (cases) and Y (person-time)") data <- data[,c("A","P","D","Y")] data <- data[complete.cases(data),] A <- data$A P <- data$P D <- data$D Y <- data$Y } else { # if single vectors supplied, check they are all there nm <- c(missing(A), missing(P), missing(D), missing(Y)) if (any(nm)) stop("Variable", if (sum(nm) > 1) "s", paste(c(" A", " P", " D", " Y")[nm], collapse = ","), " missing from input") # and that they have the same length if( diff(range( lv <- c( length(A), length(P), length(D), length(Y) ) )) != 0 ) stop( "\nLengths of variables (", paste(paste(names(lv), lv, sep = ":"), collapse = ", "), ") are not the same." ) } # end of data acquisition # code-simplifier for knot calculation eqqnt <- function(n) round( (1:n-0.5)/n, 2 ) # Define knots - we compute also the knots not needed if( is.list(npar) ) { # Check if npar is a *named* list if( is.null(names(npar)) ) stop( "If npar= is a list, it must be a *named* list.\n" ) # Fill in a bogus 1 if some of the items are missing for(ee in c('a.kn','p.kn','c.kn','pi.kn','ci.kn') ) if(is.null(npar[[ee]])) npar[[ee]] <- 1 a.kn <- if( length(npar$a )>1 ) npar$a else quantile( rep( A,D), probs=eqqnt(npar$a ) ) p.kn <- if( length(npar$p )>1 ) npar$p else quantile( rep(P ,D), probs=eqqnt(npar$p ) ) c.kn <- if( length(npar$c )>1 ) npar$c else quantile( rep(P-A,D), probs=eqqnt(npar$c ) ) pi.kn <- if( length(npar$pi)>1 ) npar$pi else quantile( rep( A,D), probs=eqqnt(npar$pi) ) ci.kn <- if( length(npar$ci)>1 ) npar$ci else quantile( rep( A,D), probs=eqqnt(npar$ci) ) } else { # if npar is too short fill it up npar <- rep( npar, 5 )[1:5] # if not named, name it and notify if( is.null(names(npar)) ) names(npar) <- c("a","p","c","pi","ci") a.kn <- quantile( rep( A,D), probs=eqqnt(npar["a"] ) ) p.kn <- quantile( rep(P ,D), probs=eqqnt(npar["p"] ) ) c.kn <- quantile( rep(P-A,D), probs=eqqnt(npar["c"] ) ) pi.kn <- quantile( rep( A,D), probs=eqqnt(npar["pi"]) ) ci.kn <- quantile( rep( A,D), probs=eqqnt(npar["ci"]) ) } # Reference points if( missing( p.ref) ) p.ref <- median( rep(P ,D) ) if( missing( c.ref) ) c.ref <- median( rep(P-A,D) ) if( missing(pi.ref) ) pi.ref <- median( rep( A,D) ) if( missing(ci.ref) ) ci.ref <- median( rep( A,D) ) ############################################################################ # Here starts the actual modelling commence <- Sys.time() # Matrices to extract the age-interaction terms at reference points Ap <- Ns( rep(pi.ref,length(A)), knots=pi.kn, intercept=TRUE ) Ac <- Ns( rep(ci.ref,length(A)), knots=ci.kn, intercept=TRUE ) # Current age-effects (in the iteration these will be term predictions) ba <- matrix( 1, length(A), 2 ) # cbind( rep(1,length(A)), 1 ) # set to 0 if term is not in model at all if( !mainP ) ba[,1] <- 0 if( !mainC ) ba[,2] <- 0 # Main effects model with (at least one) age-interaction # --- at this stage it is either 0 or 1 mat <- glm( D ~ -1 + Ns( A, knots=a.kn, intercept=TRUE ) + Ns( P , knots=p.kn, ref=p.ref):ba[,1] + Ns( P-A, knots=c.kn, ref=c.ref):ba[,2], offset = log(Y), family = poisson ) oldmb <- oldmat <- mat$deviance # Terms prediction --- three terms here. # No need to divide by the ba at this point, it is eiter 1 or 0 pat <- predict( mat, type="terms" ) # iteration counter and continuation indicator nit <- 0 one.more <- TRUE # For simple formatting of the iteration output fC <- function(x,d) formatC(x,format="f",digits=d) # now, iterate till convergence while( one.more ) { nit <- nit+1 # The estimated terms from the modeling of the APC-effects to be used # as offsets Aoff <- pat[,1] Pint <- Poff <- pat[,2] Cint <- Coff <- pat[,3] # P or C terms with main effects should be either in interaction or # offset, so one of these should always be 0 if( intP ) Poff <- Poff*0 else Pint <- Pint*0 if( intC ) Coff <- Coff*0 else Cint <- Cint*0 # Iteration of the age-components of the interaction mb <- glm( D ~ -1 + Ns( A, knots=pi.kn, intercept=TRUE ):Pint + Ns( A, knots=ci.kn, intercept=TRUE ):Cint, offset = Aoff + Poff + Coff + log(Y), family = poisson ) # Get the age-interaction terms only, and if one is not needed set to 0 ba <- predict( mb, type="terms" ) / cbind(Pint,Cint) / cbind( ci.lin( mb, subset="pi.kn", ctr.mat=Ap)[,1], # These are the values at the reference ci.lin( mb, subset="ci.kn", ctr.mat=Ac)[,1] ) # point for A; we want the RRs as effects ba[is.na(ba)] <- 0 # If no interaction only main should be fitted; if no main effect, set to 0 using mainP/C if( !intP ) ba[,1] <- rep(1,length(A)) * mainP if( !intC ) ba[,2] <- rep(1,length(A)) * mainC # apc model with assumed known interactions with age mat <- glm( D ~ -1 + Ns( A, knots=a.kn, intercept=TRUE ) + Ns( P , knots=p.kn, ref=p.ref):ba[,1] + Ns( P-A, knots=c.kn, ref=c.ref):ba[,2], offset = log(Y), family = poisson ) # extract age and period terms - rmoving the interactions pat <- predict( mat, type="terms" ) / cbind( 1, ba ) pat[is.na(pat)] <- 0 # convergence? Check both that the two models give the same deviance # and that the chnage in each is small newmat <- mat$deviance newmb <- mb$deviance conv <- ( reldif <- max( abs(newmat-newmb )/(newmat+newmb)/2, abs(oldmat-newmat)/ newmat, abs(oldmb -newmb )/ newmb) ) < eps one.more <- ( !conv & ( nit < maxit ) ) oldmat <- newmat oldmb <- newmb if( !quiet & nit==1 ) cat( " Deviances: model(AT) model(A) Rel. diff.\n" ) if( !quiet ) cat( "Iteration", formatC( nit, width=3, flag=" "), "", fC(mat$deviance,3), fC( mb$deviance,3), fC( reldif, 7 ), "\n" ) } # end of iteration loop # Deviance and d.f - there is a "+1" because the intercept is in both models # but not explicit, (both models fitted with "-1"), hence the df.null # is the total no. observations dev <- mb$deviance df <- mat$df.null - ( mb$df.null- mb$df.res # no. parms in mb + mat$df.null-mat$df.res # no. parms in mat - 1 ) # common intercept if( conv ) cat( "LCa.fit convergence in ", nit, " iterations, deviance:", dev, "on", df, "d.f.\n") if( !conv ) cat( "LCa.fit *not* converged in ", nit, " iterations:\ndeviance (AT):", mat$deviance, ", deviance (B):" , mb$deviance, "\n", if( VC ) "...no variance-covariance computed.\n" ) fin <- Sys.time() if( !quiet ) cat("...using", round(difftime(fin,commence,units="secs"),1), "seconds.\n") # unique values of A, P and C in the dataset for reporting effects a.pt <- sort(unique( A)) p.pt <- sort(unique(P )) c.pt <- sort(unique(P-A)) # extract effects from final models after convergence ax <- ci.exp( mat, subset= "a.kn", ctr.mat=Ns(a.pt,knots= a.kn,intercept=TRUE ) ) kp <- ci.exp( mat, subset= "p.kn", ctr.mat=Ns(p.pt,knots= p.kn,ref=p.ref) ) kc <- ci.exp( mat, subset= "c.kn", ctr.mat=Ns(c.pt,knots= c.kn,ref=c.ref) ) pi <- ci.exp( mb , subset="pi.kn", ctr.mat=Ns(a.pt,knots=pi.kn,intercept=TRUE), Exp=FALSE ) ci <- ci.exp( mb , subset="ci.kn", ctr.mat=Ns(a.pt,knots=ci.kn,intercept=TRUE), Exp=FALSE ) # Label the estimated effects rownames( ax ) <- rownames( pi ) <- rownames( ci ) <- a.pt rownames( kp ) <- p.pt rownames( kc ) <- c.pt # do we bother about the correct variance-covariance? if( VC & conv ) # ...certainly not without convergence { commence <- Sys.time() if( !quiet ) cat("...computing Hessian by numerical differentiation...\n") # the number of parameters for each of the 5 effects na <- length( grep( "a.kn", names(coef(mat)) ) ) np <- length( grep( "p.kn", names(coef(mat)) ) ) nc <- length( grep( "c.kn", names(coef(mat)) ) ) npi <- length( grep( "pi.kn", names(coef(mb )) ) ) nci <- length( grep( "ci.kn", names(coef(mb )) ) ) # get only the parameters for effects that are non-zero (the others # are in the models but they are 0) ml.cf <- c( coef(mat)[c(rep(TRUE,na), rep(mainP,np), rep(mainC,nc))], coef(mb)[c(rep(intP,npi), rep(intC,nci))] ) # and some more snappy names for the parameters: first all names all.nam <- c( paste("ax",1:na,sep=""), paste("kp",1:np,sep=""), paste("kc",1:nc,sep=""), paste("pi",1:npi,sep=""), paste("ci",1:nci,sep="") ) # ...then those actually present in the model names( ml.cf ) <- all.nam[c(rep( TRUE,na), rep(mainP,np), rep(mainC,nc), rep(intP,npi), rep(intC,nci))] # We need the variance-covariance of the estimates as the 2nd # derivative of the log-likelihood, D*log(lambda) - lambda*Y, # or for eta=log(lambda), D*eta - exp(eta)*Y, # assuming the sequence of parameters is ax, kp, kc, pi, ci # (first A, P, C from model mat, then Pa, Ca from model mb) # Note that we cannot simplify this calculation because the model is # non-linear in pi,kp resp. ci,kc # Matrices to use in calculation of the terms of the model for each parms MA <- Ns( A, knots= a.kn, intercept=TRUE ) Mp <- Ns( P , knots= p.kn, ref=p.ref ) Mc <- Ns( P-A, knots= c.kn, ref=c.ref ) Mpi <- Ns( A, knots=pi.kn, intercept=TRUE ) Mci <- Ns( A, knots=ci.kn, intercept=TRUE ) # Computing the log-likelihood for any set of parameters llik <- function( parms ) { ax <- MA %*% parms[ 1:na] ; nn <- na if( mainP ) { kp <- Mp %*% parms[nn+1:np] ; nn <- nn+np } else kp = rep(0,length(ax)) if( mainC ) { kc <- Mc %*% parms[nn+1:nc] ; nn <- nn+nc } else kc = rep(0,length(ax)) if( intP ) { pi <- Mpi %*% parms[nn+1:npi] ; nn <- nn+npi} else pi = rep(1,length(ax)) if( intC ) { ci <- Mci %*% parms[nn+1:nci] } else ci = rep(1,length(ax)) eta <- ax + pi*kp + ci*kc sum( D*eta - exp(eta)*Y ) } # Numerical calculation of the Hessian for llik ivar <- -numDeriv::hessian( llik, ml.cf ) # Sometimes not quite positive definite, fix that after inverting the Hessian vcov <- Matrix::nearPD( solve( ivar ) ) vcov <- as.matrix( vcov$mat ) fin <- Sys.time() if( !quiet ) cat("...done - in", round(difftime(fin,commence,units="secs"),1), "seconds.\n") # Since we now have the variances of the parameters for each of the # effects we can compute corrected c.i.s for the effects se.eff <- function( sub, cM, Alpha=alpha ) { wh <- grep( sub, names(ml.cf) ) res <- cbind( cM %*% ml.cf[wh], sqrt( diag( cM %*% vcov[wh,wh] %*% t(cM) ) ) ) %*% ci.mat(alpha=Alpha) colnames(res)[1] <- paste( "Joint", colnames(res)[1] ) res } # Append the corrected c.i.s to the effect objects ax <- cbind( ax, exp( se.eff( "ax", Ns(a.pt,knots= a.kn,intercept=TRUE) ) ) ) if( mainP ) kp <- cbind( kp, exp( se.eff( "kp", Ns(p.pt,knots= p.kn,ref=p.ref) ) ) ) if( mainC ) kc <- cbind( kc, exp( se.eff( "kc", Ns(c.pt,knots= c.kn,ref=c.ref) ) ) ) if( intP ) pi <- cbind( pi, se.eff( "pi", Ns(a.pt,knots=pi.kn,intercept=TRUE) ) ) if( intC ) ci <- cbind( ci, se.eff( "ci", Ns(a.pt,knots=ci.kn,intercept=TRUE) ) ) } # Collect refs and knots in lists klist <- list( a.kn=a.kn, pi.kn=pi.kn, p.kn=p.kn, ci.kn=ci.kn, c.kn=c.kn ) rlist <- list( pi.ref=pi.ref, p.ref=p.ref, ci.ref=ci.ref, c.ref=c.ref ) # Finally output object res <- list( model = model, ax = ax, pi = if( intP ) pi else NULL, kp = if( mainP ) kp else NULL, ci = if( intC ) ci else NULL, kc = if( mainC ) kc else NULL, mod.at = mat, mod.b = mb, coef = if( VC & conv ) ml.cf else NULL, vcov = if( VC & conv ) vcov else NULL, knots = klist, refs = rlist, deviance = dev, df.residual = df, iter = nit ) # Remove redundant stuff before returning res <- res[!sapply(res,is.null)] class( res ) <- "LCa" invisible( res ) } ###################################################################### ### utility to determine the types of terms in a model model.terms <- function( x ) list( intP = as.logical(length(grep("Pa",x$model))), mainP = as.logical(length(grep("P" ,x$model))), intC = as.logical(length(grep("Ca",x$model))), mainC = as.logical(length(grep("C" ,x$model))) ) ###################################################################### ### print method print.LCa <- function( x, ... ) { # terms in the model mt <- model.terms( x ) # no. of parameters in each term npar <- sapply(x$knots,length)-1 npar[1] <- npar[1] + 1 npar <- npar[c(TRUE,mt$intP,mt$mainP,mt$intC,mt$mainC)] npar <- paste( paste( npar, c(rep(", ",length(npar)-2)," and ",""), sep=""), collapse=rep("") ) cat( paste( x$model, ": Lee-Carter model with natural splines:\n", " log(Rate) = ax(Age)", if( mt$mainP ) " + ", if( mt$intP ) "pi(Age)", if( mt$mainP ) "kp(Per)", if( mt$mainC ) " + ", if( mt$intC ) "ci(Age)", if( mt$mainC ) "kc(Coh)", "\nwith ", npar, " parameters respectively.\n", "Deviance: ", round(x$deviance,3), " on ", x$df, " d.f.\n", sep=""), if( !("vcov" %in% names(x)) ) "(only conditional c.i.s for effects)\n" ) } ###################################################################### ### summary method summary.LCa <- function( object, show.est=FALSE, ... ) { # terms in the model mt <- model.terms( object ) print( object ) # the number of parameters for each of the 5 effects na <- length( grep( "a.kn", names(coef(object$mod.at)) ) ) np <- length( grep( "p.kn", names(coef(object$mod.at)) ) ) nc <- length( grep( "c.kn", names(coef(object$mod.at)) ) ) npi <- length( grep( "pi.kn", names(coef(object$mod.b )) ) ) nci <- length( grep( "ci.kn", names(coef(object$mod.b )) ) ) # Show knots used cat( "\nKnots used:\n") for( nm in names(object$knots[c(TRUE,mt$mainP,mt$intP,mt$mainC,mt$intC)]) ) { cat( nm,"\n" ) ; print(object$knots[[nm]] ) } cf <- rbind( ci.lin(object$mod.at)[c(rep(TRUE ,na), rep(mt$mainP,np), rep(mt$mainC,nc)),1:2], ci.lin(object$mod.b )[c(rep(mt$intP ,npi), rep(mt$intC ,nci)),1:2] ) if( "vcov" %in% names(object) ) { cf <- cbind( cf, sqrt( diag(object$vcov) ) ) colnames( cf )[-1] <- c("cond.se","joint.se") } if( show.est ) print( cf ) invisible( cf ) } ###################################################################### ### plot method plot.LCa <- function( x, ... ) { # terms in the model mt <- model.terms( x ) # A small plot utility to exploit the structure of the effects plc <- function( x, ... ) matplot( as.numeric( rownames(x) ), x[,ncol(x)-2:0], type="l", lty=1, lwd=c(3,1,1), ... ) plc( x$ax, col="black", xlab="Age", ylab="Age-specific rates", log="y" ) rug( x$knots$a.kn, lwd=2 ) if( mt$intP ){ plc( x$pi, col="black", xlab="Age", ylab="Relative period log-effect multiplier" ) abline(h=1,v=x$refs$pi.ref) rug( x$knots$pi, lwd=2 ) } if( mt$mainP ){ plc( x$kp, col="black", log="y", xlab="Date of follow-up (period)", ylab="Period effect (RR)" ) abline(h=1,v=x$refs$p.ref) rug( x$knots$kp, lwd=2 ) } if( mt$intC ){ plc( x$ci, col="black", xlab="Age", ylab="Relative cohort log-effect multiplier" ) abline(h=1,v=x$refs$ci.ref) rug( x$knots$ci, lwd=2 ) } if( mt$mainC ){ plc( x$kc, col="black", log="y", xlab="Date of birth (cohort)", ylab="Cohort effect (RR)" ) abline(h=1,v=x$refs$c.ref) rug( x$knots$kc, lwd=2 ) } } ###################################################################### ### predict method predict.LCa <- function( object, newdata, alpha = 0.05, level = 1-alpha, sim = ( "vcov" %in% names(object) ), ... ) { # What main effects and interactions are in the model mt <- model.terms( object ) # is person-years suppied, otherwise use units as in the model if( "Y" %in% names(newdata) ) Y <- newdata$Y else Y <- rep(1,nrow(newdata)) # Matrices to extract effects at newdata rows Ma <- Ns( newdata$A, knots = object$knots$a.kn, intercept = TRUE) Mp <- Ns( newdata$P , knots = object$knots$p.kn, ref=object$refs$p.ref ) Mc <- Ns( newdata$P-newdata$A, knots = object$knots$c.kn, ref=object$refs$c.ref ) Mpi <- Ns( newdata$A, knots = object$knots$pi.kn, intercept = TRUE) Mci <- Ns( newdata$A, knots = object$knots$ci.kn, intercept = TRUE) # Default terms values for models without interactions kp <- kc <- rep( 0, nrow(newdata) ) pi <- ci <- rep( 1, nrow(newdata) ) # P, C and interaction term(s) if included in the model if( mt$intP ) { pi <- ci.lin( object$mod.b , subset="pi.kn", ctr.mat=Mpi )[,1] kp <- ci.lin( object$mod.at, subset= "p.kn", ctr.mat=Mp )[,1] } if( mt$intC ) { ci <- ci.lin( object$mod.b , subset="ci.kn", ctr.mat=Mci )[,1] kc <- ci.lin( object$mod.at, subset= "c.kn", ctr.mat=Mc )[,1] } # First fitted values from mod.at # Note that the model object mod.at always has the same number of # parameters, for some of the models either period or cohort parameters # are 0, hence not used. pr0 <- ci.exp( object$mod.at, alpha=alpha, ctr.mat=cbind(Ma,Mp*pi,Mc*ci) ) # Then fitted values from mod.b # But mod.b has an offset beyond log(Y), namely all the APC terms lp.b <- ci.lin( object$mod.b , ctr.mat=cbind(Mpi*kp,Mci*kc) )[,1:2] lp.b[,1] <- lp.b[,1] + ci.lin( object$mod.at, ctr.mat=cbind(Ma,Mp*(!mt$intP),Mc*(!mt$intC)) )[,1] pr0 <- cbind( pr0, exp( lp.b %*% ci.mat(alpha=alpha) ) ) # label the estimates colnames( pr0 )[c(1,4)] <- c("at|b Est.","b|at Est.") # The doings above gives confidence intervals based on the conditional # models, so if we want proper intervals we should simulate instead, # using the posterior distribuion of all parameters, albeit under the # slightly fishy assumption that the joint posterior is normal... if( sim ) # also renders TRUE if sim is numerical (and not 0) { if( is.logical(sim) & sim ) sim <- 1000 # Check that there is a vcov component of the model if( !( "vcov" %in% names(object) ) ) warning( "No variance-covariance in LCa object, only conditional c.i.s available.\n", "no simulation (parametric bootstrap) is done.\n" ) else { # using the parametric bootstrap based on the parameters and the # (numerically computed) Hessian eta <- NArray( list( pt = 1:nrow(pr0), it = 1:sim ) ) parms <- MASS::mvrnorm( n = sim, mu = object$coef, Sigma = object$vcov ) na <- ncol( Ma ) np <- ncol( Mp ) nc <- ncol( Mc ) npi <- ncol( Mpi ) nci <- ncol( Mci ) # Compute the linear predictor in each of the simulated samples # period and cohort effects if not in the model kp <- kc <- rep( 0, nrow(newdata) ) pi <- ci <- rep( 1, nrow(newdata) ) for( i in 1:sim ){ ax <- Ma %*% parms[i, 1:na] ; nn <- na if( mt$mainP ) { kp <- Mp %*% parms[i,nn+1:np] ; nn <- nn+np } if( mt$mainC ) { kc <- Mc %*% parms[i,nn+1:nc] ; nn <- nn+nc } if( mt$intP ) { pi <- Mpi %*% parms[i,nn+1:npi] ; nn <- nn+npi} if( mt$intC ) { ci <- Mci %*% parms[i,nn+1:nci] } eta[,i] <- ax + pi*kp + ci*kc } # predicted rates with bootstrap confidence limits pr.sim <- exp( t( apply( eta, 1, quantile, probs=c(0.5,alpha/2,1-alpha/2), na.rm=TRUE ) ) ) colnames( pr.sim )[1] <- "Joint est." return( pr.sim ) } } else return( pr0 ) } Epi/R/Lexis.lines.R0000644000176200001440000000631012531361077013515 0ustar liggesusersLexis.lines <- function( entry.date = NA, exit.date = NA, birth.date = NA, entry.age = NA, exit.age = NA, risk.time = NA, col.life = "black", lwd.life = 2, fail = NA, cex.fail = 1, pch.fail = c(NA,16), col.fail = col.life, data = NULL ) { ## Get variables from data argument, if supplied, or from parent ## frame if not. entry.date <- eval(substitute(entry.date), data) entry.age <- eval(substitute(entry.age ), data) exit.date <- eval(substitute(exit.date ), data) exit.age <- eval(substitute(exit.age ), data) risk.time <- eval(substitute(birth.date), data) birth.date <- eval(substitute(birth.date), data) fail <- eval(substitute(fail ), data) # If fail is numeric make it logical if( is.numeric( fail ) ) fail <- ( fail > 0 ) # Complete the information on lifelines XX <- Life.lines( entry.date = entry.date, entry.age = entry.age, exit.date = exit.date, exit.age = exit.age, risk.time = risk.time, birth.date = birth.date ) # Expand lwd.life/col.life/pch.fail/col.fail/cex.fail # Np <- nrow( XX ) if( length( col.life )==1 ) col.life <- rep( col.life, Np ) else if( length( col.life )!=length(fail) ) stop("col.life must have length 1 or length(fail)" ) if( length( lwd.life )==1 ) lwd.life <- rep( lwd.life, Np ) else if( length( lwd.life )!=length(fail) ) stop("lwd.life must have length 1 or length(fail)" ) if( length( col.fail )==1 ) col.fail <- rep( col.fail, Np ) else { if( length( col.fail )==2 ) col.fail <- col.fail[fail+1] } if( length( col.fail )!=length(fail) ) stop("col.fail must have length 1,2 or length(fail)" ) if( length( pch.fail )==1 ) pch.fail <- rep( pch.fail, Np ) else if( length( pch.fail )==2 ) pch.fail <- pch.fail[fail+1] if( length( pch.fail )!=length(fail) ) stop("pch.fail must have length 1,2 or length(fail)" ) if( length( cex.fail )==1 ) cex.fail <- rep( cex.fail, Np ) else if( length( cex.fail )==2 ) cex.fail <- cex.fail[fail+1] if( length( cex.fail )!=length(fail) ) stop("cex.fail must have length 1,2 or length(fail)" ) # Was XX returned as a Date-object? # If so make a numerical version i LL, otherwise just a copy. # if( attr( XX, "Date" ) ) { LL <- data.frame( lapply( XX, unclass ) ) LL[,c(1,3,5)] <- LL[,c(1,3,5)] / 365.25 + 1970 LL[,c(2,4,6)] <- LL[,c(2,4,6)] / 365.25 } else LL <- XX # Find age and date ranges in the current plot. # date <- par( "usr" )[1:2] age <- par( "usr" )[3:4] # Plot the lifelines segments( LL[,1], LL[,2], LL[,3], LL[,4], lwd=lwd.life, col=col.life ) # If there are any non-NAs for pch.fail then blank out the space # where they go before plotting the symbols if( any( !is.na(pch.fail) ) ) points( LL[!is.na(pch.fail),3], LL[!is.na(pch.fail),4], pch=16, col="white", #par()$bg, cex=cex.fail[!is.na(pch.fail)] ) points( LL[,3], LL[,4], pch=pch.fail, col=col.fail, cex=cex.fail ) # Return the untouched version of the completed dataframe # invisible( data.frame( XX, fail=fail ) ) } Epi/R/ncut.r0000644000176200001440000000074012531361077012332 0ustar liggesusersncut <- function( x, breaks, type="left" ) { # Sorting to get the opportunity to call the function recursively. breaks <- sort( breaks ) # Get the indices, but fix the 0 indices to produce NAs: fi <- findInterval( x, breaks ) fi[fi==0] <- length( breaks ) + 1 switch( toupper( substr( type, 1, 1 ) ), "L" = breaks[fi], "R" = -ncut( -x, -breaks ), "M" = ( breaks[fi] - ncut( -x, -breaks ) ) / 2 ) } Epi/R/rcutLexis.R0000644000176200001440000000221514013245047013275 0ustar liggesusersrcutLexis <- function(Lx, cut, timescale = 1, precursor.states = transient(Lx)) { # avoid note about no visible binding new.state <- NULL lex.id <- NULL # All new states should be precursor states # new.state may be factor, hnece the as.character pr.st <- unique(c(precursor.states, unique(as.character(cut$new.state)))) # utility to select n'th element in vector getn <- function(x,n) x[n] # make the data frame a sorted, grouped tibble # note that the cut in arrange is the variable cut in the tibble cut <- group_by(cut, lex.id) cut <- arrange(cut, cut, .by_group = TRUE) # the Lexis object to return eventually nxL <- Lx # max no transitions for one person maxn <- max(table(cut$lex.id)) # loop over transition number per person for(n in 1:maxn) { # the n'th transitions for each person nx.cut <- summarize(cut, cut = getn( cut, n), new.state = getn(new.state, n) ) # update with cuts at these for each person nxL <- cutLexis(nxL, cut = nx.cut, timescale = timescale, precursor.states = pr.st ) } # done, return result nxL } Epi/R/gen.exp.R0000644000176200001440000002472713403770433012677 0ustar liggesusers# Acronyms: # dop: date of purchase # dpt: dose per time # amt: amount # dur: duration # dof: date of follow-up ###################################################################### # A function to compute cumulative doses etc. at the purchase dates # *and* derive intervals of drug coverage resp no coverage from the # purchase date, amounts and dosage per time use.amt.dpt <- function( purchase, # data frame with dop, amt and dpt push.max, rm.dose ) { do.call( "rbind", lapply( split( purchase, purchase$id ), function(set) { np <- nrow(set) if( np==1 ) # return data frame of 2 rows { dfR <- data.frame( id = set$id, dof = set$dop + c(0,set$amt/set$dpt), amt = c(set$amt,0), dpt = c(set$dpt,0), off = c(FALSE,TRUE), cum.amt = c(0,set$amt), cum.tim = c(0,set$amt/set$dpt) ) return( dfR ) } set <- set[order(set$dop),] # Compute length of exposure periods drug.dur <- set$amt / set$dpt # Put the exposed period head to foot new.start <- min( set$dop ) + c(0,cumsum(drug.dur[-np])) # Move them out so that the start of a period is never earlier than # the dop exp.start <- new.start + cummax( pmax(set$dop-new.start,0) ) # Compute the pushes push.one <- exp.start - set$dop # Revise them to the maximally acceptable push.adj <- pmin( push.one, push.max ) # Revise the starting dates of exposure exp.start <- exp.start - push.one + push.adj # Revise the durations to be at most equal to differences between the # revised starting dates drug.dur <- pmin( drug.dur, c(diff(exp.start),Inf) ) # Compute the end of the intervals exp.end <- exp.start + drug.dur # Find out which exposure intervals that are followed by a gap: followed.by.gap <- c( exp.start[-1]-exp.end[-np] > 0, TRUE ) # To facilitate further calculations we add records for the gaps # and also a record for the date of drug expiration dfR <- rbind( data.frame( id = set$id[1], dof = exp.start, amt = set$amt, dpt = set$dpt ), data.frame( id = set$id[1], dof = exp.end[followed.by.gap], amt = 0, dpt = 0 ) ) dfR <- dfR[order(dfR$dof),] # Logical indicator of intervals off drug dfR$off <- (dfR$dpt==0) | (dfR$dof < min(set$dop)) # Finally compute the cumulative dose and time on drug at the end of # the interval using interval length and dpt: if( rm.dose ) { dfR$cum.amt <- with( dfR, cumsum( c(0, diff(dof)* dpt[-length(dpt)]) ) ) } else dfR$cum.amt <- cumsum( c( 0, dfR$amt[-nrow(dfR)] ) ) dfR$cum.tim <- with( dfR, cumsum( c(0, diff(dof)*!off[-length(dpt)]) ) ) return( dfR ) } ) ) } ###################################################################### # Compute the cumulative dose at all purcase dates and at the last # (unknown) future expiry date, computed based on previous # consumption. The resulting data frame has one more line per person # than no. of purchases. use.only.amt <- function( purchase, pred.win ) { do.call( "rbind", lapply( split( purchase, purchase$id ), function(set) { np <- nrow(set) if( np==1 ) return( NULL ) set <- set[order(set$dop),] # The points to include in the calculation: # All dates after pred.win before last purchase, # but at least the last two purchase dates, wp <- ( set$dop > pmin( max(set$dop)-pred.win, sort(set$dop,decreasing=TRUE)[2] ) ) # Cumulative amount consumed at each dop since first cum.amt <- cumsum(c(0,set$amt)) # Average slope to use to project the duration of last purchase avg.slp <- diff(range(cum.amt[c(wp,FALSE)]))/ diff(range(set$dop[wp])) # Purchase dates and the date of last consumption dof <- c( set$dop, set$dop[np]+set$amt[np]/avg.slp ) # Cumulative time since first cum.tim <- dof - set$dop[1] # The only time without drug is after last dispense expired off <- rep( c(FALSE,TRUE), c(length(dof)-1,1) ) return( data.frame( id = set$id[1], dof = dof, cum.amt = cum.amt, cum.tim = cum.tim, off = off ) ) # will be used in the subsequent code } ) ) } ###################################################################### # Function to interpolate the drug exposures to the dates of FU. dex.int <- function( set, breaks, lags, lag.dec ) { dof <- NULL # If only one record return null if( nrow(set) < 2 ) return( NULL ) # All values of these are identical within each set (=person) doe <- set$doe[1] dox <- set$dox[1] # The first date of drug exposure according to the assumption doi <- min(set$dof) # Breakpoints and the entry end exit dates are the dates we care for # - but only within breaks doin <- max( min(breaks), doe ) doex <- min( max(breaks), dox ) breaks <- sort( unique( c(breaks,doin,doex) ) ) # only the breaks inside the follow-up interval xval <- breaks[breaks>=doin & breaks<=doex] if( length(xval) == 0 ) return( NULL ) # Merge a) the purchase dates (set$dof) and # indicator being off drug (set$off) and # the date a person goes off drug, doff (set to NA for remaining records) # with b) the break dates (which is where we want things computed) # Note we merge on the variable dof and have the data frame with # dof=xval as the >first< so that values of xval will be in the # resulting dfr$dof even if dof-values in set are almost equal til # an xval value. Ensures that sum(dfr$dof %in% xval)==length(xval) dfr <- merge( data.frame( id = set$id[1], dof = xval ), data.frame( set[,c("id","dof","off")], doff = ifelse(set$off,set$dof,NA) ), all=TRUE ) # carry the off drug indicator forward to all break dates dfr$off <- zoo::na.locf( dfr$off, na.rm=FALSE ) # possible NAs are before any drug purchase hence off-drug dfr$off <- ifelse( is.na(dfr$off), TRUE, dfr$off ) # carry date of going off drug forward, but only for the off period dfr$doff <- zoo::na.locf( dfr$doff, na.rm=FALSE ) * ifelse(dfr$off,1,NA) # time from cessation can now be computed dfr$tfc <- dfr$dof - dfr$doff # time from initiation of drug dfr$tfi <- pmax( 0, dfr$dof-doi ) # restrict to the desired timepoints dfr <- subset( dfr, dof %in% xval ) dfr <- dfr[!duplicated(dfr$dof),] # linear interpolation of the cumulative dose and time from the # purchase data (set) dfr$cdos <- approx( set$dof, set$cum.amt, xout=xval, rule=2 )$y dfr$ctim <- approx( set$dof, set$cum.tim, xout=xval, rule=2 )$y # the same for the desired lags for( lg in lags ) dfr[,paste( "lag.pre", formatC(lg,format="f",digits=lag.dec), sep="" )] <- approx( set$dof, set$cum.amt, xout=xval-lg, rule=2 )$y dfr$doff <- zoo::na.locf( dfr$doff, na.rm=FALSE ) dfr$tfc[is.na(dfr$tfc)] <- 0 dfr$dur <- c( diff(dfr$dof), NA ) return( dfr[-nrow(dfr),] ) } ###################################################################### # The function that ties it all together gen.exp <- function( purchase, id="id" , dop="dop", amt="amt", dpt="dpt", fu, doe="doe", dox="dox", breaks, use.dpt = ( dpt %in% names(purchase) ), push.max = Inf, rm.dose = FALSE, lags = NULL, lag.dec = 1, lag.pre = "lag.", pred.win = Inf ) { # to aviod a NOTE from R CMD check dof <- NULL # Make sure that the data frames have the right column names wh <- match( c(id,dop,amt), names(purchase) ) if( any( is.na(wh) ) ) stop("Wrong column names for the purchase data frame") names( purchase )[wh] <- c("id","dop","amt") # Allow dpt to be entered as numerical scalar common for all records if( use.dpt ) if( is.numeric(dpt) ) { if( length(dpt) > 1 ) stop("If dpt is numeric it must have length 1\n", "otherwise it must be the name of the dpt variable in the dataset") purchase$dpt <- dpt } else names( purchase )[match(dpt,names(purchase))] <- "dpt" wh <- match( c(id,doe,dox), names(fu) ) if( any( is.na(wh) ) ) stop("Wrong column names for the follow-up data frame") names( fu )[wh] <- c("id","doe","dox") if( use.dpt ) { tmp.dfr <- use.amt.dpt( purchase, push.max = push.max, rm.dose = rm.dose ) } else { tmp.dfr <- use.only.amt( purchase, pred.win = pred.win ) } # Having done what needs to be done about the purchase records we turn # to the follow-up records, but we first need to accommodate the fact # that there might be more fu records per person: # Generate record no within id in fu (ordering in fu is immaterial) fu$no <- ave( fu$id, fu$id, FUN=function(x) 1:length(x) ) # Set up the object to collect the resulting follow-up res <- NULL # loop through subsets of fu with different ids for( ni in 1:max(fu$no) ) { # Merge the follow-up period for the persons to the correponding # exposure records (hence the all.y=T) tm.dfr <- merge( tmp.dfr, fu[fu$no==ni,], by="id", all.y=TRUE ) # Interpolate to find the cumulative doses at the dates in the vector breaks res.dfr <- do.call( "rbind", lapply( split( tm.dfr, tm.dfr$id ), dex.int, breaks, lags, lag.dec ) ) # end of do.call res <- rbind( res, res.dfr ) # append to result from other fu$no } # end of for( ni in 1:max(fu$no) ) var.order <- c("id","dof","dur","off","doff","tfc","tfi","ctim","cdos", names(res)[grep("lag.prefix",names(res))] ) res <- res[order(res$id,res$dof),var.order] names(res) <- gsub( "lag.prefix", lag.pre, names(res) ) res } # end of gen.ex Epi/R/list.lex.R0000644000176200001440000000057513562341466013076 0ustar liggesuserslist.lex <- function( Lx, dig, sh="_" ) { wh <- c("lex.id",timeScales(Lx),"lex.dur","lex.Cst","lex.Xst") oth <- setdiff(names(Lx),wh) tmpLx <- Lx[,c(wh,oth)] wh.num <- sapply(tmpLx,is.numeric) tmpLx[,wh.num] <- round(tmpLx[,wh.num],dig) names(tmpLx) <- gsub("lex.",sh,names(tmpLx)) print( tmpLx, row.names=FALSE ) return( NULL ) } Epi/R/lls.R0000644000176200001440000000242113052220176012102 0ustar liggesuserslls <- # A function that expands the functionality of ls() function( pos = 1, pat = "", all=FALSE, print=TRUE ) { # First a function that returns length/dim when you ask for it dimx <- function(dd) if (is.null(dim(dd))) length(dd) else dim(dd) # A vector of object names lll <- ls( pos=pos, pattern=pat, all.names=all ) # Are there any objects at all? if( length(lll) > 0 ) { obj.mode <- obj.clas <- obj.dimx <- obj.size <- character(0) # Then find mode, class, name and dimension of them and return it for(i in 1:length(lll)) { obj.mode[i] <- eval( parse(text = paste( "mode(`", lll[i], "`)",sep=""))) obj.clas[i] <- paste( eval( parse(text = paste( "class(`", lll[i], "`)",sep=""))), collapse=" " ) obj.dimx[i] <- paste( eval( parse(text = paste( "dimx(`", lll[i], "`)",sep=""))), collapse=" " ) obj.size[i] <- formatC( eval( parse(text = paste("unclass(object.size(`", lll[i], "`))",sep="")))/2^10, format="f", digits=1, big.mark=",", width=14, flag=" " ) } dfr <- data.frame( name = lll, mode = obj.mode, class = obj.clas, dim = obj.dimx, sizeKbytes = obj.size, stringsAsFactors=FALSE ) names( dfr )[5] <- " size(Kb)" print( invisible( dfr ), right=FALSE ) } } Epi/R/print.floated.R0000644000176200001440000000160312531361077014071 0ustar liggesusers"print.floated" <- function(x, digits=max(3, getOption("digits") - 3), level = 0.95, ...) { K <- qnorm((1+level)/2) n <- length(x$coef) mat <- matrix("", n, 4) ci.mat <- matrix(0, n, 2) cm <- x$coefmat cat("Floating treatment contrasts for factor ", x$factor, "\n\n") mat[,1] <- names(x$coef) se <- sqrt(x$var) ci.mat[, 1] <- x$coef - K * se ci.mat[, 2] <- x$coef + K * se mat[,2] <- format(x$coef, digits=digits) mat[,3] <- format(se, digits=digits) ci.mat <- format(ci.mat, digits=digits) mat[,4] <- paste("(", ci.mat[,1], ",", ci.mat[,2], ")", sep="") dimnames(mat) <- list(rep("", n), c("Level", "Coefficient", "Std. Error", "95% Floating CI")) print(mat, quote=FALSE) cat("\nError limits over all contrasts: ", paste(format(c(0.99, x$limits), digits=2)[-1], collapse=","),"\n") } Epi/R/clogistic.R0000644000176200001440000001474113052766107013311 0ustar liggesuserssplitMatrix <- function (x, f, drop=FALSE) { lapply(split(seq_len(nrow(x)), f, drop = drop), function(ind) x[ind, , drop = FALSE]) } fixEvent <- function(event) { ### Convert outcome in clogit model to 0/1 binary coding if (any(is.na(event))) stop("Event contains missing values") if (is.logical(event)) { status <- is.numeric(event) } else if (is.numeric(event)) { status <- if (max(event) == 2) event - 1 else event temp <- (status == 0 | status == 1) if (!all(temp)) { warning("If outcome is numeric then it must be coded 0/1 or 1/2") } } else if (is.factor(event)) { if (nlevels(event) != 2) stop("If outcome is a factor then it must have 2 levels") status <- event == levels(event)[2] } return(as.integer(status)) } isInformative <- function(Xsplit, ysplit, strata) { ## Identify which observations are informative in a conditional ## logistic regression. is.homogeneous <- function(x) { all(x==x[1]) } y.bad <- sapply(ysplit, is.homogeneous) X.bad <- sapply(Xsplit, function(x) { all(apply(x, 2, is.homogeneous)) }) is.informative <- vector("list", length(ysplit)) for (i in seq(along=is.informative)) { canuse <- (!y.bad[i]) && (!X.bad[i]) is.informative[[i]] <- rep(canuse, length(ysplit[[i]])) } return(unsplit(is.informative, strata)) } fitClogit <- function(X, y, offset, strata, init, iter.max, eps, toler.chol) { ## Safe wrapper around the C function "clogit" that ensures all ## arguments have the correct type and storage mode. y <- fixEvent(y) if (!is.matrix(X)) { X <- as.matrix(X) } if (!is.double(X)) { X <- matrix(as.double(X), nrow(X), ncol(X)) } if (is.null(offset)) { offset <- rep(0, nrow(X)) } offset <- as.double(offset); ## Split into strata Xsplit <- splitMatrix(X, strata, drop=TRUE) ysplit <- split(y, strata, drop=TRUE) osplit <- split(offset, strata, drop=TRUE) info <- isInformative(Xsplit, ysplit, strata) if (!any(info)) { stop("There are no informative observations") } ans <- .Call(C_clogit, Xsplit, ysplit, osplit, as.double(init), as.integer(iter.max), as.double(eps), as.double(toler.chol)) ans$informative <- info return(ans) } clogistic <- function (formula, strata, data, subset, na.action, init, model = TRUE, x = FALSE, y = TRUE, contrasts = NULL, iter.max=20, eps=1e-6, toler.chol = sqrt(.Machine$double.eps)) { ## User interface, edited version of glm call <- match.call() if (missing(data)) data <- environment(formula) mf <- match.call(expand.dots = FALSE) m <- match(c("formula", "data", "subset", "na.action", "offset", "strata"), names(mf), 0L) mf <- mf[c(1, m)] mf$drop.unused.levels <- TRUE mf[[1L]] <- as.name("model.frame") mf <- eval(mf, parent.frame()) mt <- attr(mf, "terms") Y <- model.response(mf, "any") if (is.null(Y)) stop("missing outcome") if (length(dim(Y)) == 1L) { nm <- rownames(Y) dim(Y) <- NULL if (!is.null(nm)) names(Y) <- nm } X <- if (!is.empty.model(mt)) model.matrix(mt, mf, contrasts) else stop("Invalid model matrix") offset <- as.vector(model.offset(mf)) if (!is.null(offset)) { if (length(offset) != NROW(Y)) stop(gettextf("number of offsets is %d should equal %d (number of observations)", length(offset), NROW(Y)), domain = NA) } strata <- model.extract(mf, "strata") if (is.null(strata)) stop("argument 'strata' missing") contrasts <- attr(X, "contrasts") if (attr(mt, "intercept") > 0) { X <- X[,-1, drop=FALSE] } if (missing(init)) init <- rep(0, ncol(X)) if (iter.max < 0) stop("'iter.max' must be non-negative") if (eps <= 0) stop("'eps' must be positive") if (toler.chol <= 0) stop("'toler.chol' must be positive") if (eps < toler.chol) stop("'toler.chol' must be smaller than 'eps'") fit <- fitClogit(X = X, y = Y, offset = offset, strata=strata, init=init, toler.chol=toler.chol, eps=eps, iter.max=iter.max) if (fit$flag <= 0) { stop("Information matrix is not positive definite") } else if (fit$flag == 1000) { warning("Iteration limit exceeded") } nvar <- length(init) which.sing <- if (fit$flag < nvar) { diag(fit$var)==0 } else { rep(FALSE, nvar) } fit$coefficients[which.sing] <- NA fit$flag <- NULL ## Add back in parameter names cfnames <- colnames(X) names(fit$coefficients) <- cfnames dimnames(fit$var) <- list(cfnames, cfnames) fit$n <- sum(fit$informative) if (model) { fit$model <- mf } else { ## Without model frame this cannot be interpreted fit$informative <- NULL } fit$na.action <- attr(mf, "na.action") if (x) fit$x <- X if (!y) fit$y <- NULL fit <- c(fit, list(call = call, formula = formula, terms = mt, contrasts = contrasts, xlevels = .getXlevels(mt, mf))) class(fit) <- c("clogistic") fit } coef.clogistic <- function(object,...) { object$coefficients } vcov.clogistic <- function(object, ...) { object$var } print.clogistic <- function (x, digits = max(options()$digits - 4, 3), ...) { ## Print method for clogistic objects, edited from print.coxph cat("\nCall: ", deparse(x$call), "\n\n", sep="\n") savedig <- options(digits = digits) on.exit(options(savedig)) coef <- coef.clogistic(x) se <- sqrt(diag(vcov.clogistic(x))) if (is.null(coef) | is.null(se)) stop("Input is not valid") coefmat <- cbind(coef, exp(coef), se, coef/se, signif(1 - pchisq((coef/se)^2, 1), digits - 1)) dimnames(coefmat) <- list(names(coef), c("coef", "exp(coef)", "se(coef)", "z", "p")) cat("\n") prmatrix(coefmat) logtest <- -2 * (x$loglik[1] - x$loglik[2]) if (is.null(x$df)) df <- sum(!is.na(coef)) else df <- round(sum(x$df), 2) cat("\n") cat("Likelihood ratio test=", format(round(logtest, 2)), " on ", df, " df,", " p=", format(1 - pchisq(logtest, df)), ", n=", x$n, sep = "") cat("\n") invisible() } Epi/R/Icens.R0000644000176200001440000000620012531361077012357 0ustar liggesusersIcens <- function(first.well, last.well, first.ill, formula, model.type=c("MRR","AER"), breaks, boot=FALSE, alpha=0.05, keep.sample=FALSE, data) { ## Create follow-up matrix containing three event times fu.expression <- substitute(cbind(first.well, last.well, first.ill)) fu <- if (missing(data)) { eval(fu.expression) } else { eval(fu.expression, data) } ## Check consistency of arguments missing.f1 <- is.na(fu[,1]) missing.f2 <- is.na(fu[,2]) if (any(missing.f1 & missing.f2)) { stop("You must supply at least one of \"first.well\" and \"last.well\"") } if (any(fu[,1] > fu[,2], na.rm=TRUE) | any(fu[,2] > fu[,3], na.rm=TRUE)) { stop("Some units do not meet: first.well < last.well < first.ill" ) } ## Fill in any gaps fu[,1][missing.f1] <- fu[,2][missing.f1] fu[,2][missing.f2] <- fu[,1][missing.f2] ## Recensor cases that fall after the last break point is.censored <- fu[,3] > max(breaks) is.censored[is.na(is.censored)] <- FALSE fu[is.censored,3] <- NA exp.dat <- expand.data(fu, formula, breaks, data) model.type <- match.arg(model.type) if (missing(formula)) { fit.out <- with(exp.dat, fit.baseline(y, rates.frame)) lambda <- coef(fit.out) } else { fit.out <- switch(model.type, "MRR"=with(exp.dat, fit.mult(y, rates.frame, cov.frame)), "AER"=with(exp.dat, fit.add(y, rates.frame, cov.frame))) lambda <- coef(fit.out$rates) } beta <- if (is.null(fit.out$cov)) numeric(0) else coef(fit.out$cov) params <- c(lambda,beta) if (boot) { nboot <- ifelse (is.numeric(boot), boot, 100) boot.coef <- matrix(NA, nrow=nboot, ncol=length(lambda) + length(beta)) colnames(boot.coef) <- names(params) for (i in 1:nboot) { subsample <- sample(nrow(fu), replace=TRUE) exp.dat <- expand.data(fu[subsample,], formula, breaks, data[subsample,]) if (missing(formula)) { sim.out <- with(exp.dat, fit.baseline(y, rates.frame, params)) boot.coef[i,] <- coef(sim.out) } else { sim.out <- switch(model.type, "MRR"=with(exp.dat, fit.mult(y, rates.frame, cov.frame, params)), "AER"=with(exp.dat, fit.add(y, rates.frame, cov.frame, params))) boot.coef[i,] <- switch(model.type, "MRR"=c(coef(sim.out[[1]]), coef(sim.out[[2]])), "AER"=coef(sim.out[[1]])) } } ci.quantiles=c(0.5, alpha/2, 1 - alpha/2) boot.ci <- t(apply(boot.coef,2,quantile,ci.quantiles)) lower.ci.lab <- paste("lower ", formatC(100 * alpha/2, format="f", digits=1),"%", sep="") upper.ci.lab <- paste("upper ", formatC(100 * (1-alpha/2), format="f", digits=1),"%", sep="") colnames(boot.ci) <- c("median", lower.ci.lab, upper.ci.lab) fit.out$boot.ci <- boot.ci if (keep.sample) { fit.out$sample <- boot.coef } } class( fit.out ) <- "Icens" attr( fit.out, "model" ) <- model.type return( fit.out ) } Epi/R/simLexis.R0000644000176200001440000002747013451655454013136 0ustar liggesusers# First the utility functions ###################################################################### lint <- function( ci, tt, u ) { # Makes a linear interpolation, but does not crash if all ci values are # identical, but requires that both ci and tt are non-decreasing. # ci plays the role of cumulative intensity, tt of time if( any( diff(ci)<0 ) | any( diff(tt)<0 ) ) stop("Non-increasing arguments") c.u <- min( c( ci[ci>u], max(ci) ) ) c.l <- max( c( ci[ciu], max(tt) ) ) t.l <- max( c( tt[ci1 ) stop( "More than one lex.Cst present:\n", cst, "\n" ) # Expand each person by the time points prfrm <- nd[rep(1:nr,each=np),] prfrm[,tS] <- prfrm[,tS] + rep(time.pts,nr) prfrm$lex.dur <- il <- min( diff(time.pts) ) # Poisson-models should use the estimated rate at the midpoint of the # intervals, and have risk time equal to 1 in order to accommodate # both poisson and poisreg families - they only produce identical # predictions if lex.dur is 1 (i.e. offset is 0), scaling is after prediction prfrp <- prfrm prfrp[,"lex.dur"] <- 1 prfrp[,tS] <- prfrp[,tS]+il/2 # Make a data frame with predicted rates for each of the transitions # out of this state for these times rt <- data.frame( lex.id = prfrm$lex.id ) for( i in 1:length(Tr[[cst]]) ) { if( inherits( Tr[[cst]][[i]], "glm" ) ) rt <- cbind( rt, predict( Tr[[cst]][[i]], type="response", newdata=prfrp ) * il ) # scaled to interval else if( inherits( Tr[[cst]][[i]], "coxph" ) ) rt <- cbind( rt, predict( Tr[[cst]][[i]], type="expected", newdata=prfrm ) ) else if( is.function( Tr[[cst]][[i]] ) ) rt <- cbind( rt, Tr[[cst]][[i]](prfrm) ) else stop( "Invalid object supplied as transition, elements of the list must be either:\n", "- a glm(poisson) object fitted to a Lexis object\n", "- a coxph object fitted to a Lexis object\n", "- a function that takes a Lexis object as argument and returns\n", " average rates for each record in the same units as lex.dur.") } names( rt )[-1] <- names( Tr[[cst]] ) # Then find the transition time and exit state for each person: xx <- match( c("lex.dur","lex.Xst"), names(nd) ) if( any(!is.na(xx)) ) nd <- nd[,-xx[!is.na(xx)]] merge( nd, do.call( rbind, lapply( split( rt, rt$lex.id ), sim1, time.pts ) ), by="lex.id" ) } ###################################################################### get.next <- function( sf, tr.st, tS, tF ) { # Produces an initial Lexis object for the next simulation for those # who have ended up in a transient state. # Note that this exploits the existence of the "time.since" attribute # for Lexis objects and assumes that a character vector naming the # transient states is supplied as argument. if( nrow(sf)==0 ) return( sf ) nxt <- sf[sf$lex.Xst %in% tr.st,] if( nrow(nxt) == 0 ) return( nxt ) nxt[,tS] <- nxt[,tS] + nxt$lex.dur wh <- tF for( i in 1:length(wh) ) if( wh[i] != "" ) nxt[nxt$lex.Xst==wh[i],tS[i]] <- 0 nxt$lex.Cst <- nxt$lex.Xst return( nxt ) } ###################################################################### chop.lex <- function( obj, tS, cens ) { # A function that chops off all follow-up beyond cens since entry for # each individual # Entry times on 1st timescale zz <- entry( obj, 1, by.id=TRUE ) # Merge with the revised exit times on this timescale ww <- merge( obj, data.frame( lex.id = as.numeric(names(zz)), cens = zz+cens ) ) # Only retain records with an entry time prior to the revised exit time ww <- ww[ww[,tS[1]] < ww$cens,] # Revise the duration according the the revised exit time x.dur <- pmin( ww$lex.dur, ww[,"cens"]-ww[,tS[1]] ) # Change lex.Xst to lex.Cst for those with shortened follow-up ww$lex.Xst[x.dur0] nt <- length(tt) warning("\nSome initiators start in a absorbing state\n", "Initiator states represented are: ", paste( rbind( names(tt), rep(":",nt), paste(tt), rep(" ",nt) ), collapse="" ), "\n", "Transient states are: ", paste( names( Tr ), coll=" " ) ) if( nrow(nxt)==0 ) stop( "\nNo initiators in transient states!" ) } # Then we update those who are in a transient states and keep on doing # that till all are in absorbing states or censored while( nrow(nxt) > 0 ) { nx <- do.call( rbind.data.frame, lapply( split( nxt, nxt$lex.Cst ), simX, Tr, time.pts, tS ) ) sf <- rbind.data.frame( sf, nx ) nxt <- get.next( nx, tr.st, tS, tF ) } # Doctor lex.Xst levels, fix values for the censored sf$lex.Xst <- factor( sf$lex.Xst, levels=levels(sf$lex.Cst) ) sf$lex.Xst[is.na(sf$lex.Xst)] <- sf$lex.Cst[is.na(sf$lex.Xst)] # Nicely order the output by persons, then times and states nord <- match( c( "lex.id", tS, "lex.dur", "lex.Cst", "lex.Xst" ), names(sf) ) noth <- setdiff( 1:ncol(sf), nord ) sf <- sf[order(sf$lex.id,sf[,tS[1]]),c(nord,noth)] rownames(sf) <- NULL # Finally, supply attributes - note we do not supply the "breaks" # attribute as this is irrelevant for simulated objects attr( sf, "time.scales" ) <- tS attr( sf, "time.since" ) <- tF chop.lex( sf, tS, max(time.pts) ) } ###################################################################### nState <- function ( obj, at, from, time.scale = 1 ) { # Counts the number of persons in each state of the Lexis object 'obj' # at the times 'at' from the time 'from' in the time scale # 'time.scale' # Determine timescales and absorbing and transient states tS <- check.time.scale(obj,time.scale) TT <- tmat(obj) absorb <- rownames(TT)[apply(!is.na(TT),1,sum)==0] transient <- setdiff( rownames(TT), absorb ) # Expand each record length(at) times tab.frm <- obj[rep(1:nrow(obj),each=length(at)), c(tS,"lex.dur","lex.Cst","lex.Xst")] # Stick in the corresponding times on the chosen time scale tab.frm$when <- rep( at, nrow(obj) ) + from # For transient states keep records that includes these points in time tab.tr <- tab.frm[tab.frm[,tS] <= tab.frm$when & tab.frm[,tS]+tab.frm$lex.dur > tab.frm$when,] tab.tr$State <- tab.tr$lex.Cst # For absorbing states keep records where follow-up ended before tab.ab <- tab.frm[tab.frm[,tS]+tab.frm$lex.dur <= tab.frm$when & tab.frm$lex.Xst %in% absorb,] tab.ab$State <- tab.ab$lex.Xst # Make a table using the combination of those in transient and # absorbing states. with( rbind( tab.ab, tab.tr ), table( when, State ) ) } ###################################################################### pState <- function( nSt, perm=1:ncol(nSt) ) { # Compute cumulative proportions of persons across states in order # designate by 'perm' tt <- t( apply( nSt[,perm], 1, cumsum ) ) tt <- sweep( tt, 1, tt[,ncol(tt)], "/" ) class( tt ) <- c("pState","matrix") tt } ###################################################################### plot.pState <- function( x, col = rainbow(ncol(x)), border = "transparent", xlab = "Time", ylim = 0:1, ylab = "Probability", ... ) { # Function to plot cumulative probabilities along the time scale. matplot( as.numeric(rownames(x)), x, type="n", ylim=ylim, yaxs="i", xaxs="i", xlab=xlab, ylab=ylab, ... ) lines.pState( x, col = col, border = border, ... ) } ###################################################################### lines.pState <- function( x, col = rainbow(ncol(x)), border = "transparent", ... ) { # Function to plot cumulative probabilities along the time scale. # Fixing the colors: nc <- ncol(x) col <- rep( col , nc )[1:nc] border <- rep( border, nc )[1:nc] # Just for coding convenience when plotting polygons pSt <- cbind( 0, x ) for( i in 2:ncol(pSt) ) { polygon( c( as.numeric(rownames(pSt)) , rev(as.numeric(rownames(pSt))) ), c( pSt[,i ], rev(pSt[,i-1]) ), col=col[i-1], border=border[i-1], ... ) } } Epi/R/contr.orth.R0000644000176200001440000000040712531361077013421 0ustar liggesuserscontr.orth <- function( n ) { if( is.numeric( n ) && length( n )==1 ) levs <- 1:n else { levs <- n n <- length( n ) } Z <- contr.sum( n ) L <- 1:n - mean(1:n) contr <- Z - L%*%( ( t(L) %*% L )^(-1) ) %*% ( t(L) %*% Z ) contr[,1:(n-2)] } Epi/R/clear.R0000644000176200001440000000072312773674456012430 0ustar liggesusers# Clear the workspace of all objects whose names don't start with a # full stop, and remove objects attached immediately after the global clear <- function () { env <- as.environment(1) to.go <- ls(env, all.names = FALSE) continue <- TRUE while (continue) { nxt <- search()[[2]] if (substr(nxt, 1, 8) != "package:") detach() else continue <- FALSE } remove(list = to.go, envir = env) } Epi/R/summary.Lexis.r0000644000176200001440000000641613430534203014137 0ustar liggesuserssummary.Lexis <- function( object, simplify=TRUE, scale=1, by=NULL, Rates=FALSE, timeScales=FALSE, ... ) { # If we have a by argument find out what to do if (!is.null(by)) { if (is.character(by)) { if (!all(by %in% names(object))) stop("Wrong 'by' argument: '", paste(by,collapse="','"), "' - must be name(s) of variable(s) in the Lexis object") else res <- lapply(split(object, object[, by]), summary.Lexis, by = NULL, simplify = simplify, scale = scale, Rates = Rates, timeScales=timeScales, ...) } else { if (length(by) != nrow(object)) stop("Wrong length of 'by' argument:", length(by), "must be same length as rows of the Lexis object:", nrow(object) ) else res <- lapply(split(object, by), summary.Lexis, by = NULL, simplify = simplify, scale = scale, Rates = Rates, timeScales=timeScales, ...) } # to avoid printing the time scale information repeatedly for( i in 1:(length(res)-1) ) res[[i]]$timeScales <- NULL return( res ) } # Table(s) of all transitions (no. records) tr <- trans <- with( object, table(lex.Cst,lex.Xst) ) # Remove diagonal, i.e. records with no transition for( i in intersect(rownames(trans),colnames(trans)) ) tr[i,i] <- 0 # Margins added trans <- addmargins(trans) tr <- addmargins(tr) # Sum omitting the diagonal trm <- tr[,ncol(tr)] # Compute person-years in each Cst-state pyrs <- with( object, addmargins( tapply( lex.dur,lex.Cst,sum,na.rm=TRUE), FUN=function(x) sum(x,na.rm=TRUE) ) )/scale pers <- with( object, c( tapply( lex.id, lex.Cst, function(x) length(unique(x)) ), length(unique(lex.id)) ) ) # Amend the table of records with column of events and person-years trans <- cbind( trans, trm, pyrs, pers ) # Annotate the table nicely colnames( trans )[ncol(trans)-2:0] <- c(" Events:","Risk time:"," Persons:" ) colnames( trans )[ncol(tr)] <- " Records:" names( dimnames( trans ) ) <- c("From","\nTransitions:\n To") # Make the rates and annotate the table nicely rates <- sweep( tr, 1, pyrs, "/" ) colnames( rates )[ncol(rates)] <- "Total" names( dimnames( rates ) ) <- c("From", paste("\nRates", if( scale != 1 ) paste(" (per ",scale,")",sep=""), ":\n To", sep="") ) if( simplify ) { trans <- trans[!is.na(pyrs),] rates <- rates[!is.na(pyrs),] } if( nrow(trans)==2 ) trans <- trans[1,,drop = FALSE] res <- list( Transitions = trans, Rates = rates[-nrow(rates),,drop=FALSE], timeScales = timeSince(object) ) if( !timeScales ) res <- res[-3] if( !Rates ) res <- res[-2] class( res ) <- "summary.Lexis" res } print.summary.Lexis <- function( x, ..., digits=2 ) { print( round( x$Transitions, digits ) ) if( "Rates" %in% names(x) ) print( round( x$Rates , digits ) ) # if( "timeScales" %in% names(x) ) if( !is.null(x$timeScales) ) { cat("\nTimescales:\n") print( x$timeScales ) } } Epi/R/fit.baseline.R0000644000176200001440000000065012531361077013664 0ustar liggesusersfit.baseline <- function(y, rates.frame, start) { if (missing(start)) { ## Get starting values from logistic regression model glm.out.init <- glm(y~., family=binomial, data=rates.frame) mu.init <- fitted(glm.out.init, type="response") glm(y~-1 + ., family=binomial(link=log), data=rates.frame, mustart=mu.init) } else { glm(y~-1 + ., family=binomial(link=log), data=rates.frame, start=start) } } Epi/R/summary.Icens.r0000644000176200001440000000140712531361077014117 0ustar liggesuserssummary.Icens <- function( x, scale=1, ... ) { if( attr( x, "model" ) == "MRR" ) { if( is.null( x$rates ) ) { class( x ) <- "glm" emat <- ci.lin( x ) } else { rate.est <- ci.lin( x$rates ) rate.est[,-(3:4)] <- rate.est[,-(3:4)] * scale emat <- rbind( cbind( rate.est, RR=NA )[,c(1:4,7,5:6)], ci.lin( x$cov, Exp=T ) ) } } if( attr( x, "model" ) == "AER" ) { rate.est <- ci.lin( x$rates ) rate.est[,-(3:4)] <- rate.est[,-(3:4)] * scale emat <- rate.est } if( length( x ) == 4 ) { b.est <- x[["boot.ci"]] colnames( b.est ) <- c( "Boot-med", "lo", "hi" ) emat <- cbind( emat, b.est ) } emat } Epi/R/stackedCIF.R0000644000176200001440000000354413564775635013306 0ustar liggesusersstackedCIF <- function( x, group = 1, col = "black", fill = "white", ylim = c(0,1), xlab = "Time", ylab = "Cumulative incidence", ...) { ne <- ncol(x$pstate) - 1 ng <- length(x$n) if (group %in% 1:ng) { r1 <- ifelse(group == 1 | ng == 1, 1, cumsum(x$strata)[group - 1] + 1) r2 <- ifelse(ng == 1, length(x$time), cumsum(x$strata)[group]) pSt0 <- matrix(0, nrow = nrow(x$pstate[r1:r2, ]), ncol = ne + 2) pSt0[, 1] <- x$pstate[r1:r2, 2] for (c in 2:ne) pSt0[, c] <- pSt0[, c - 1] + x$pstate[r1:r2, c+1] pSt0[, ne + 1] <- 1 pSt0[, ne + 2] <- x$time[r1:r2] pSt <- cbind(0, pSt0) pSt2 <- matrix(0, nrow = 2 * (dim(pSt)[1] - 1), ncol = dim(pSt)[2]) pSt2[1, ne + 3] <- pSt[1, ne + 3] pSt2[nrow(pSt2), ne + 3] <- pSt[nrow(pSt), ne + 3] for (j in 1:(dim(pSt)[1] - 1)) { pSt2[2 * j - 1, ne + 3] <- pSt[j, ne + 3] pSt2[2 * j, ne + 3] <- pSt[j + 1, ne + 3] pSt2[2 * j - 1, 1:(ne + 2)] <- pSt[j, 1:(ne + 2)] pSt2[2 * j, 1:(ne + 2)] <- pSt[j, 1:(ne + 2)] } plot(as.numeric(pSt0[, ne + 2]), pSt0[, 2], type = "n", ylim = ylim, yaxs = "i", xlab = xlab, ylab = ylab, ...) for (i in 2:(ne + 1)) { polygon(c(pSt2[, ne + 3], rev(pSt2[, ne + 3])), c(pSt2[, i], rev(pSt2[, i - 1])), col = fill[i - 1], border = NULL, ...) } matlines( as.numeric(pSt0[, ne + 2]), pSt0[, 1:ne], type = "s", col = col) abline(v = max(x$time[r1:r2]), lwd = 2, col = "white") box() } else print(paste("Error: group indicator must be an integer from 1 to", ng)) } Epi/R/addCov.Lexis.R0000644000176200001440000001067614015422370013606 0ustar liggesusers# The addCov method addCov <- function (Lx, ...) UseMethod("addCov") addCov.default <- addCov.Lexis <- function(Lx, clin, timescale = 1, exnam, tfc = "tfc") { # Function to add clinically measured covariates to a Lexis object # The point is to cut the Lexis object at the examination dates # and subsequently add the clinical records # to avoid notes in check org.Cst <- NULL org.Xst <- NULL lex.Cst <- NULL lex.Xst <- NULL # ...but first the usual cheking of paraphernalia if(!inherits(Lx ,"Lexis")) stop("Lx must be a Lexis object.\n") if( inherits(clin,"Lexis")) stop("clin cannot be a Lexis object.\n") # Is the timescale argument a timescale in Lx and is it a variable in clin? ts <- if(is.numeric(timescale)) timeScales(Lx)[timescale] else timescale if(!(ts %in% timeScales(Lx))) stop("timescale argument (", ts, ") must be among the timescales in the Lexis object ", deparse(substitute(Lx)),":", timeScales(Lx), ".\n" ) clin.nam <- deparse(substitute(clin)) if( !( ts %in% names(clin) & "lex.id" %in% names(clin) ) ) stop("'lex.id' and timescale '", ts, "' must be variables in the clin object ", clin.nam, "\n" ) # order clin to get the possible construction of examination names ok clin <- clin[order(clin$lex.id, clin[,ts]),] # check that examination dates are unique within persons if(any(dd <- duplicated(clin[,c("lex.id",ts)]))) { warning("Examination dates must be unique within persons\n", sum(dd), " records with duplicate dates from clin object ", clin.nam, " excluded.") clin <- clin[!dd,] } # the variable holding the name of the examination if(missing(exnam)) exnam <- "exnam" # and if it is not there, construct it if(!(exnam %in% names(clin))) clin[,exnam] <- paste("ex", ave(clin$lex.id, clin$lex.id, FUN = function(x) cumsum(x/x)), sep="" ) # exnam cannot have values that are also states if( length(common <- intersect(levels(Lx), unique(clin[,exnam]))) ) stop("Levels of Lx and examination names in clin must be disjoint", "\nbut", paste(common, collapse=", "), "are in both") #...done checking # variables to merge by mvar <- c("lex.id", ts) # clinical variables to be merged in # --- note we take examination date and name as a cinical variable too cvar <- setdiff(names(clin), mvar) # A data frame of cutting times of the examinations cfr <- data.frame(lex.id = clin$lex.id, cut = clin[,ts], new.state = clin[,exnam]) # a copy of Lx with a saved copy of the state variables in org. Lc <- transform(Lx, org.Cst = lex.Cst, org.Xst = lex.Xst) # Now cut Lc at each new examination date, state variables will be # changed to examination names Lc <- rcutLexis(Lc, cut = cfr, timescale = ts) # Lc now has the exnam in the variable lex.Cst, so we can merge the # clinical data to this if we rename to exnam # the lex.Cst contains the examination name, except where # the original levels are left Lc[,exnam] <- as.factor(ifelse(Lc$lex.Cst %in% levels(Lx), NA, as.character(Lc$lex.Cst))) mvar <- c("lex.id", exnam) # timescale is present in both Lc and clin, # so rename in clin, it will be the date of clin names(clin)[grep(ts, names(clin))] <- tfc # merge with clinical measurements keeping the attributes att.Lc <- attributes(Lc) Lc <- left_join(Lc, clin, by = mvar) att.Lc$names <- attributes(Lc)$names # attributes(Lc) <- att.Lc # compute time since last examination Lc[,tfc] <- Lc[,ts] - Lc[,tfc] # we have problems if a clical date falls in an interval # ending with a transition, they need to be fixed: wh <- with(Lc, which(c(org.Xst[-nrow(Lc)] != org.Cst[-1] & lex.id [-nrow(Lc)] == lex.id [-1]))) Lc$org.Xst[wh] <- Lc$org.Cst[wh+1] # move the original states back Lc <- select(Lc, -lex.Cst, -lex.Xst) %>% rename(lex.Cst = org.Cst, lex.Xst = org.Xst) # Add tfc as a time.scale, time.since and breaks: attr(Lc, "time.scales") <- c(attr(Lx, "time.scales"), tfc) attr(Lc, "time.since" ) <- c(attr(Lx, "time.since" ), "" ) brt <- list(x = NULL) names(brt) <- tfc attr(Lc, "breaks") <- c(attr(Lx, "breaks"), brt) attr(Lc, "class") <- c("Lexis","data.frame") # Done! - well order first sortLexis(Lc) } Epi/R/Relevel.Lexis.R0000644000176200001440000000337314003571117014001 0ustar liggesusers# The factorize method factorize <- function (x, ...) UseMethod("factorize") # Default method is just the Lexis method factorize.default <- factorize.Lexis <- function(x, ...) { Cst <- Xst <- NULL # If lex.Cst and lex.Xst are not factors, make sure they are, and # if they are restrict levels to to actually ocurring Cst <- factor(x$lex.Cst) Xst <- factor(x$lex.Xst) all.levels <- union(levels(Cst), levels(Xst)) # then amend them to have the same set of levels x$lex.Cst <- factor(Cst, levels = all.levels) x$lex.Xst <- factor(Xst, levels = all.levels) # Note if levels changed if(length(setdiff(all.levels, levels(Cst))) > 0 | length(setdiff(all.levels, levels(Xst))) > 0) cat( "NOTE: lex.Cst and lex.Xst now have levels:\n", all.levels, "\n") return(x) } # The Lexis version of Relevel Relevel.Lexis <- function(x, ref, ...) { # Is this really a Lexis object if(!inherits(x, "Lexis")) stop("First argument must be a Lexis object") # Make sure the states are factors with the same levels if(!is.factor(x$lex.Cst) | !is.factor(x$lex.Xst)) stop("lex.Cst and lex.Xst must be factors") if(any(levels(x$lex.Xst) != levels(x$lex.Cst))) stop("lex.Cst and lex.Xst must have same levels\n", "you may want to factorize.Lexis()\n") # Then use the same Relevel on the factors x$lex.Cst <- Relevel.factor(x$lex.Cst, ref, ...) x$lex.Xst <- Relevel.factor(x$lex.Xst, ref, ...) return(x) } # The levels method is already defined (in the base package) # and hence imported in the NAMESPACE file levels.Lexis <- function( x ) { union(levels(x$lex.Cst), levels(x$lex.Xst)) } ## # The Lexis version of levels ## "levels.Lexis<-" <- ## function(x, value) ## { ## base::levels(x$lex.Cst) <- value ## base::levels(x$lex.Xst) <- value ## x ## } Epi/R/Aplot.R0000644000176200001440000000622112531361077012400 0ustar liggesusersAplot <- function( rates, age = as.numeric( dimnames( rates )[[1]] ), per = as.numeric( dimnames( rates )[[2]] ), grid = FALSE, a.grid = grid, ygrid = grid, col.grid = gray( 0.9 ), a.lim = range( age, na.rm=TRUE ), ylim = range( rates[rates>0], na.rm=TRUE ), at = NULL, labels = paste( at ), a.lab = names( dimnames( rates ) )[1], ylab = deparse( substitute( rates ) ), type = "l", lwd = 2, lty = 1, col = par( "fg" ), log.ax = "y", las = 1, c.col = col, p.col = col, c.ann = FALSE, p.ann = FALSE, xannx = 1/20, cex.ann = 0.8, c.thin = seq( 2, length( age ) + length( per ) - 1, 2 ), p.thin = seq( 1, length( per ), 2 ), p.lines = TRUE, c.lines = !p.lines, ... # arguments passed on to matlines() ) { # Plot the frame if( p.ann ) a.lim <- a.lim + c(0,diff( range( age ) ) * xannx) if( c.ann ) a.lim <- a.lim - c( diff( range( age ) ) * xannx,0) matplot( age, rates, type="n", xlim=a.lim, ylim=ylim, xlab=a.lab, ylab=ylab, log=log.ax, las=las, yaxt=if( !is.null( at ) ) "n" else "s" ) if( !is.null( at ) ) axis( side=2, at=at, labels=labels, yaxt="s", las=las ) # and the grid if required: if( !missing( a.grid ) | !missing( grid ) ) { if( is.logical( a.grid ) & a.grid[1] ) a.grid <- nice( age, log=par("xlog") ) abline( v=a.grid, col=col.grid ) } if( !missing( ygrid ) | !missing( ygrid ) ) { if( is.logical( ygrid ) & ygrid[1] ) ygrid <- nice( rates[!is.na(rates)], log=par("ylog") ) abline( h=ygrid, col=col.grid ) } box() # What lines were required? if( !missing( c.lines ) & missing( p.lines ) ) p.lines <- !c.lines # Period curves: if( p.lines ){ matlines( age, rates, type=type, lwd=lwd, lty=lty, col=p.col, ... ) # annotate them if required (every second by default): if( p.ann ) { nr <- nrow( rates ) nc <- ncol( rates ) text( rep( age[nr], nc )[p.thin], rates[nr,][p.thin], paste( "", per[p.thin] ), adj=c(0,0.5), cex=cex.ann, col=if( length(p.col)==1 ) p.col else p.col[p.thin] ) } } # Cohort curves: if( c.lines ){ # First convert the age-period table to an age-cohort frame rt <- as.table( rates ) dimnames( rt ) <- list( age = age, per = per ) rtf <- data.frame( rt ) rtf$age <- as.numeric( as.character( rtf$age ) ) rtf$per <- as.numeric( as.character( rtf$per ) ) ac <- tapply( rtf$Freq, list( rtf$age, rtf$per-rtf$age ), mean ) matlines( age, ac, type=type, lwd=lwd, lty=lty, col=c.col, ... ) # annotate them if required (every other by default): if( c.ann ) { nr <- nrow( rt ) nc <- ncol( rt ) # Find the ages, cohorts and rates where the cohort curves starts a.min <- c( rev( age ), rep( age[1], nc-1 ) ) p.min <- c( rep( per[1], nr-1 ), per ) c.min <- p.min - a.min r.min <- c(rt[nr:1,1],rt[1,2:nc]) text( a.min[c.thin], r.min[c.thin], paste( "", c.min[c.thin] ), adj=c(1,0.5), cex=cex.ann, col=if( length(c.col)==1 ) c.col else c.col[c.thin] ) } } } Epi/R/rateplot.R0000644000176200001440000001551012531361077013154 0ustar liggesusersrateplot <- function( rates, which = c("ap","ac","pa","ca"), age = as.numeric( dimnames( rates )[[1]] ), per = as.numeric( dimnames( rates )[[2]] ), grid = FALSE, a.grid = grid, p.grid = grid, c.grid = grid, ygrid = grid, col.grid = gray( 0.9 ), a.lim = range( age, na.rm=TRUE ) + c(0,diff( range( age ) )/30), p.lim = range( per, na.rm=TRUE ) + c(0,diff( range( age ) )/30), c.lim = NULL, ylim = range( rates[rates>0], na.rm=TRUE ), at = NULL, labels = paste( at ), a.lab = "Age at diagnosis", p.lab = "Date of diagnosis", c.lab = "Date of birth", ylab = "Rates", type = "l", lwd = 2, lty = 1, log.ax = "y", las = 1, ann = FALSE, a.ann = ann, p.ann = ann, c.ann = ann, xannx = 1/20, cex.ann = 0.8, a.thin = seq( 1, length( age ), 2 ), p.thin = seq( 1, length( per ), 2 ), c.thin = seq( 2, length( age ) + length( per ) - 1, 2 ), col = par( "fg" ), a.col = col, p.col = col, c.col = col, ... ) { # Remove 0 rates, in order to avoid warnings rates[rates==0] <- NA # then do the plots for( i in 1:length( which ) ) { if( toupper( which[i] ) == "AP" ) Aplot( rates, age = age, per = per, a.grid = a.grid, ygrid = ygrid, col.grid = col.grid, a.lim = a.lim, ylim = ylim, a.lab = a.lab, ylab = ylab, at = at, labels = labels, type = type, lwd = lwd, lty = lty, col = col, log.ax = log.ax, las = las, p.ann = p.ann, xannx = xannx, p.col = p.col, cex.ann = cex.ann, p.thin = p.thin, p.lines = TRUE, c.lines = FALSE, ... ) if( toupper( which[i] ) == "AC" ) Aplot( rates, age = age, per = per, a.grid = a.grid, ygrid = ygrid, col.grid = col.grid, a.lim = a.lim, ylim = ylim, a.lab = a.lab, ylab = ylab, at = at, labels = labels, type = type, lwd = lwd, lty = lty, col = col, log.ax = log.ax, las = las, c.ann = c.ann, p.ann = p.ann, xannx = xannx, c.col = c.col, p.col = p.col, cex.ann = cex.ann, c.thin = c.thin, p.lines = FALSE, c.lines = TRUE, ... ) if( toupper( which[i] ) %in% c("APC","ACP") ) Aplot( rates, age = age, per = per, a.grid = a.grid, ygrid = ygrid, col.grid = col.grid, a.lim = a.lim, ylim = ylim, a.lab = a.lab, ylab = ylab, at = at, labels = labels, type = type, lwd = lwd, lty = lty, col = col, log.ax = log.ax, las = las, c.ann = c.ann, p.ann = p.ann, xannx = xannx, c.col = c.col, p.col = p.col, cex.ann = cex.ann, c.thin = c.thin, p.thin = p.thin, p.lines = TRUE, c.lines = TRUE, ... ) if( toupper( which[i] ) == "PA" ) Pplot( rates, age = age, per = per, grid = grid, p.grid = p.grid, ygrid = ygrid, col.grid = col.grid, p.lim = p.lim, ylim = ylim, p.lab = p.lab, ylab = ylab, at = at, labels = labels, type = type, lwd = lwd, lty = lty, col = col, log.ax = log.ax, las = las, ann = a.ann, xannx = xannx, cex.ann = cex.ann, a.thin = a.thin, ... ) if( toupper( which[i] ) == "CA" ) Cplot( rates, age = age, per = per, grid = grid, c.grid = c.grid, ygrid = ygrid, col.grid = col.grid, c.lim = c.lim, ylim = ylim, c.lab = c.lab, ylab = ylab, at = at, labels = labels, type = type, lwd = lwd, lty = lty, col = col, log.ax = log.ax, las = las, ann = a.ann, xannx = xannx, cex.ann = cex.ann, a.thin = a.thin, ... ) } } Epi/R/effx.match.r0000644000176200001440000001531612531361077013411 0ustar liggesusers## Program to calculate effects for matched case-control studies ## Michael Hills ## Improved by BxC and MP ## Post Tartu 2007 version June 2007 effx.match<-function(response, exposure, match, strata=NULL, control=NULL, base=1, digits=3, alpha=0.05, data=NULL) { ## stores the variable names for response, etc. rname<-deparse(substitute(response)) ename<-deparse(substitute(exposure)) if (!missing(strata))sname<-deparse(substitute(strata)) ## The control argument is more complex, as it may be a name or ## list of names if(!missing(control)) { control.arg <- substitute(control) if (length(control.arg) > 1) { control.names <- sapply(control.arg, deparse)[-1] } else { control.names <- deparse(control.arg) } } ## If data argument is supplied, evaluate the arguments in that ## data frame. if (!missing(data)) { exposure <- eval(substitute(exposure), data) response <- eval(substitute(response), data) match <- eval(substitute(match),data) if (!missing(strata)) { strata <- eval(substitute(strata), data) } if (!missing(control)) control <- eval(substitute(control), data) } ## performs a few other checks if(rname==ename)stop("Same variable specified as response and exposure") if (!missing(strata)) { if(rname==sname)stop("Same variable specified as response and strata") if(sname==ename)stop("Same variable specified as strata and exposure") } if(!is.numeric(response))stop("Response must be numeric, not a factor") if(!missing(strata)&!is.factor(strata))stop("Stratifying variable must be a factor") tmp<-(response==0 | response==1) if(all(tmp,na.rm=TRUE)==FALSE) stop("Binary response must be coded 0,1 or NA") if(class(exposure)[1]=="ordered") { exposure<-factor(exposure, ordered=F) } ## Fix up the control argument as a named list if (!missing(control)) { if (is.list(control)) { names(control) <- control.names } else { control <- list(control) names(control) <- control.names } } ## prints out some information about variables cat("---------------------------------------------------------------------------","\n") cat("response : ", rname, "\n") cat("exposure : ", ename, "\n") if(!missing(control))cat("control vars : ",names(control),"\n") if(!missing(strata)) cat("stratified by : ",sname,"\n") cat("\n") if(is.factor(exposure)) { cat(ename,"is a factor with levels: ") cat(paste(levels(exposure),collapse=" / "),"\n") cat( "baseline is ", levels( exposure )[base] ,"\n") exposure <- Relevel( exposure, base ) } else { cat(ename,"is numeric","\n") } if(!missing(strata)) { cat(sname,"is a factor with levels: ") cat(paste(levels(strata),collapse="/"),"\n") } cat("effects are measured as odds ratios","\n") cat("---------------------------------------------------------------------------","\n") cat("\n") ## gets number of levels for exposure if a factor if(is.factor(exposure)) { nlevE<-length(levels(exposure)) } else { nlevE<-1 } ## labels the output if(is.factor(exposure)) { cat("effect of",ename,"on",rname,"\n") } else { cat("effect of an increase of 1 unit in",ename,"on",rname,"\n") } if(!missing(control)) { cat("controlled for",names(control),"\n\n") } if(!missing(strata)) { cat("stratified by",sname,"\n\n") } ## no stratifying variable if(missing(strata)) { if(missing(control)) { m<-clogit(response~exposure+strata(match)) cat("number of observations ",m$n,"\n\n") } else { m<-clogit(response~.+exposure+strata(match), subset=!is.na(exposure),data=control) cat("number of observations ",m$n,"\n\n") mm<-clogit(response~.+strata(match), subset=!is.na(exposure),data=control) } res<-ci.lin(m,subset=c("exposure"),Exp=TRUE,alpha=alpha)[,c(5,6,7)] res<-signif(res,digits) if(nlevE<3) { names(res)[1]<-c("Effect") } else { colnames(res)[1]<-c("Effect") if(is.factor(exposure)) { ln <- levels(exposure) rownames(res)[1:nlevE-1]<-paste(ln[2:nlevE],"vs",ln[1]) } } print(res) if(missing(control)) { chisq<-round(summary(m)$logtest[1],2) df<-round(summary(m)$logtest[2]) p<-round(summary(m)$logtest[3],3) cat("\n") cat("Test for no effects of exposure: ","\n") cat("chisq=",chisq, " df=",df, " p-value=",format.pval(p,digits=3),"\n") invisible(list(res,paste("Test for no effects of exposure on", df,"df:","p=",format.pval(p,digits=3)))) } else { aov <- anova(mm,m,test="Chisq") cat("\nTest for no effects of exposure on", aov[2,3],"df:", "p-value=",format.pval(aov[2,5],digits=3),"\n") invisible(list(res,paste("Test for no effects of exposure on", aov[2,3],"df:","p=",format.pval(aov[2,5],digits=3)))) } } ## stratifying variable if(!missing(strata)) { sn <- levels(strata) nlevS<-length(levels(strata)) if(missing(control)) { m<-clogit(response~strata/exposure+strata(match)) cat("number of observations ",m$n,"\n\n") mm<-clogit(response~strata+exposure+strata(match)) } else { m <-clogit(response~strata/exposure + . +strata(match), data=control) cat("number of observations ",m$n,"\n\n") mm <-clogit(response~strata+exposure + . +strata(match), data=control) } res<-ci.lin(m,Exp=TRUE,alpha=alpha,subset="strata")[c(-1:-(nlevS-1)),c(5,6,7)] res<-signif(res,digits) colnames(res)[1]<-c("Effect") if(is.factor(exposure)) { ln<-levels(exposure) newrownames<-NULL for(i in c(1:(nlevE-1))) { newrownames<-c(newrownames, paste("strata",sn[1:nlevS],"level",ln[i+1],"vs",ln[1])) } } else { newrownames<-paste("strata",sn[1:nlevS]) } rownames(res)<-newrownames aov<-anova(mm,m,test="Chisq") print( res ) cat("\nTest for effect modification on", aov[2,3],"df:","p-value=",format.pval(aov[2,5],digits=3),"\n") invisible(list(res,paste("Test for effect modification on", aov[2,3],"df:","p-value=",format.pval(aov[2,5],digits=3)))) } } Epi/R/cutLexis.R0000644000176200001440000002575713763207377013152 0ustar liggesusers doCutLexis <- function(data, cut, timescale, new.scale=FALSE ) { ## new.scale is a character constant with the name of the new timescale ## Code each new interval using new variable lex.cut: ## 0 = unchanged interval (cut occurs after exit) ## 1 = first part of split interval ## 2 = second part of split interval (or cut occurs before interval) cut[is.na(cut)] <- Inf #If a cut time is missing, it never happens ## First intervals (before the cut) in.1 <- entry(data, timescale) ex.1 <- pmin(cut, exit(data, timescale)) ## Create Lexis object for first intervals lx.1 <- data lx.1$lex.dur <- ex.1 - in.1 lx.1$lex.cut <- ifelse(cut < exit(data, timescale), 1, 0) if( new.scale ) lx.1[,"lex.new.scale"] <- NA ## Second intervals (after the cut) in.2 <- pmax(cut, entry(data, timescale)) ex.2 <- exit(data, timescale) ## Create Lexis object for second intervals lx.2 <- data lx.2$lex.dur <- ex.2 - in.2 lx.2$lex.cut <- 2 if( new.scale ) lx.2[,"lex.new.scale"] <- in.2 - cut ## Update entry times lx.2[, timeScales(data)] <- exit(data) - lx.2$lex.dur return(rbind(lx.1, lx.2)) } setStatus.default <- function(data, new.state) { data$lex.Xst[data$lex.cut == 1] <- new.state[data$lex.cut == 1] data$lex.Cst[data$lex.cut == 2] <- new.state return(data) } setStatus.numeric <- function(data, new.state, precursor.states=NULL, progressive=TRUE) { if (!is.numeric(new.state)) { stop("If lex.Cst, lex.Xst are numeric, new.state must be numeric too") } data$lex.Xst[data$lex.cut == 1] <- new.state[data$lex.cut == 1] data$lex.Cst[data$lex.cut == 2] <- new.state exit.state <- data$lex.Xst[data$lex.cut == 2] is.precursor <- exit.state %in% precursor.states if (progressive) { is.precursor <- is.precursor | (exit.state < new.state) } data$lex.Xst[data$lex.cut == 2][is.precursor] <- new.state[is.precursor] return(data) } setStatus.factor <- function( data, new.state, precursor.states=NULL, progressive=TRUE) { if (!is.character(new.state)) { stop("new.state must be a character vector, but it is ",str(new.state)) } current.states <- levels(data$lex.Cst) new.states <- setdiff(new.state,current.states) new.states <- new.states[!is.na(new.states)] ## Modify factor levels if necessary if (length(new.states) > 0) { all.states <- c(current.states, sort(new.states)) new.order <- match( c(intersect(precursor.states,current.states), new.states, setdiff(current.states,precursor.states)), all.states ) levels(data$lex.Cst) <- all.states levels(data$lex.Xst) <- all.states } data$lex.Xst[data$lex.cut == 1] <- new.state[data$lex.cut == 1] data$lex.Cst[data$lex.cut == 2] <- new.state exit.state <- data$lex.Xst[data$lex.cut==2] is.precursor <- exit.state %in% precursor.states if (progressive) { if (is.ordered(data$lex.Xst)) { is.precursor <- is.precursor | (exit.state < new.state) } else { warning("progressive=TRUE argument ignored for unordered factor") } } data$lex.Xst[data$lex.cut==2][is.precursor] <- new.state[is.precursor] # Reorder factor levels sensibly if (!progressive & length(new.states)>0){ data$lex.Cst <- Relevel( data$lex.Cst, new.order ) data$lex.Xst <- Relevel( data$lex.Xst, new.order ) } return(data) } # Added by BxC match.cut <- function( data, cut ) { if(sum(!is.na(match(c("lex.id", "cut", "new.state"), names(cut)))) < 3 ) stop("The dataframe supplied in the cut= argument must have columns", "'lex.id','cut','new.state', but the columns are:\n", names(cut)) else { if( length(unique(cut$lex.id)) < nrow(cut) ) stop("Values of 'lex.id' must be unique in the 'cut' dataframe\n", "- maybe you are looking for rcutLexis?") else zz <- merge( data[,"lex.id",drop=FALSE], cut, all.x=TRUE ) if(is.factor( data$lex.Cst)) zz$new.state <- as.character(zz$new.state) if(is.numeric(data$lex.Cst)) zz$new.state <- as.numeric(zz$new.state) return( zz ) } } # End of addition / change cutLexis <- function(data, cut, timescale = 1, new.state = nlevels(data$lex.Cst)+1, new.scale = FALSE, split.states = FALSE, progressive = FALSE, precursor.states = transient(data), count = FALSE) { if (!inherits(data, "Lexis")) stop("data must be a Lexis object") if( count ) return( countLexis( data=data, cut=cut, timescale=timescale ) ) if( inherits( cut, "data.frame" ) ){ zz <- match.cut( data, cut ) cut <- zz$cut new.state <- zz$new.state } else if (length(cut) == 1) { cut <- rep(cut, nrow(data)) } else if (length(cut) != nrow(data)) { stop("'cut' must have length 1 or nrow(data) (=", nrow(data), "),\n --- but it has length ", length(cut),".") } timescale <- check.time.scale(data, timescale) if (length(timescale) > 1) { stop("Multiple time scales") } ## If we want to add a new timescale, construct the name if( is.logical(new.scale) ) { if( new.scale ) scale.name <- paste( "tf", new.state[1], sep="" ) } else { scale.name <- new.scale new.scale <- TRUE } if (missing(new.state)) { new.state <- data$lex.Cst #Carry forward last state } else if (length(new.state) == 1) { new.state <- rep(new.state, nrow(data)) } else if (length(new.state) != nrow(data)) { stop("'new.state' must have length 1 or nrow(data) (=", nrow(data), "),\n --- but it has length ", length(new.state)) } if (progressive) { if (is.factor(data$lex.Cst) && !is.ordered(data$lex.Cst)) { stop("progressive=TRUE invalid for unordered factors") } if (any(data$lex.Xst < data$lex.Cst)) { stop("Lexis object is not progressive before splitting") } } lx <- doCutLexis( data, cut, timescale, new.scale=TRUE ) if (is.factor(data$lex.Cst)) { lx <- setStatus.factor(lx, new.state, precursor.states, progressive) } else if (is.numeric(data$lex.Cst)) { lx <- setStatus.numeric(lx, new.state, precursor.states, progressive) } else { lx <- setStatus.default(lx, new.state) } ## Remove redundant intervals lx <- lx[lx$lex.dur > 0,] ## Remove the lex.cut column lx <- lx[,-match("lex.cut",names(lx))] ## Update the states visited after the cut if( split.states & is.factor( data$lex.Cst ) ) { post.states <- setdiff( levels(data$lex.Cst), precursor.states ) tmp.Cst <- as.character( lx$lex.Cst ) tmp.Cst <- ifelse( !is.na(lx$lex.new.scale) & lx$lex.new.scale>0 & tmp.Cst %in% post.states, paste( tmp.Cst,"(",new.state,")",sep="" ), tmp.Cst ) tmp.Xst <- as.character( lx$lex.Xst ) tmp.Xst <- ifelse( !is.na(lx$lex.new.scale) & tmp.Xst %in% post.states, paste( tmp.Xst,"(",new.state,")",sep="" ), tmp.Xst ) all.levels <- unique( c(tmp.Cst,tmp.Xst) ) ## put all the new levels after the old ones xtr.levels <- setdiff( all.levels, levels(lx$lex.Cst) ) new.levels <- c( levels(lx$lex.Cst), xtr.levels ) lx$lex.Cst <- factor( tmp.Cst, levels=new.levels ) lx$lex.Xst <- factor( tmp.Xst, levels=new.levels ) } ## Include the new timescale if( new.scale ) { ## Rename the new timescale variable names(lx)[match("lex.new.scale",names(lx))] <- scale.name ## The timescales' position among columns - used to reorder columns tn <- c( match( attr( data, "time.scales" ), names( lx ) ), ncol(lx) ) oth <- setdiff( 1:ncol(lx), tn ) ## Reorder columns (lx will then lose attributes) and sort rows lx <- lx[order(lx$lex.id,lx[,timescale]),c(tn,oth)] ## Update the attributes new.br <- c( attr( data, "breaks" ), list(NULL) ) names( new.br )[length(new.br)] <- scale.name attr( lx, "time.scales" ) <- c( attr( data, "time.scales" ), scale.name ) attr( lx, "time.since" ) <- c( attr( data, "time.since" ), names(table(new.state)) ) attr( lx, "breaks" ) <- new.br attr( lx, "class" ) <- attr( data, "class" ) } else { # Remove the new timescale and sort rows lx <- lx[order(lx$lex.id,lx[,timescale]),-match("lex.new.scale",names(lx))] # and transfer all the other attributes attr( lx, "time.scales" ) <- attr( data, "time.scales" ) attr( lx, "time.since" ) <- attr( data, "time.since" ) attr( lx, "breaks" ) <- attr( data, "breaks" ) attr( lx, "class" ) <- attr( data, "class" ) } lx } countLexis <- function(data, cut, timescale = 1) { if (!inherits(data, "Lexis")) stop("data must be a Lexis object") if( inherits( cut, "data.frame" ) ){ zz <- match.cut( data, cut ) cut <- zz$cut new.state <- zz$new.state } else if (length(cut) == 1) { cut <- rep(cut, nrow(data)) } else if (length(cut) != nrow(data)) { stop("'cut' must have length 1 or nrow(data) (=", nrow(data), "),\n --- but it has length ", length(cut),".") } timescale <- check.time.scale(data, timescale) if (length(timescale) > 1) { stop("Multiple time scales not meaningful") } lx <- doCutLexis(data, cut, timescale) ## Update status variables lx$lex.Xst[lx$lex.cut == 1] <- lx$lex.Cst[lx$lex.cut == 1] + 1 lx$lex.Cst[lx$lex.cut == 2] <- lx$lex.Cst[lx$lex.cut == 2] + 1 lx$lex.Xst[lx$lex.cut == 2] <- lx$lex.Xst[lx$lex.cut == 2] + 1 ## Remove redundant intervals lx <- lx[lx$lex.dur > 0,] ## Remove the lex.cut column lx <- lx[,-match("lex.cut",names(lx))] ## Retain the attributes attr( lx, "breaks" ) <- attr( data, "breaks" ) attr( lx, "time.scales" ) <- attr( data, "time.scales" ) attr( lx, "class" ) <- attr( data, "class" ) return(lx[order(lx$lex.id,lx[,timescale]),]) } tsNA20 <- function( x, all.scales=FALSE ) { tsc <- timeSince(x) if( !all.scales ) tsc <- tsc[tsc!=""] if( length(tsc)>0 ) for( ts in names(tsc) ) { x[,ts] <- ifelse( is.na(x[,ts]), 0, x[,ts] ) } x } Epi/R/ccwc.R0000644000176200001440000001264213626052376012251 0ustar liggesusersccwc <- function(entry=0, exit, fail, origin=0, controls=1, match=list(), include=list(), data=NULL, silent=FALSE) { # Check arguments entry <- eval(substitute(entry), data) exit <- eval(substitute(exit), data) fail <- eval(substitute(fail), data) origin <- eval(substitute(origin), data) n <- length(fail) if (length(exit)!=n) stop("All vectors must have same length") if (length(entry)!=1 && length(entry)!=n) stop("All vectors must have same length") if (length(origin)==1) { origin <- rep(origin, n) } else { if (length(origin)!=n) stop("All vectors must have same length") } # Transform times to correct scale t.entry <- as.numeric(entry - origin) t.exit <- as.numeric(exit - origin) # match= argument marg <- substitute(match) if (mode(marg)=="name") { match <- list(eval(marg, data)) names(match) <- as.character(marg) } else if (mode(marg)=="call" && marg[[1]]=="list") { mnames <- names(marg) nm <- length(marg) if (nm>1) { if (!is.null(mnames)) { for (i in 2:nm) { if (mode(marg[[i]])=="name") mnames[i] <- as.character(marg[[i]]) else stop("illegal argument (match)") } } else { for (i in 2:nm) { if (mode(marg[[i]])=="name") mnames[i] <- as.character(marg[[i]]) else stop("illegal argument (match)") } mnames[1] <= "" } } names(marg) <- mnames match <- eval(marg, data) } else { stop("illegal argument (match)") } m <- length(match) mnames <- names(match) if (m>0) { for (i in 1:m) { if (length(match[[i]])!=n) { stop("incorrect length for matching variable") } } } # include= argument iarg <- substitute(include) if (mode(iarg)=="name") { include <- list(eval(iarg, data)) names(include) <- as.character(iarg) } else if (mode(iarg)=="call" && iarg[[1]]=="list") { ni <- length(iarg) inames <- names(iarg) if (ni>1) { if (!is.null(inames)) { for (i in 2:ni) { if (mode(iarg[[i]])=="name") inames[i] <- as.character(iarg[[i]]) else stop("illegal argument (include)") } } else { for (i in 2:ni) { if (mode(iarg[[i]])=="name") inames[i] <- as.character(iarg[[i]]) else stop("illegal argument (include)") } inames[1] <= "" } } names(iarg) <- inames include <- eval(iarg, data) } else { stop("illegal argument (include)") } ni <- length(include) inames <- names(include) if (ni>0) { for (i in 1:ni) { if (length(include[[i]])!=n) { stop("incorrect length for included variable") } } } # create group codes using matching variables grp <- rep(1,n) pd <- 1 if (m>0) { for (im in 1:m) { v <- match[[im]] if (length(v)!=n) stop("All vectors must have same length") if (!is.factor(v)) v <- factor(v) grp <- grp + pd*(as.numeric(v) - 1) pd <- pd*length(levels(v)) } } # Create vectors long enough to hold results nn <- (1+controls)*sum(fail!=0) pr <- numeric(nn) sr <- numeric(nn) tr <- vector("numeric", nn) fr <- numeric(nn) nn <- 0 # Sample each group if (!silent) { cat("\nSampling risk sets: ") } set <- 0 nomatch <- 0 incomplete <- 0 ties <- FALSE fg <- unique(grp[fail!=0]) for (g in fg) { # Failure times ft <- unique( t.exit[(grp==g) & (fail!=0)] ) # Create case-control sets for (tf in ft) { if (!silent) { cat(".") } set <- set+1 case <- (grp==g) & (t.exit==tf) & (fail!=0) ncase <- sum(case) if (ncase>1) ties <- TRUE noncase <- (grp==g) & (t.entry<=tf) & (t.exit>=tf) & !case ncont <- controls*ncase if (ncont>sum(noncase)) { ncont <- sum(noncase) if (ncont>0) incomplete <- incomplete + 1 } if (ncont>0) { newnn <- nn+ncase+ncont sr[(nn+1):newnn] <- set tr[(nn+1):newnn] <- tf fr[(nn+1):(nn+ncase)] <- 1 fr[(nn+ncase+1):newnn] <- 0 pr[(nn+1):(nn+ncase)] <- (1:n)[case] ## Work around bad behaviour of sample for vectors of length 1 noncase.id <- (1:n)[noncase] pr[(nn+ncase+1):(newnn)] <- noncase.id[sample.int(length(noncase.id), size=ncont)] nn <- newnn } else { nomatch <- nomatch + ncase } } } if (!silent) { cat("\n") } res <- vector("list", 4+m+ni) if (nn>0) { res[[1]] <- sr[1:nn] res[[2]] <- map <- pr[1:nn] res[[3]] <- tr[1:nn] + origin[map] res[[4]] <- fr[1:nn] } if (m>0) { for (i in 1:m) { res[[4+i]] <- match[[i]][map] } } if (ni>0) { for (i in 1:ni) { res[[4+m+i]] <- include[[i]][map] } } names(res) <- c("Set", "Map", "Time", "Fail", mnames, inames) if (incomplete>0) warning(paste(incomplete, "case-control sets are incomplete")) if (nomatch>0) warning(paste(nomatch, "cases could not be matched")) if (ties) warning("there were tied failure times") data.frame(res) } Epi/R/matshade.R0000644000176200001440000000325513563764541013124 0ustar liggesusersmatshade <- function( x, y, lty = 1, col = 1:(ncol(y)/3), col.shade = col, alpha = 0.15, plot = dev.cur()==1, ... ) { # check sanity of x and y if( !is.vector(x) ) stop( "x must be a vector\n") if( ncol(y)%%3 != 0 ) warning( "number of columns in y, ", ncol(y), " is not divisible by 3\n") # create a new plot? if( plot ) matplot( x, y, col="transparent", ... ) # number of curves to draw ncrv <- ncol(y) %/% 3 # The recycling rule for colors and alpha: col <- rep(col ,ncrv)[1:ncrv] col.shade <- rep(col.shade,ncrv)[1:ncrv] alpha <- rep(alpha ,ncrv)[1:ncrv] # First shaded areas - allowing NA to create holes draw.shade <- function( xx, yu, yl, col ) { # Find NAs and plot shades for non-missing sequences wh <- 1:length(xx) # NAs where at least one is missing wh[apply( cbind(xx,yl,yu), 1, function(x) any(is.na(x)) )] <- NA idx <- 1 + cumsum( is.na( wh ) ) not.na <- !is.na( wh ) chunks <- split( wh[not.na], idx[not.na] ) for( ch in chunks ) if( length(ch) > 1 ) polygon( c( xx[ch], rev(xx[ch]) ), c( yu[ch], rev(yl[ch]) ), col = col, pch = NULL, border = "transparent" ) } # Then the shades for each set of 3 columns for( i in 1:ncrv ) draw.shade( x, y[,i*3-1], y[,i*3-0], col = adjustcolor( col.shade[i], alpha.f=alpha[i] ) ) # then curves on top of these matlines( x, y[,(1:ncrv)*3-2], col=col, lty=lty, ... ) } Epi/R/contr.diff.R0000644000176200001440000000057512531361077013363 0ustar liggesuserscontr.diff <- function(n) { if (is.numeric(n) && length(n) == 1) levs <- 1:n else { levs <- n n <- length(n) } contr <- array(0, c(n, n), list(levs, levs)) contr[col(contr) == row(contr)] <- 1 contr[row(contr) - col(contr) == 1] <- -1 if (n < 2) stop(paste("Contrasts not defined for", n - 1, "degrees of freedom")) contr } Epi/R/ci.lin.R0000644000176200001440000003571313640636047012511 0ustar liggesusers# The coef() methods in nlme and lme4 do something different, # other objects do not even have coef or vcov methods defined, # so we make a workaround by specifying our own generic methods: COEF <- function( x, ... ) UseMethod("COEF") COEF.default <- function( x, ... ) coef( x, ... ) VCOV <- function( x, ... ) UseMethod("VCOV") VCOV.default <- function( x, ... ) vcov( x, complete=TRUE, ... ) # Then we can get from these methods what we want from lme, mer etc. COEF.lme <- function( x, ... ) nlme::fixed.effects( x ) COEF.mer <- function( x, ... ) lme4::fixef( x ) COEF.lmerMod <- function( x, ... ) lme4::fixef( x ) # The vcov returns a matrix with the wrong class so we strip that: VCOV.lme <- function( x, ... ) as.matrix(vcov( x )) VCOV.mer <- function( x, ... ) as.matrix(vcov( x )) VCOV.lmerMod <- function( x, ... ) as.matrix(vcov( x )) # For the rest of the non-conforming classes we then just need the methods not defined # VCOV.coxph <- function( object, ... ) survival:A::vcov.coxph( object, complete=FALSE, ... ) COEF.crr <- function( object, ... ) object$coef VCOV.crr <- function( object, ... ) object$var COEF.MIresult <- function( object, ... ) object$coefficients VCOV.MIresult <- function( object, ... ) object$variance COEF.mipo <- function( object, ... ) object$qbar VCOV.mipo <- function( object, ... ) object$t COEF.polr <- function( object, ... ) summary(object)$coefficients VCOV.gnlm <- function( object, ... ) object$cov VCOV.rq <- function( object, ... ) summary(object, cov=TRUE)$cov df2ctr <- function( obj, nd ) { if( !( inherits(obj,"lm") | inherits(obj,"coxph") ) ) stop("data frame facility not inplemented for ", class(obj), " objects" ) # Factors in the prediction frame must have more than one level, which # they typically do not have in the specification, so we find the # factors in the prediction frame and expand levels to the complete # set of levels which should secure the working of model.matrix() dcl <- attr( obj$terms, "dataClasses" ) whf <- ( dcl == "factor" ) if( any(whf) ) for( fn in names(dcl)[which(whf)] ) nd[,fn] <- factor( nd[,fn], levels=obj$xlevels[[fn]] ) # The contrast matrix from the model - differs a bit between (g)lm, gam and coxph # this is needed to keep NA rows from the data frame supplied org.op <- options( na.action='na.pass' ) on.exit( options( org.op ) ) if( inherits(obj,"coxph") ) MM <- model.matrix( obj , data=nd ) if( inherits(obj,"gam" ) ) MM <- model.matrix( obj , newdata=nd ) else if( inherits(obj,"lm" ) ) MM <- model.matrix( formula(obj)[-2], data=nd ) return( MM ) } ci.dfr <- function( obj, ndx, ndr, xvars = NULL, vcov = FALSE, alpha = 0.05, Exp = FALSE, sample = FALSE ) { if( nrow(ndr)==1 ) ndr <- ndr[rep(1,nrow(ndx)),,drop=FALSE] if( ( ( nrow(ndx) != nrow(ndr)) ) | ( any(names(ndx) != names(ndr)) ) ) stop("\nThe two prediction frames must have same dimensions and column names:", "but dimensions are: (", paste( dim(ndx),collapse=","), ") and (", paste( dim(ndr),collapse=","), ")\n", "and column names are:\n", "exp: ", paste( names(ndx), collapse=", " ), "\n", "ref: ", paste( names(ndr), collapse=", " ), "\n") # Now supply and fix those variables that are needed in order to get model.matrix working: # Supplied variable names: cols <- names( ndx ) # Factors in model; which are supplied; derive names of omitted factors (ofacs) facs <- names( obj$xlevels ) ofacs <- setdiff( facs, cols ) # omitted *variables* must be supplied ovars <- setdiff( xvars, facs ) # Construct the extra columns with bogus data (their contribution will be null) xcols <- ndx[,NULL] if( length(ofacs) > 0 ) for( fn in ofacs ) xcols[,fn] <- obj$xlevels[[fn]][1] if( length(ovars) > 0 ) for( vn in ovars ) xcols[,vn] <- 1 if( dim(xcols)[2]>0 ) { ndx <- cbind( ndx, xcols ) ndr <- cbind( ndr, xcols ) } ci.lin( obj, ctr.mat = df2ctr( obj, ndx ) - df2ctr( obj, ndr ), vcov = vcov, alpha = alpha, Exp = Exp, sample = sample ) } ci.dfr2 <- function( obj, nd1, nd2, nd3, nd4, xvars = NULL, vcov = FALSE, alpha = 0.05, Exp = FALSE, sample = FALSE ) { if( nrow(nd2)==1 ) nd2 <- nd2[rep(1,nrow(nd1)),,drop=FALSE] if( nrow(nd3)==1 ) nd3 <- nd3[rep(1,nrow(nd1)),,drop=FALSE] if( nrow(nd4)==1 ) nd4 <- nd4[rep(1,nrow(nd1)),,drop=FALSE] if( ( nrow(nd2) != nrow(nd1)) | ( nrow(nd3) != nrow(nd1)) | ( nrow(nd4) != nrow(nd1)) | any(names(nd2) != names(nd1)) | any(names(nd3) != names(nd1)) | any(names(nd4) != names(nd1)) ) stop("\nThe prediction frames must have same dimensions and column names:", "but dimensions are: (", paste( dim(nd1),collapse=","), ") and (", paste( dim(nd2),collapse=","), ") and (", paste( dim(nd3),collapse=","), ") and (", paste( dim(nd4),collapse=","), ")\n", "and column names are:\n", "1: ", paste( names(nd1), collapse=", " ), "\n", "2: ", paste( names(nd2), collapse=", " ), "\n", "3: ", paste( names(nd3), collapse=", " ), "\n", "4: ", paste( names(nd4), collapse=", " ), "\n") # Now supply and fix those variables that are needed in order to get model.matrix working: # Supplied variable names: cols <- names( nd1 ) # Factors in model; which are supplied; derive names of omitted factors (ofacs) facs <- names( obj$xlevels ) ofacs <- setdiff( facs, cols ) # omitted *variables* must be supplied ovars <- setdiff( xvars, facs ) # Construct the extra columns with bogus data (their contribution will be null) xcols <- nd1[,NULL] if( length(ofacs) > 0 ) for( fn in ofacs ) xcols[,fn] <- obj$xlevels[[fn]][1] if( length(ovars) > 0 ) for( vn in ovars ) xcols[,vn] <- 1 if( dim(xcols)[2]>0 ) { nd1 <- cbind( nd1, xcols ) nd2 <- cbind( nd2, xcols ) nd3 <- cbind( nd3, xcols ) nd4 <- cbind( nd4, xcols ) } ci.lin( obj, ctr.mat = df2ctr( obj, nd1 ) -df2ctr( obj, nd2 ) -df2ctr( obj, nd3 ) +df2ctr( obj, nd4 ), vcov = vcov, alpha = alpha, Exp = Exp, sample = sample ) } ci.lin <- function( obj, ctr.mat = NULL, subset = NULL, subint = NULL, xvars = NULL, diffs = FALSE, fnam = !diffs, vcov = FALSE, alpha = 0.05, df = Inf, Exp = FALSE, sample = FALSE ) { # If ctr.mat is a data frame, call df2ctr if( inherits( ctr.mat, "data.frame" ) ) ctr.mat <- df2ctr( obj, ctr.mat ) # If ctr.mat is a list of two dataframes then call ci.dfr if( inherits( ctr.mat, "list" ) ) { if( length(ctr.mat)==2 ) { if( !inherits( ctr.mat[[1]], "data.frame" ) | !inherits( ctr.mat[[2]], "data.frame" ) ) stop("If ctr.mat is a list it must be a list of data frames") return( ci.dfr( obj, ctr.mat[[1]], ctr.mat[[2]], xvars = xvars, vcov = vcov, alpha = alpha, Exp = Exp, sample = sample ) ) } # If ctr.mat is a list of two dataframes then call ci.dfr2 for 2nd # order differences if( length(ctr.mat)==4 ) { if( !inherits( ctr.mat[[1]], "data.frame" ) | !inherits( ctr.mat[[2]], "data.frame" ) | !inherits( ctr.mat[[3]], "data.frame" ) | !inherits( ctr.mat[[4]], "data.frame" ) ) stop("If ctr.mat is a list it must be a list of data frames") return( ci.dfr2( obj, ctr.mat[[1]], ctr.mat[[2]], ctr.mat[[3]], ctr.mat[[4]], xvars = xvars, vcov = vcov, alpha = alpha, Exp = Exp, sample = sample ) ) } } # First extract all the coefficients and the variance-covariance matrix cf <- COEF( obj ) vcv <- VCOV( obj ) # Alised parameters are set to 0 if( any( is.na( cf ) ) ) cf[is.na(cf )] <- 0 if( any( is.na( vcv ) ) ) vcv[is.na(vcv)] <- 0 # Function for computing a contrast matrix for all possible # differences between a set of parameters. all.dif <- function( cf, pre=FALSE ) { nn <- length( cf ) nr <- nn * ( nn - 1 ) / 2 nam <- names( cf ) # Work out the indexes of parameter pairs to compare # xx <- numeric( 0 ) for( j in 2:nn ) xx <- c(xx, j:nn ) ctr <- cbind( rep( 1:(nn-1), (nn-1):1 ), xx ) # Now for the annotation: # Find out how large a proportion of rownames are identical i <- 1 while( all( substr( nam, 1, i ) == substr( nam[1], 1, i ) ) ) i <- i+1 # If a factor name is given, then use this, otherwise the identical part # of the parameter names if( is.character( pre ) ) { prefix <- pre pre <- TRUE } else { prefix <- substr( nam[1], 1, i-1 ) } rn <- paste( if( pre ) prefix else "", substring( nam[ctr[,1]], i ), "vs.", substring( nam[ctr[,2]], i ) ) # Finally, construct the contrast matrix and attach the rownames cm <- matrix( 0, nr, nn ) cm[cbind(1:nr,ctr[,1])] <- 1 cm[cbind(1:nr,ctr[,2])] <- -1 rownames( cm ) <- rn cm } # end of the function all.dif for all differences # Were all differences requested? if( diffs ) { if( is.character( subset ) ) { if ( inherits( obj, "lm" ) & length( grep( subset, names( obj$xlevels ) ) )>0 ) { # The case of factor level differences we find the relevant # subset of parameters by reconstructing names of parameters wf <- grep( subset, af <- names( obj$xlevels ) ) # All factor levels fn <- obj$xlevels[[af[wf]]] # Reconstruct names of relevant parameter names pnam <- paste( af[wf], fn, sep="" ) # Find them in the parameter vector wh <- match( pnam, names( coef( obj ) ) ) # Get the relevant subset, and stick in 0s for NAs cf <- coef( obj )[wh] cf[is.na( cf )] <- 0 vcv <- vcov( obj, complete=FALSE )[wh,wh] vcv[is.na( vcv )] <- 0 names( cf ) <- rownames( vcv ) <- colnames( vcv ) <- paste( subset, ": ", fn, sep="" ) } else { subset <- grep( subset, names( cf ) ) cf <- cf[subset] vcv <- vcv[subset,subset] } } else { cf <- cf[subset] vcv <- vcv[subset,subset] } ctr.mat <- all.dif( cf, pre=fnam ) } if( !diffs ) { if( is.character( subset ) ) { sb <- numeric(0) for( i in 1:length( subset ) ) sb <- c(sb,grep( subset[i], names( cf ) )) subset <- sb # unique( sb ) } if( is.character( subint ) ) { sb <- 1:length(cf) for( i in 1:length(subint) ) sb <- intersect( sb, grep(subint[i],names(cf)) ) subset <- sb # unique( sb ) } if( is.null( subset ) & is.null( subint ) ) subset <- 1:length( cf ) # Exclude units where aliasing has produced NAs. # Not needed after replacement with 0s # subset <- subset[!is.na( cf[subset] )] cf <- cf[subset] vcv <- vcv[subset,subset] if( is.null( ctr.mat ) ) { ctr.mat <- diag( length( cf ) ) rownames( ctr.mat ) <- names( cf ) } if( dim( ctr.mat )[2] != length(cf) ) stop( paste("\n Dimension of ", deparse(substitute(ctr.mat)), ": ", paste(dim(ctr.mat), collapse = "x"), ", not compatible with no of parameters in ", deparse(substitute(obj)), ": ", length(cf), sep = "")) } # Finally, here is the actual computation if( sample ) { # mvrnorm() returns a vector if sample=1, otherwise a sample by # length(cf) matrix - hence the rbind so we always get a row # matrix and res then becomes an nrow(ctr.mat) by sample matrix res <- ctr.mat %*% t( rbind(mvrnorm( sample, cf, vcv )) ) } else { ct <- ctr.mat %*% cf vc <- ctr.mat %*% vcv %*% t( ctr.mat ) se <- sqrt( diag( vc ) ) ci <- cbind( ct, se ) %*% ci.mat( alpha=alpha, df=df ) t0 <- cbind( se, ct/se, 2 * ( pnorm( -abs( ct / se ) ) ) ) colnames(t0) <- c("StdErr", "z", "P") res <- cbind(ci, t0)[, c(1, 4:6, 2:3), drop=FALSE] if( Exp ) { res <- cbind( res[,1:4 ,drop=FALSE], exp( res[,c(1,5,6),drop=FALSE] ) ) colnames( res )[5] <- "exp(Est.)" } # class( res ) <- c("ci.lin","matrix") } # Return the requested structure if( sample ) invisible( res ) else if( vcov ) invisible( list( coef=ct[,1], vcov=vc ) ) else res } # print.ci.lin <- # function( x, ..., digits=3 ) # { # print( round( unclass(x), digits ) ) # } # Handy wrapper ci.exp <- function( ..., Exp=TRUE, pval=FALSE ) { res <- if( Exp ) { ci.lin( ..., Exp=TRUE )[,if(pval) c(5:7,4) else 5:7 ,drop=FALSE] } else { ci.lin( ..., Exp=FALSE )[,if(pval) c(1,5,6,4) else c(1,5,6),drop=FALSE] } # class( res ) <- c( "ci.lin", "matrix" ) res } # Wrapper for predict.glm to give estimates and confidence intervals ci.pred <- function( obj, newdata, Exp = NULL, alpha = 0.05 ) { if( !inherits( obj, "lm" ) ) stop("Not usable for non-(g)lm objects") if( !inherits( obj, "glm" ) & inherits( obj, "lm" ) ) return( predict.lm( obj, newdata=newdata, interval="confidence" ) ) # get the prediction and se on the link scale else { zz <- predict( obj, newdata=newdata, se.fit=TRUE, type="link" ) # compute ci on link scale zz <- cbind( zz$fit, zz$se.fit ) %*% ci.mat( alpha=alpha ) # transform as requested if( missing(Exp) ) { return( obj$family$linkinv(zz) ) } else { if( Exp ) { return( exp(zz) ) } else if( !Exp ) return( zz ) } } } # Function to calculate RR with CIs from independent rates with CIs; # r1 and r2 are assumed to be vectors or 2 or 3-column matrices with # rate, lower and upper confidence limits repectively. ci.ratio <- function( r1, r2, se1 = NULL, # standard error of rt1 se2 = NULL, # standard error of rt2 log.tr = !is.null(se1) & !is.null(se2), # is this log-rates? alpha = 0.05, pval = FALSE ) { if( is.data.frame(r1) ) r1 <- as.matrix( r1 ) if( is.data.frame(r2) ) r2 <- as.matrix( r2 ) if( is.matrix(r1) & !is.null(se1) ) warning("r1 is matrix, se1 is ignored") if( is.matrix(r2) & !is.null(se2) ) warning("r2 is matrix, se2 is ignored") # if supplied as 1-column matrix change to vector if( is.matrix(r1) ) if( ncol(r1)==1 ) r1 <- as.vector( r1 ) if( is.matrix(r2) ) if( ncol(r2)==1 ) r2 <- as.vector( r2 ) # move to log scale if( !log.tr ) { r1 <- log( r1 ) r2 <- log( r2 ) } # how wide are the condidence intervals if( is.matrix(r1) ) if( ncol(r1)>1 ) rg1 <- t( apply(r1,1,range) ) if( is.matrix(r2) ) if( ncol(r2)>1 ) rg2 <- t( apply(r2,1,range) ) # get the estimates on the log-scale R1 <- if( is.matrix(r1) ) apply( rg1, 1, mean ) else r1 R2 <- if( is.matrix(r2) ) apply( rg2, 1, mean ) else r2 if( is.null(se1) ) se1 <- apply( rg1, 1, diff ) / (2*qnorm(1-alpha/2)) if( is.null(se2) ) se2 <- apply( rg2, 1, diff ) / (2*qnorm(1-alpha/2)) # compute the RR and the c.i. and optionally the p-value lrr <- R1 - R2 slrr <- sqrt( se1^2 + se2^2 ) rr <- cbind(lrr,slrr) %*% ci.mat(alpha=alpha) if( !log.tr ) rr <- exp( rr ) if( pval ) return( cbind( rr, 1-pchisq( (lrr/slrr)^2, 1 ) ) ) else return( rr ) } Epi/R/Pplot.R0000644000176200001440000000346512531361077012426 0ustar liggesusersPplot <- function( rates, age = as.numeric( dimnames( rates )[[1]] ), per = as.numeric( dimnames( rates )[[2]] ), grid = FALSE, p.grid = grid, ygrid = grid, col.grid = gray( 0.9 ), p.lim = range( per, na.rm=TRUE ) + c(0,diff(range(per))/30), ylim = range( rates[rates>0], na.rm=TRUE ), p.lab = names( dimnames( rates ) )[2], ylab = deparse( substitute( rates ) ), at = NULL, labels = paste( at ), type = "l", lwd = 2, lty = 1, col = par( "fg" ), log.ax = "y", las = 1, ann = FALSE, cex.ann = 0.8, xannx = 1/20, a.thin = seq( 1, length( age ), 2 ), ... ) { # Plot the frame if( ann ) p.lim <- p.lim + c(0,diff( range( age ) ) * xannx ) matplot( per, t(rates), type="n", xlim=p.lim, ylim=ylim, xlab=p.lab, ylab=ylab, log=log.ax, las=las, yaxt=if( !is.null( at ) ) "n" else "s" ) if( !is.null( at ) ) axis( side=2, at=at, labels=labels, yaxt="s", las=las ) # and the grid if required if( !missing( p.grid ) | !missing( grid ) ) { if( is.logical( p.grid ) & p.grid[1] ) p.grid <- nice( per, log=par("xlog") ) abline( v=p.grid, col=col.grid ) } if( !missing( ygrid ) | !missing( ygrid ) ) { if( is.logical( ygrid ) & ygrid[1] ) ygrid <- nice( rates[!is.na(rates)], log=par("ylog") ) abline( h=ygrid, col=col.grid ) } box() # then the curves matlines( per, t(rates), lwd=lwd, lty=lty, col=col, type=type, ... ) # annotate them if required (every second by default ) if( ann ) { nr <- nrow( rates ) nc <- ncol( rates ) text( rep( per[nc], nr )[a.thin], rates[,nc][a.thin], paste( "", age[a.thin] ), adj=c(0,0.5), cex=cex.ann, col=if( length(col)==1 ) col else col[a.thin] ) } } Epi/R/float.R0000644000176200001440000000666612531361077012443 0ustar liggesusers"float" <- function(object, factor, iter.max = 50) { float.variance <- function(V, tol=1.0e-3, iter.max = 50) { ## Calculate floated variances for variance matrix V, which is ## assumed to represent a set of treatment contrasts m <- nrow(V) if (!is.matrix(V) || ncol(V) != m || m == 1) stop ("V must be a square matrix of size 2 x 2 or more") evals <- eigen(V, only.values=TRUE)$values if(any(evals < 0)) stop("V not positive definite") ## Starting values from Easton et al (1991) R <- V - diag(diag(V)) V00 <- sum(R)/(m * (m-1)) V10 <- apply(R, 1, sum)/(m-1) fv <- c(V00, V00 - 2 * V10 + diag(V)) for(iter in 1:iter.max) { w <- 1/fv S <- sum(w) w1 <- w[-1]/S ##Augment data matrix V10 <- as.vector(V %*% w1) V00 <- as.vector(1/S + t(w1) %*% V %*% w1) ##Calculate new estimates fv.old <- fv fv <- c(V00, V00 - 2 * V10 + diag(V)) ## Check convergence if(max(abs(fv.old - fv)/fv) < tol) break } if (iter == iter.max) warning("Floated variance estimates did not converge") Vmodel.inv <- S * (diag(w1) - w1 %*% t(w1)) evals <- 1/(eigen(V %*% Vmodel.inv, only.values=TRUE)$values) divergence <- sum(1/evals - 1 + log(evals))/2 return(list(variance=fv, error.limits=sqrt(range(evals)), divergence=divergence)) } if (is.null(object$xlevels)) { stop("No factors in model") } if (missing(factor)) { i <- 1 factor <- names(object$xlevels)[1] } else { i <- pmatch(factor, names(object$xlevels)) if (is.na(i)) { stop(paste("Factor",i,"not found in model")) } } xcontrasts <- object$contrasts[[i]] xlevels <- object$xlevels[[i]] xname <- names(object$xlevels)[i] nlevels <- length(xlevels) ## Extract the coefficients and variance matrix for a single factor ## from object if (nlevels <= 2) { stop ("Floated variances undefined for factors with less than 3 levels") } ## Get contrast matrix C <- if (is.matrix(xcontrasts)) { xcontrasts } else { get(xcontrasts, mode="function")(xlevels) } if (qr(C)$rank < nlevels - 1) { stop ("Impossible to reconstruct treatment contrasts") } ## Get coefficients and variance matrix if(is.null(cnames <- colnames(C))) cnames <- 1:(nlevels-1) contr.names <- paste(xname, cnames, sep="") coef <- coef(object)[contr.names] V <- vcov(object)[contr.names, contr.names] ## Convert to treatment contrast parameterization if (identical(xcontrasts, "contr.treatment")) { V.tc <- V coef.tc <- c(0, coef) } else { D.inv <- cbind(rep(-1,nlevels-1), diag(nlevels-1)) S <- D.inv %*% cbind(rep(1, nlevels), C) S <- S[,-1] ## coefficients coef.tc <- c(0, S %*% coef) ## If we find a baseline level (implicitly defined ## by having a row of zeros in the contrast matrix) ## then adjust the coefficients is.base <- apply(abs(C), 1, sum) == 0 if (any(is.base)) coef.tc <- coef.tc - coef.tc[is.base] ## variance matrix V.tc <- S %*% V %*% t(S) } names(coef.tc) <- xlevels float.out <- float.variance(V.tc, iter.max = iter.max) var <- float.out$var names(var) <- xlevels ans <- list(coef=coef.tc, var=var, limits=float.out$error.limits, factor=factor) class(ans) <- "floated" return(ans) } Epi/R/rm.tr.R0000644000176200001440000000274112743677240012375 0ustar liggesusersrm.tr <- function( obj, from, to ) { # checks if( from==to) stop( "Don't be silly, 'from' and 'to' are identical." ) if( !(from %in% levels(obj) ) ) stop( "'from' not a state in the object." ) if( !( to %in% levels(obj) ) ) stop( " 'to' not a state in the object." ) ### These things do not change over the purging iterations # Sort the rows of the object and count them obj <- obj[order(obj$lex.id,obj[,timeScales(obj)[1]]),] nrw <- nrow( obj ) # First obs for each person no1 <- !duplicated( obj$lex.id ) wh1 <- which( no1 ) ### Utility function doing the work inside the loop purge.one <- function( obj, from, to, nrw, wh1 ) { # Where are the illegal transitions chX <- ( paste( obj$lex.Cst, obj$lex.Xst ) == paste( from, to ) ) whX <- which( chX ) if( length(whX)>0 ) { # Change lex.Xst in this record obj$lex.Xst[whX] <- obj$lex.Cst[whX] # and lex.Cst in next record, but only if it is not a new person whX <- setdiff( whX[whX=sum( x*w*y). # Avoids computing the entire projection matrix # X %*% inverse( X'WX ) %*% (XW)' by first computing # inverse( X'WX ) %*% (XW)'M # (which is (p x p) %*% (p x n) %*% (n x k), i.e. (p x k) ) # and then premultiplying X (n x p) hence avoiding making # a n x n matrix underway (note that n is large, p is small). # Note multiplication by W (diagional matrix) is done by # vector multiplication using the recycling facility of R. { if( nrow(X) != length(weight) ) stop( "Dimension of space and length of weights differ!" ) if( nrow(X) != nrow(M) ) stop( "Dimension of space and rownumber of model matrix differ!" ) Pp <- solve( crossprod( X * sqrt(weight) ), t( X * weight ) ) %*% M PM <- X %*% Pp if (orth) PM <- M - PM else PM } Epi/R/bootLexis.R0000644000176200001440000000444413340467163013300 0ustar liggesusers# The method nid <- function ( Lx, ... ) UseMethod("nid") nid.default <- nid.Lexis <- function( Lx, by=NULL, ... ) { if( !is.null(by) ) { if( !(by %in% names(Lx)) ) stop( "'by' must be the name of a variable in Lx" ) if( !is.factor(Lx[,by]) ) Lx[,by] <- factor(Lx[,by]) } if( is.null(by) ) length( unique( Lx$lex.id ) ) else sapply( split( Lx, Lx[,by] ), nid.Lexis ) } # Make a boostrap sample of a Lexis object: # Sample the *persons* with replacement, possibly sampling within levels of by= bootLexis <- function( Lx, size = NULL, by = NULL, replace = TRUE ) { if( !inherits( Lx, "Lexis" ) ) stop("Only meaningful for Lexis objects.") isDT <- inherits( Lx, "data.table" ) if( isDT ) class( Lx ) <- c("Lexis","data.frame") # determine size of the bootstrap samples if not given if( is.null( size ) ) size <- nid.Lexis( Lx, by = by ) # allowing for a length 1 x-vector REsample <- function(x,sz) x[sample.int(length(x),size=sz,replace=replace)] if( is.null(by) ) { # Simple bootstrap bLx <- subid.Lexis( Lx, REsample( unique(Lx$lex.id), size ) ) } else { # Bootstrap by groups bLx <- NULL spL <- split( Lx, Lx[,by] ) for( i in 1:length(spL) ) { bLx <- rbind( bLx, cbind( bootLexis( spL[[i]], size = size[i] ), bgr = paste(i) ) ) } bLx$lex.id <- as.integer( interaction(bLx$lex.id,bLx$bgr) ) bLx <- bLx[,-grep("bgr",names(bLx))] } # return the result after converting to data.table if needed if( isDT ) class( bLx ) <- c("Lexis","data.table","data.frame") bLx } # A utility function that returns a Lexis object subsetted to a set of # lex.ids, allowing for repeat values of lex.id subid.Lexis <- function( Lx, ids ) { tt <- table( ids ) bLx <- NULL max.id <- 0 for( j in 1:max(tt) ) { # avoid note about no visible binding wh <- NULL lex.id <- NULL # who appears at least j times in the sample ? wh <<- names(tt[tt>=j]) sb <- subset( Lx, lex.id %in% wh ) # remember their original id sb$old.id <- sb$lex.id # to assure that different samples of the same person has different lex.id sb$lex.id <- sb$lex.id + max.id max.id <- max( sb$lex.id ) bLx <- rbind( bLx, sb ) } # Generate new lex.ids in the order 1:N bLx$lex.id <- as.integer( factor(bLx$lex.id) ) bLx } Epi/R/expand.data.r0000644000176200001440000000436212531361077013554 0ustar liggesusersexpand.data <- function(fu, formula, breaks, data) { Nsubject <- nrow(fu) ## The model matrix to be merged up to the expanded data if (!missing(formula)) { covariate.frame <- data.frame(model.matrix(formula,data)[,-1]) cov.names <- names(covariate.frame) covariate.frame$id <- 1:Nsubject } else { covariate.frame <- NULL cov.names <- character(0) } ## 1-responses for the survival intervals Nbreak <- length(breaks) ILENGTH <- function(x) { pmax(pmin(x[2], breaks[-1]) - pmax(x[1], breaks[-Nbreak]), 0) } well.mat <- -matrix(apply(fu[,c(1,2), drop=FALSE], 1, ILENGTH), nrow=Nbreak-1) ## For the sake of the stability of the fitting procedure, each record ## with a 1-response is further split into separate records for each ## follow-up interval: id.vec <- c(diag(Nbreak-1)) well.mat <- matrix(apply(well.mat, 2, "*", id.vec), nrow=Nbreak-1) well.id <- rep(1:Nsubject, each=Nbreak-1) valid.cols <- apply(well.mat!=0, 2, any) well.mat <- well.mat[,valid.cols, drop=FALSE] #Remove cols that are all zero well.id <- well.id[valid.cols] ## 0-responses for the event intervals is.case <- !is.na(fu[,3]) # Observed to become ill fu.cases <- subset(fu, is.case) ill.mat <- -matrix(apply(fu.cases[,c(2,3), drop=FALSE], 1, ILENGTH), nrow=Nbreak-1) ill.id <- which(is.case) ## The dataframe for analysis is one observation per survival interval ## (well.mat) and one per event interval (ill.mat): rates.frame <- as.data.frame(t(cbind(well.mat, ill.mat))) rates.names <- paste("(", breaks[-Nbreak],",",breaks[-1],")", sep="") names(rates.frame) <- rates.names rates.frame$y <- rep(c(1,0), c(ncol(well.mat), ncol(ill.mat))) rates.frame$id <- c(well.id, ill.id) ## Merge the covariates on to the model matrix for the baseline if (!is.null(covariate.frame)) { model.frame <- merge(rates.frame, covariate.frame, by="id") } else { model.frame <- rates.frame } model.frame[["id"]] <- NULL #Remove id variable return( list( rates.frame = model.frame[,rates.names, drop=FALSE], cov.frame = model.frame[, cov.names, drop=FALSE], y = model.frame[, "y", drop=TRUE ] ) ) } Epi/R/as.Date.cal.yr.R0000644000176200001440000000014312531361077013764 0ustar liggesusersas.Date.cal.yr <- function( x, ... ) { structure( round( ( x - 1970 ) * 365.25 ), class="Date" ) } Epi/R/ci.mat.R0000644000176200001440000000045012531361077012472 0ustar liggesusersci.mat <- function( alpha=0.05, df=Inf ) { ciM <- rbind( c(1,1,1), qt(1-alpha/2,df)*c(0,-1,1) ) colnames( ciM ) <- c("Estimate", paste( formatC( 100* alpha/2 , format="f", digits=1 ), "%", sep="" ), paste( formatC( 100*(1-alpha/2), format="f", digits=1 ), "%", sep="" ) ) ciM } Epi/R/fit.mult.r0000644000176200001440000000260212531361077013122 0ustar liggesusersfit.mult <- function(y, rates.frame, cov.frame, start) { if (missing(start)) { ## Fit model without covariates to get initial rates estimates glm.out.rates <- fit.baseline(y, rates.frame) ## Initial values for iterative fitting lambda <- coef(glm.out.rates) beta <- rep(0, ncol(cov.frame)) } else { lambda <- start[1:ncol(rates.frame)] beta <- start[ncol(rates.frame) + 1:ncol(cov.frame)] } niter <- 1 cy <- 1 - y while(TRUE) { ## covariates model off <- log(-as.matrix(rates.frame) %*% lambda) glm.out.cov <- glm(cy ~ -1 + offset(off) + ., family=binomial(link=cloglog), data=cov.frame, start=beta, maxit=100) beta <- coef(glm.out.cov) ## rates model wgt <- exp(as.matrix(cov.frame) %*% beta) temp.rates.frame <- wgt * rates.frame glm.out.rates <- glm(y ~ -1 + ., family=binomial(link=log), data=temp.rates.frame, start=lambda, maxit=100) lambda <- coef(glm.out.rates) ## Check convergence ## Convergence <==> deviances are equal TOL <- max(glm.out.cov$control$epsilon, glm.out.rates$control$epsilon) dev1 <- glm.out.cov$deviance dev2 <- glm.out.rates$deviance if (abs(dev1 - dev2)/(0.1 + abs(dev1)) < TOL) break else niter <- niter + 1 } return(list( rates=glm.out.rates, cov=glm.out.cov, niter=niter)) } Epi/R/contr.cum.R0000644000176200001440000000056612531361077013237 0ustar liggesuserscontr.cum <- function(n) { if (is.numeric(n) && length(n) == 1) levs <- 1:n else { levs <- n n <- length(n) } contr <- array(0, c(n, n), list(levs, levs)) contr[col(contr) <= row(contr)] <- 1 if (n < 2) stop(paste("Contrasts not defined for", n - 1, "degrees of freedom")) contr <- contr[, -1, drop = FALSE] contr } Epi/R/print.Icens.r0000644000176200001440000000020012531361077013544 0ustar liggesusersprint.Icens <- function( x, digits=4, scale=1, ... ) { emat <- summary.Icens( x, scale=scale ) print( round( emat, digits ) ) } Epi/R/plotevent.r0000644000176200001440000000217112531361077013401 0ustar liggesusersplotevent <- function(last.well,first.ill,data) { subsetdata <- data[!is.na(data[,first.ill]),c(last.well,first.ill)] subsetdata$n <- seq(1,dim(subsetdata)[1]) plot(c(subsetdata[,1], subsetdata[,2]),rep(0,2*nrow(subsetdata)), bty="n", yaxt="n", type="n", xlim=c(round(min(subsetdata[,1],subsetdata[,2],na.rm=T)),round(max(subsetdata[,1],subsetdata[,2],na.rm=T))), ylim=c(-2, max(subsetdata[,3])), xlab="Time",ylab="Conversions", main=paste("Times between ",last.well," and ",first.ill,"",sep="")) mtext(seq(0,nrow(subsetdata),5)[-1],side=2,at=seq(0,nrow(subsetdata),5)[-1],las=1,line=0) mtext("Eq Cl",side=2,at=-2,las=1, padj=0,col="blue",font=2) segments(subsetdata[,1],subsetdata[,3],subsetdata[,2],subsetdata[,3],lwd=1) left <- unique(subsetdata[,1]) right <- unique(subsetdata[,2]) names(left) <- rep("0",length(left)) names(right) <- rep("1",length(right)) MM <- sort(c(left,right)) type <- as.numeric(names(MM)) type2 <- c(type[-1],0) diff <- type-type2 int <- MM[diff<0|diff>0] mat <- matrix(int,length(int)/2,2,byrow=TRUE) d <- mat[,1] - mat[,2] segments(mat[,1][d!=0],-2,mat[,2][d!=0],-2,lwd=3,col="blue") } Epi/R/erl.R0000644000176200001440000001541113673706023012106 0ustar liggesuserserl <- function( int, muW, muD, lam = NULL, age.in = 0, A = NULL, immune = is.null(lam), yll = TRUE, note = TRUE ) { # Computes expected residual life time for Well and Dis states # respectively in an illness-death model, optionally ignoring # the well->ill transition # Utility to integrate a survival function from the last point where # it is 1, assuming points are 1 apart trsum <- function( x ) { x[c(diff(x)==0,TRUE)] <- NA sum( ( x[-length(x)] + x[-1] ) / 2, na.rm=TRUE ) } # Check sensibility if( !immune & is.null(lam) ) stop( "'lam' is required when immune=FALSE\n" ) # Replace NAs with 0s if( !is.null(lam) ) { if( any(is.na(lam)) ){ lam[is.na(lam)] <- 0 ; warning("NAs in agument 'lam' set to 0") } } if( any(is.na(muD)) ){ muD[is.na(muD)] <- 0 ; warning("NAs in agument 'muD' set to 0") } if( any(is.na(muW)) ){ muW[is.na(muW)] <- 0 ; warning("NAs in agument 'muW' set to 0") } # Survival functions sD <- surv1( int=int, muD, age.in = age.in, A = A ) if( immune ) sW <- surv1( int=int, muW, age.in = age.in, A = A ) else sW <- surv2( int=int, muW, muD, lam, age.in = age.in, A = A ) # Area under the survival functions erl <- cbind( apply( sW[,-1], 2, trsum ), apply( sD[,-1], 2, trsum ) ) * int colnames( erl ) <- c("Well","Dis") rownames( erl ) <- colnames( sW )[-1] # Should we compute years of life lost? if( yll ) erl <- cbind( erl, YLL = erl[,"Well"] - erl[,"Dis"] ) # Cautionary note if( immune ) { attr( erl, "NOTE" ) <- "Calculations assume that Well persons cannot get Ill (quite silly!)." if( note ) cat("NOTE:", attr( erl, "NOTE" ), "\n" ) } return( erl ) } # yll is just a simple wrapper for erl, only selecting the YLL column. yll <- function( int, muW, muD, lam = NULL, age.in = 0, A = NULL, immune = is.null(lam), note = TRUE ) erl( int = int, muW = muW, muD = muD, lam = lam, age.in = age.in, A = A, immune = immune, yll = TRUE, note = note )[,"YLL"] surv1 <- function( int, mu, age.in=0, A=NULL ) { # Computes the survival function from age A till the end, assuming # that mu is a vector of mortalities in intervals of length int. # int and mu should be in compatible units that is T and T^-1 for # some unit T (months, years, ...) # impute 0s for NAs if( any(is.na(mu)) ){ mu[is.na(mu)] <- 0 ; warning("NAs in agument 'mu' set to 0") } # age-class boundaries age <- 0:length(mu)*int + age.in # cumulative rates and survival at the boundaries Mu <- c( 0, cumsum( mu )*int ) Sv <- exp( -Mu ) surv <- data.frame( age=age, surv=Sv ) # if a vector of conditioning ages A is given if( cond <- !is.null(A) ) { j <- 0 # actual conditioning ages cage <- NULL for( ia in A ) { j <- j+1 # Where is the age we condition on cA <- which( diff(age>ia)==1 ) # survival up to condtioning age is set to 1 surv <- cbind( surv, pmin( 1, surv$surv/(surv$surv[cA]) ) ) cage[j] <- surv$age[cA] } } names( surv )[-1] <- paste( "A", c( age.in, if( cond ) cage else NULL ), sep="" ) rownames( surv ) <- NULL return( surv ) } erl1 <- function( int, mu, age.in = 0 ) { # Computes expected residual life time at all ages age <- 0:length(mu)*int + age.in # Small utility: cumulative cumulative sum from the end of a vector musmuc <- function( x ) rev( cumsum( rev(x) ) ) # The survival function with a 0 at end, and the integral from the upper end surv <- surv1( int = int, mu = mu, age.in = age.in )[,2] cbind( age = age, surv = surv, erl = c( musmuc( ( surv[-1]-diff(surv)/2 ) ) / surv[-length(surv)], 0 ) * int ) } surv2 <- function( int, muW, muD, lam, age.in=0, A=NULL ) { # check the vectors if( length(muW) != length(muD) | length(muD) != length(lam) ) stop( "Vectors with rates must have same length:\n", "length(muW)=", length(muW), ", length(muD)=", length(muD), ", length(lam)=", length(lam) ) # Replace NAs with 0s if( !is.null(lam) ) { if( any(is.na(lam)) ){ lam[is.na(lam)] <- 0 ; warning("NAs in agument 'lam' set to 0") } } if( any(is.na(muD)) ){ muD[is.na(muD)] <- 0 ; warning("NAs in agument 'muD' set to 0") } if( any(is.na(muW)) ){ muW[is.na(muW)] <- 0 ; warning("NAs in agument 'muW' set to 0") } # First the workhorse that computes the survival function for a # person in Well assuming that the mortality rate from this state is # muW, disease incidence is in lam, and mortality in the diseased # state is muD, and that all refer to constant rates intervals of # length int starting from age.in, conditional on survival to A wsurv2 <- function( int, muW, muD, lam, age.in=0, A=0 ) { # age-class boundaries - note one longer than rate vectors as it # refers to boundaries of intervals not midpoints age <- 0:length(muW)*int + age.in # cumulative rates at the boundaries, given survival to A MuW <- cumsum( c( 0, muW ) * ( age > A ) ) * int MuD <- cumsum( c( 0, muD ) * ( age > A ) ) * int Lam <- cumsum( c( 0, lam ) * ( age > A ) ) * int # probability of being well pW <- exp( -( Lam + MuW ) ) # probability of diagnosis at s --- first term in the integral for # P(DM at a). Note that we explicitly add a 0 at the start so we get a # probability of 0 of transition at the first age point Dis <- c(0,lam) * ( age > A ) * exp( -(Lam+MuW) ) * int # for each age (age[ia]) we compute the integral over the range # [0,age] of the product of the probability of diagnosis and the # probability of surviving from diagnosis till age ia pDM <- Dis * 0 for( ia in 1:length(age) ) pDM[ia] <- sum( Dis[1:ia] * exp( -(MuD[ia]-MuD[1:ia]) ) ) # 1st term as function of s (1:ia) # 2nd term integral over range s:age # upper integration limit is age (ia) and the lower # limit is the intermediate age (at DM) (1:ia) # Finally, we add the probabilities of being in Well resp. DM to get # the overall survival: surv <- data.frame( age = age, surv = pDM + pW ) return( surv ) } # survival from start surv <- wsurv2( int, muW, muD, lam, age.in=age.in, A=0 ) # add columns for conditioning ages if( !is.null(A) ) { for( j in 1:length(A) ) { surv <- cbind( surv, wsurv2( int, muW, muD, lam, age.in=age.in, A=A[j] )[,2] ) } } Al <- A for( i in 1:length(A) ) Al[i] <- max( surv$age[surv$age <= A[i]] ) colnames( surv )[-1] <- paste( "A", c( age.in, Al ), sep="" ) # done! return( surv ) } Epi/R/twoby2.R0000644000176200001440000000702013521223020012526 0ustar liggesuserstwoby2 <- function( exposure, outcome, alpha = 0.05, print = TRUE, dec = 4, conf.level = 1-alpha, F.lim = 10000 ) # What is the limit for trying the # Fisher.test { if( !missing( conf.level ) ) alpha <- 1 - conf.level if( inherits( exposure, c( "table", "matrix" ) ) ) tab <- exposure else tab <- table( exposure, outcome ) tab <- tab[1:2,1:2] a <- tab[1, 1] b <- tab[1, 2] c <- tab[2, 1] d <- tab[2, 2] bin.ci <- function( x, n ) { # Confidence interval for proportion based on Taylor-expansion of # the log-odds --- surprisingly good coverage. ef <- exp( qnorm(1-alpha/2)/sqrt(x*(n-x)/n) ) p <- x / n c( x/n, p/(p+(1-p)*ef), p/(p+(1-p)/ef) ) } rr <- (a/(a + b))/(c/(c + d)) se.log.rr <- sqrt((b/a)/(a + b) + (d/c)/(c + d)) lci.rr <- exp(log(rr) - qnorm( 1-alpha/2 ) * se.log.rr) uci.rr <- exp(log(rr) + qnorm( 1-alpha/2 ) * se.log.rr) or <- (a/b)/(c/d) se.log.or <- sqrt(1/a + 1/b + 1/c + 1/d) lci.or <- exp(log(or) - qnorm( 1-alpha/2 ) * se.log.or) uci.or <- exp(log(or) + qnorm( 1-alpha/2 ) * se.log.or) # Computing the c.i. for the probability difference as method # 10 from Newcombe, Stat.Med. 1998, 17, pp.873 ff. pr.dif <- ci.pd( a, c, b, d, alpha=alpha, print=FALSE )[5:7] pd <- pr.dif[1] lci.pd <- pr.dif[2] uci.pd <- pr.dif[3] as.pval <- 1 - pchisq( log( or )^2 / sum( 1/tab[1:2,1:2] ), 1 ) # If the numers are too large we don't bother about computing Fisher's test Fisher <- ( sum( tab ) < F.lim ) ft <- if( !Fisher ) NA else fisher.test( tab, conf.level=1-alpha ) # We need row and colum names for annotating the output if( is.null( rownames( tab ) ) ) rownames( tab ) <- paste( "Row", 1:2 ) if( is.null( colnames( tab ) ) ) colnames( tab ) <- paste( "Col", 1:2 ) tbl <- cbind( tab[1:2,1:2], rbind( bin.ci( a, a+b ), bin.ci( c, c+d ) ) ) colnames( tbl )[3:5] <- c(paste( " P(", colnames( tab )[1], ")", sep=""), paste( 100*(1-alpha),"% conf.", sep="" ), "interval") if( print ) cat("2 by 2 table analysis:", "\n------------------------------------------------------", "\nOutcome :", colnames( tab )[1], "\nComparing :", rownames( tab )[1], "vs.", rownames( tab )[2], "\n\n" ) if( print ) print( round( tbl, dec ) ) if( print ) cat( "\n" ) rmat <- rbind( c( rr, lci.rr, uci.rr ), c( or, lci.or, uci.or ), if( Fisher) c( ft$estimate, ft$conf.int ), c( pd, lci.pd, uci.pd ) ) rownames( rmat ) <- c(" Relative Risk:", " Sample Odds Ratio:", if( Fisher) "Conditional MLE Odds Ratio:", " Probability difference:") colnames( rmat ) <- c(" ", paste( 100*(1-alpha),"% conf.", sep="" ), "interval" ) if( print ) print( round( rmat, dec ) ) if( print ) cat( if( Fisher ) "\n Exact P-value:", if( Fisher ) formatC( ft$p.value, format="f", digits=dec ), "\n Asymptotic P-value:", formatC( as.pval, format="f", digits=dec ), "\n------------------------------------------------------\n") invisible( list( table = tbl, measures = rmat, p.value = c(as.pval,if( Fisher )ft$p.value) ) ) } Epi/R/contr.2nd.R0000644000176200001440000000037112531361077013130 0ustar liggesuserscontr.2nd <- function( n ) { if( is.numeric(n) && length(n) == 1 ) levs<- 1:n else { levs <- n n <- length(n) } if( n<3 ) stop( "Contrasts not defined for ", n-2, " degrees of freedom" ) outer( 1:n, 3:n-1, FUN=function(x,y) pmax( x-y, 0 ) ) } Epi/R/poisreg.R0000644000176200001440000000563013521051303012760 0ustar liggesuserspoisreg <- function (link = "log") { linktemp <- substitute(link) if (!is.character(linktemp)) linktemp <- deparse(linktemp) okLinks <- c("log", "identity", "sqrt") if (linktemp %in% okLinks) stats <- make.link(linktemp) else if (is.character(link)) { stats <- make.link(link) linktemp <- link } else { ## what else shall we allow? At least objects of class link-glm. if(inherits(link, "link-glm")) { stats <- link if(!is.null(stats$name)) linktemp <- stats$name } else { stop(gettextf('link "%s" not available for poisreg family; available links are %s', linktemp, paste(sQuote(okLinks), collapse =", ")), domain = NA) } } variance <- function(mu) mu validmu <- function(mu) all(is.finite(mu)) && all(mu>0) dev.resids <- function(y, mu, wt) { ## faster than 2 * wt * (y * log(ifelse(y == 0, 1, y/mu)) - (y - mu)) r <- mu*wt p <- which(y > 0) r[p] <- (wt * (y*log(y/mu) - (y - mu)))[p] 2*r } aic <- function(y, n, mu, wt, dev) { -2*sum(ifelse(n > 0, (wt/n), 0)*dpois(round(y*n), mu*n, log=TRUE)) } initialize <- expression({ if (NCOL(y) == 1) { n <- rep.int(1, nobs) y[weights == 0] <- 0 if (any(y < 0)) { stop("y values must be >= 0") } m <- weights * y if (any(abs(m - round(m)) > 0.001)) { warning("non-integer #successes in poisreg glm!") } mustart <- m + 0.1 } else if (NCOL(y) == 2) { if (any(y[,1] < 0)) { stop("negative values not allowed for the 'poisreg' family") } if (any(y[,2] < 0)) { stop("negative time not allowed for the 'poisreg' family") } if(any(y[,1] > 0 & y[,2] == 0)) { stop("non-zero counts in zero time in a poisreg glm!") } if(any(abs(y[,1] - round(y[,1])) > 1e-3)) { warning("non-integer counts in a poisreg glm!") } n <- y[,2] y <- ifelse(n == 0, 0, y[, 1]/n) weights <- weights * n mustart <- y + 0.1 } else { stop("for the 'poisreg' family, y must be a 2 column matrix where col 1 is no. events and col 2 is time") } }) simfun <- function(object, nsim) { wts <- object$prior.weights ftd <- fitted(object) rpois(nsim*length(ftd), ftd*wts) } structure(list(family = "poisson", ##Fool summary.glm link = linktemp, linkfun = stats$linkfun, linkinv = stats$linkinv, variance = variance, dev.resids = dev.resids, aic = aic, mu.eta = stats$mu.eta, initialize = initialize, validmu = validmu, valideta = stats$valideta, simulate = simfun), class = "family") } Epi/R/Ns.r0000644000176200001440000001412113252222304011725 0ustar liggesusers# ------------------------------------------------------------- # extension of ns() from splines, to allow for clamping. ns.ld <- function(x, df = NULL, knots = NULL, intercept = FALSE, Boundary.knots = range(x), fixsl=c(FALSE,FALSE) ) { nx <- names(x) x <- as.vector(x) nax <- is.na(x) if(nas <- any(nax)) x <- x[!nax] if(!missing(Boundary.knots)) { if( length(Boundary.knots)!=2 ) stop( "Argument 'Boundary.knots' must, when provided, have length 2" ) Boundary.knots <- sort(Boundary.knots) outside <- (ol <- x < Boundary.knots[1L]) | (or <- x > Boundary.knots[2L]) } else outside <- FALSE if(!missing(df) && missing(knots)) { ## df = number(interior knots) + 1 + intercept nIknots <- df - 1 - intercept if(nIknots < 0) { nIknots <- 0 warning("'df' was too small; have used ", 1 + intercept) } knots <- if(nIknots > 0) { knots <- seq.int(0, 1, length.out = nIknots + 2L)[-c(1L, nIknots + 2L)] stats::quantile(x[!outside], knots) } ## else NULL } else nIknots <- length(knots) Aknots <- sort(c(rep(Boundary.knots, 4L), knots)) if(any(outside)) { basis <- array(0, c(length(x), nIknots + 4L)) if(any(ol)) { k.pivot <- Boundary.knots[1L] xl <- cbind(1, x[ol] - k.pivot) tt <- splines::spline.des(Aknots, rep(k.pivot, 2L), 4, c(0, 1))$design basis[ol, ] <- xl %*% tt } if(any(or)) { k.pivot <- Boundary.knots[2L] xr <- cbind(1, x[or] - k.pivot) tt <- splines::spline.des(Aknots, rep(k.pivot, 2L), 4, c(0, 1))$design basis[or, ] <- xr %*% tt } if(any(inside <- !outside)) basis[inside, ] <- splines::spline.des(Aknots, x[inside], 4)$design } else basis <- splines::spline.des(Aknots, x, 4)$design # Fix the clamping if( !is.logical(fixsl) ) warning( "fixsl elements must be of mode logical" ) # Only the 4th parameter affected, should be either 1 or 2 in the two positions const <- splines::spline.des( Aknots, Boundary.knots, 4, c(2-fixsl[1],2-fixsl[2]) )$design if(!intercept) { const <- const[, -1 , drop = FALSE] basis <- basis[, -1 , drop = FALSE] } qr.const <- qr(t(const)) basis <- as.matrix((t(qr.qty(qr.const, t(basis))))[, - (1L:2L), drop = FALSE]) n.col <- ncol(basis) if(nas) { nmat <- matrix(NA, length(nax), n.col) nmat[!nax, ] <- basis basis <- nmat } dimnames(basis) <- list(nx, 1L:n.col) a <- list(degree = 3, knots = if(is.null(knots)) numeric(0) else knots, Boundary.knots = Boundary.knots, intercept = intercept) attributes(basis) <- c(attributes(basis), a) class(basis) <- c("cns", "basis", "matrix") basis } #------------------------------------------------------------------------------- # An extension of ns that automatically takes the smallest and largest knots # as boundary knots without further ado, but also allows centering # around a reference and detrending by means of projection, as well as # clamping. Ns <- function( x, ref = NULL, df = NULL, knots = NULL, intercept = FALSE, Boundary.knots = NULL, fixsl = c(FALSE,FALSE), detrend = FALSE ) { ## Check sensibility of arguments if( !is.null(ref) ) { if( !is.vector(ref) ) stop( "Argument 'ref' must be a scalar, but it is a ", class(ref), "." ) if( is.vector(ref) & length(ref)>1 ) stop( "Argument 'ref' must be a scalar, but has length ", length(ref), "." ) if( intercept ) { warning( "ref= specified, hence intercept=TRUE is ignored") intercept <- FALSE } } ## Detrending required? if( any(detrend>0) ) { # covers both logical and vector if( any(detrend<0) ) stop( "Some elements of weight are <0, e.g. no", (ww <- which(detrend<0))[1:min(5,length(ww))], "." ) if( !(length(detrend) %in% c(1,length(x))) ) { warning( "Weights in inner product diagonal matrix set to 1") weight <- rep(1,length(x)) } else weight <- if( is.numeric(detrend) ) detrend else rep(1,length(x)) detrend <- TRUE } if( detrend & intercept ) { warning( "detrend= specified, hence intercept=TRUE is ignored") intercept <- FALSE } if( detrend & any(fixsl) ) { warning( "detrend= specified, hence fixsl argument is ignored") fixsl=c(FALSE,FALSE) } ## Here is the specification of the spline basis ## knots= specified if( !is.null( knots ) ) { if( is.null( Boundary.knots ) ) { if( !is.null( knots ) ) { knots <- sort( unique( knots ) ) ok <- c(1,length(knots)) Boundary.knots <- knots[ok] knots <- knots[-ok] } } MM <- ns.ld( x, knots = knots, Boundary.knots = Boundary.knots, intercept = (intercept & is.null(ref)), fixsl = fixsl ) if( !is.null(df) ) cat("NOTE: Both knots= and df= specified, df ignored") } ## df= specified if( is.null( knots ) & !is.null( df ) ) MM <- ns.ld( x, df = df, intercept = (intercept & is.null(ref)), fixsl = fixsl ) ## Reference point specified ? if( !is.null(ref) ) { MM <- MM - ns.ld( rep(ref,length(x)), knots = attr(MM,"knots"), Boundary.knots = attr(MM,"Boundary.knots"), fixsl = fixsl ) } ## Detrending required ? if( detrend ) { DD <- detrend( MM, x, weight=weight ) ## NOTE: detrend does not preserve attributes for( aa in c("degree","knots","Boundary.knots","intercept","class") ) attr( DD, aa ) <- attr( MM, aa ) attr( DD, "detrend" ) <- TRUE attr( DD, "proj.wt" ) <- weight MM <- DD } return( MM ) } Epi/R/Cplot.R0000644000176200001440000000514312705663505012410 0ustar liggesusersCplot <- function( rates, age = as.numeric( rownames( rates ) ), per = as.numeric( colnames( rates ) ), grid = FALSE, c.grid = grid, ygrid = grid, col.grid = gray( 0.9 ), c.lim = NULL, ylim = range( rates[rates>0], na.rm=TRUE ), at = NULL, labels = paste( at ), c.lab = names( dimnames( rates ) )[2], ylab = deparse( substitute( rates ) ), type = "l", lwd = 2, lty = 1, col = par( "fg" ), log.ax = "y", las = 1, xannx = 1/20, ann = FALSE, cex.ann = 0.8, a.thin = seq( 1, length( age ), 2 ), ... ) { # Convert the age-period table to an age-cohort table rt <- as.table( rates ) dimnames( rt ) <- list( age = age, per = per ) rtf <- data.frame( rt ) rtf$age <- as.numeric( as.character( rtf$age ) ) rtf$per <- as.numeric( as.character( rtf$per ) ) # Check that age and period classe have equal lengths: wa <- diff( ag <- sort( unique(rtf$age) ) ) wp <- diff( pg <- sort( unique(rtf$per) ) ) if( unique(wa) != unique(wp) ) stop("Age and period intervals must have same width:\n", "Ages:", ag, "\n", "Periods:", pg, "\n", "No plot with cohort produced.\n" ) # Table by age and cohort ac <- tapply( rtf$Freq, list( rtf$age, rtf$per-rtf$age ), mean ) coh <- as.numeric( colnames( ac ) ) if( is.null( c.lim ) ) c.lim <- range( coh, na.rm=TRUE ) + c(0,diff( range( coh ) )/30) * ann # Plot the frame if( ann ) c.lim <- c.lim - c(diff( range( coh ) ) * xannx,0) matplot( coh, t(ac), type="n", xlim=c.lim, ylim=ylim, xlab=c.lab, ylab=ylab, log=log.ax, las=las, yaxt=if( !is.null( at ) ) "n" else "s" ) if( !is.null( at ) ) axis( side=2, at=at, labels=labels, yaxt="s", las=las ) # and the grid if required if( !missing( c.grid ) | !missing( grid ) ) { if( is.logical( c.grid ) & c.grid[1] ) c.grid <- nice( coh, log=par("xlog") ) abline( v=c.grid, col=col.grid ) } if( !missing( ygrid ) | !missing( grid ) ) { if( is.logical( ygrid ) & ygrid[1] ) ygrid <- nice( rates[!is.na(rates)], log=par("ylog") ) abline( h=ygrid, col=col.grid ) } box() # then the curves matlines( coh, t(ac), lwd=lwd, lty=lty, col=col, type=type, ... ) # annotate them if required (every second by default ) if( ann ) { nr <- nrow( ac ) nc <- ncol( ac ) # Find the cohorts for the last rates in each age-class c.end <- rev( per )[1] - age text( c.end[a.thin], rates[,ncol(rates)][a.thin], paste( "", age[a.thin] ), adj=c(0,0.5), cex=cex.ann, col=if( length(col)==1 ) col else col[a.thin] ) } } Epi/R/crr.Lexis.r0000644000176200001440000000253012777350201013230 0ustar liggesuserscrr.Lexis <- function( obj, mod, quiet=FALSE, ... ) { # Model formula to be transmitted md <- mod # Outcome variable fc <- as.character( mod[2] ) # Censoring levels cn <- unique( as.character(obj$lex.Xst)[obj$lex.Xst==obj$lex.Cst] ) # The competing causes (the remaining levels) cc <- setdiff( levels(obj$lex.Xst), union(fc,cn) ) # No l.h.s. side of formula when deriving model matrix mod[2] <- NULL # Remember no intercept term cv <- model.matrix( mod, data=obj )[,-1] # Then do it M <- crr( ftime = obj$lex.dur, fstatus = obj$lex.Xst, failcode = fc, cencode = cn, cov1 = cv, ... ) # A table of the no. of transitions N <- with( obj, table( Relevel( lex.Xst, c(fc,cc,cn) ) ) ) names( N ) <- paste( rep( c("Event:"," comp:"," cens:"), c(length(fc),length(cc),length(cn)) ), names(N) ) # add model and table to the resulting object M <- c( M, list( model.Lexis = md, transitions = cbind(N) ) ) # remember the class attribute (lost by doing "c") class( M ) <- "crr" # print overview if desired if( !quiet ) cat( "crr analysis of event", paste('"',fc,'"',sep=''), "\n versus", paste('"',cc,'"',sep=''), "\n with", paste('"',cn,'"',sep=''), "as censoring.\n" ) M } Epi/R/Termplot.R0000644000176200001440000000341412562641313013126 0ustar liggesusersTermplot <- function( obj, plot = TRUE, xlab = NULL, ylab = NULL, xeq = TRUE, yshr = 1.0, alpha = 0.05, terms = NULL, max.pt = NULL ) { # max.pt suppiled no.max <- missing( max.pt ) # Extract the curves to plot zz <- termplot( obj, se=TRUE, plot=FALSE, terms=terms ) nt <- length( zz ) for( i in 1:nt ) { # Thin the number of points in each returned term if( no.max ) max.pt <- nrow( zz[[i]] ) if( is.numeric(max.pt) & (nrow(zz[[i]]) > max.pt) ) zz[[i]] <- zz[[i]][round(seq(1,nrow(zz[[i]]),,max.pt)),] # Compute the estimate and the c.i. on log-scale zz[[i]] <- cbind( zz[[i]][,1], exp(as.matrix(zz[[i]][,2:3])%*%ci.mat(alpha=alpha)) ) } # Labels if( is.null(xlab) ) xlab <- names( zz ) if( is.null(ylab) ) ylab <- rep("",nt) ## Compute ranges of y and x xw <- sapply( zz, function(x) diff(range(x[,1 ])) ) yl <- sapply( zz, function(x) range(x[,2:4]) ) mr <- max( apply( yl, 2, function(x) exp(diff(log(x)))) ) yl <- apply( yl, 2, function(x) exp(mean(log(x))+c(-1,1)*log(mr)/2*yshr)) if( plot ) { ## Plot the effects side by side par( mfrow=c(1,nt), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 )#, bty="n", las=1 ) if( xeq ) ## Plot the terms so that x- and y-axes have the same extent { # Margins and total width in inches mw <- sum(par("mai")[c(2,4)]) tw <- par("pin")[1] # Widths of each plot, approx. at least pw <- (tw-nt*mw)*xw/sum(xw)+mw layout( rbind(1:nt), widths=pw ) } for( i in 1:nt ) matplot( zz[[i]][,1], zz[[i]][,2:4], xlab=xlab[i], xaxs="i", xlim=range(zz[[i]][,1]), ylab=ylab[i], yaxs="i", ylim=yl[,i], log="y", type="l", lty=1, lwd=c(5,2,2), col="black" ) } ## Return the extracted terms invisible( zz ) } Epi/R/ci.pd.R0000644000176200001440000000604512531361077012322 0ustar liggesusersci.pd <- function( aa, bb=NULL, cc=NULL, dd=NULL, method = "Nc", alpha = 0.05, conf.level = 0.95, digits = 3, print = TRUE, detail.labs = FALSE ) { # Computes the approximate c.i. for the probability difference # Optional methods: # -- "AC", Agresti and Caffo, Am Statistician (2000), # -- "Nc", method 10 from Newcombe, Stat.Med. 17, (1998), pp.873 ff. if ( !(method %in% c("AC", "Nc") ) ) stop( paste('Method', method, 'unsupported: Only "Nc" and "AC" supported') ) # Fix the confidence level if( missing( alpha ) ) alpha <- 1 - conf.level if( missing( conf.level ) ) conf.level <- 1 - alpha # Allow various forms of vector and matrix input prefix <- "" if( is.vector( aa ) & length( aa ) > 1 ) prefix <- names( aa ) if( length( dim( aa ) ) == 2 ) { bb <- aa[1,2] cc <- aa[2,1] dd <- aa[2,2] aa <- aa[1,1] } if( length( dim( aa ) ) == 3 ) { prefix <- paste( if( is.null( dimnames( aa ) ) ) 1:dim(aa)[3] else dimnames( aa )[[3]], ": ", sep="" ) bb <- aa[1,2,] cc <- aa[2,1,] dd <- aa[2,2,] aa <- aa[1,1,] } if( length( dim( aa ) ) > 3 ) stop( "Maximal array dimension (3) exceeded!" ) # Function to give roots in a 2nd degree polynomial # (Polyroot does not work on vectors of coefficients) pol2 <- function( Aye, Bee, Sea ) { Dee <- Bee^2 - 4 * Aye * Sea lo <- ifelse( Dee >= 0, ( -Bee - sqrt( Dee ) ) / ( 2 * Aye ), NA ) hi <- ifelse( Dee >= 0, ( -Bee + sqrt( Dee ) ) / ( 2 * Aye ), NA ) cbind( lo, hi ) } # Put the data in the right form x1 <- aa n1 <- aa+cc p1 <- x1/n1 x2 <- bb n2 <- bb+dd p2 <- x2/n2 pd <- x1/n1 - x2/n2 z <- qnorm( 1-alpha/2 ) zz <- z^2 if ( method == "AC" ) { x1.1 <- x1+1 n1.2 <- n1+2 x2.1 <- x2+1 n2.2 <- n2+2 p1.1 <- x1.1/n1.2 p2.1 <- x2.1/n2.2 pd.1 <- p1.1 - p2.1 SE.4 <- sqrt( p1.1 * ( 1-p1.1) /n1.2 + p2.1 * ( 1-p2.1) /n2.2 ) res <- cbind( n1, p1, n2, p2, pd, pd.1 - z*SE.4, pd.1 + z*SE.4 ) } else if ( method == "Nc" ) { A1 <- 1 + zz / n1 B1 <- -2*x1/n1 - zz / n1 C1 <- ( x1 / n1 )^2 r1 <- pol2( A1, B1, C1 ) A2 <- 1 + zz / n2 B2 <- -2*x2/n2 - zz / n2 C2 <- ( x2 / n2 )^2 r2 <- pol2( A2, B2, C2 ) dlt <- sqrt( ( x1/n1 - r1[,1] )^2 + ( x2/n2 - r2[,2] )^2 ) eps <- sqrt( ( x1/n1 - r1[,2] )^2 + ( x2/n2 - r2[,1] )^2 ) res <- cbind(n1, p1, n2, p2, pd, pd-dlt, pd+eps ) } colnames( res ) <- c("n1","p1","n2","p2", "diff",paste( alpha/2 *100,"%",sep=""), paste((1-alpha/2)*100,"%",sep="") ) rownames( res ) <- prefix if( detail.labs ) rownames( res ) <- paste( prefix, ": ", aa, "/(", aa, "+", cc, ") - ", bb, "/(", bb, "+", dd, ")", sep="" ) if( print ) print( round( res, digits ) ) invisible( res ) } Epi/R/pctab.R0000644000176200001440000000070212531361077012410 0ustar liggesuserspctab <- function( TT, margin=length( dim( TT ) ), dec=1 ) { nd <- length( dim( TT ) ) sw <- (1:nd)[-margin[1]] rt <- sweep( addmargins( TT, margin, list( list( All=sum, N=function( x ) sum( x )^2/100 ) ) ), sw, apply( TT, sw, sum )/100, "/" ) if( dec ) print( round( rt, dec ) ) invisible( rt ) } Epi/R/ci.cum.R0000644000176200001440000000627513471207755012516 0ustar liggesusersci.cum <- function( obj, ctr.mat = NULL, subset = NULL, intl = 1, alpha = 0.05, Exp = TRUE, ci.Exp = FALSE, sample = FALSE ) { # First extract all the coefficients and the variance-covariance matrix cf <- COEF( obj ) vcv <- VCOV( obj ) # Check if the intervals matches ctr.mat if( length( intl ) == 1 ) intl <- rep( intl, nrow( ctr.mat ) ) if( length( intl ) != nrow( ctr.mat ) ) stop( "intl must match ctr.mat" ) if( inherits( ctr.mat, "data.frame" ) ) { ctr.mat <- df2ctr( obj, ctr.mat ) } else { # Workaround to expand the vcov matrix with 0s so that it matches # the coefficients vector in case of (extrinsic) aliasing. ## NOT needed after 3.5.0 ## if( any( is.na( cf ) ) ) ## { ## vM <- matrix( 0, length( cf ), length( cf ) ) ## dimnames( vM ) <- list( names( cf ), names( cf ) ) ## vM[!is.na(cf),!is.na(cf)] <- vcv ## cf[is.na(cf)] <- 0 ## vcv <- vM ## } if( is.character( subset ) ) { sb <- numeric(0) for( i in 1:length( subset ) ) sb <- c(sb,grep( subset[i], names( cf ) )) subset <- sb # unique( sb ) } # If subset is not given, make it the entire set if( is.null( subset ) ) subset <- 1:length( cf ) # Exclude units where aliasing has produced NAs. # Not needed after replacement with 0s # subset <- subset[!is.na( cf[subset] )] cf <- cf[subset] vcv <- vcv[subset,subset] if( is.null( ctr.mat ) ) { ctr.mat <- diag( length( cf ) ) rownames( ctr.mat ) <- names( cf ) } if( dim( ctr.mat )[2] != length(cf) ) stop( paste("\n Dimension of ", deparse(substitute(ctr.mat)), ": ", paste(dim(ctr.mat), collapse = "x"), ", not compatible with no of parameters in ", deparse(substitute(obj)), ": ", length(cf), sep = "")) } # Finally, here is the actual computation of the estimates ct <- ctr.mat %*% cf vc <- ctr.mat %*% vcv %*% t( ctr.mat ) # If a sample is requested replace the estimate by a sample if( sample ) ct <- t( mvrnorm( sample, ct, vc ) ) # If Exp was requested, we take the exponential of the estimates # before we cumulate the sum if( Exp ) { ct <- exp( ct ) vc <- ( ct[,1] %*% t(ct[,1]) ) * vc } # Here is the cumulation matrix cum.mat <- 1 - upper.tri( diag(ct[,1]) ) # Multiply columns of the matrix with interval lengths cum.mat <- t( intl * t( cum.mat ) ) # This is then multiplied to the coefficients ct <- cum.mat %*% ct if( sample ) return( ct ) else { vc <- cum.mat %*% vc %*% t( cum.mat ) se <- sqrt( diag( vc ) ) if( !ci.Exp ) { cum <- cbind( ct, se ) %*% ci.mat( alpha=alpha ) return( cbind( cum, "StdErr"=se ) ) } else { cum <- exp( cbind( log(ct), se/ct ) %*% ci.mat( alpha=alpha ) ) return( cbind( cum, "Erf"=exp( qnorm(1-alpha/2)*se/as.vector(ct) ) ) ) } } } ci.surv <- function( obj, ctr.mat = NULL, subset = NULL, intl = 1, alpha = 0.05, Exp = TRUE, sample = FALSE ) { CH <- ci.cum( obj, ctr.mat = ctr.mat, subset = subset, intl = intl, alpha = alpha, Exp = Exp, ci.Exp = TRUE, sample = sample ) exp( -rbind(0,CH[1:(nrow(CH)-1),-4]) ) } Epi/R/splitLexis.R0000644000176200001440000000775612531361077013477 0ustar liggesuserssplit.lexis.1D <- function(lex, breaks, time.scale, tol) { time.scale <- check.time.scale(lex, time.scale) ## Entry and exit times on the time scale that we are splitting time1 <- lex[,time.scale, drop=FALSE] time2 <- time1 + lex$lex.dur ## Augment break points with +/- infinity breaks <- sort( unique( breaks ) ) I1 <- c(-Inf, breaks) I2 <- c(breaks,Inf) ## Arrays containing data on each interval (rows) for each subject (cols) en <- apply(time1, 1, pmax, I1) # Entry time ex <- apply(time2, 1, pmin, I2) # Exit time NR <- nrow(en) NC <- ncol(en) ## Does subject contribute follow-up time to this interval? ## (intervals shorter than tol are ignored) valid <- en < ex - tol dur <- ex - en; dur[!valid] <- 0 # Time spent in interval ## Cumulative time since entry at the start of each interval time.since.entry <- rbind(0, apply(dur,2,cumsum)[-NR,,drop=FALSE]) cal.new.entry <- function(entry.time) { sweep(time.since.entry, 2, entry.time, "+")[valid] } old.entry <- lex[, timeScales(lex), drop=FALSE] new.entry <- lapply(old.entry, cal.new.entry) ## Status calculation aug.valid <- rbind(valid, rep(FALSE, NC)) last.valid <- valid & !aug.valid[-1,] any.valid <- apply(valid,2,any) new.Xst <- matrix( lex$lex.Cst, NR, NC, byrow=TRUE) new.Xst[last.valid] <- lex$lex.Xst[any.valid] n.interval <- apply(valid, 2, sum) new.lex <- Lexis("entry" = new.entry, "duration" = dur[valid], "id" = rep(lex$lex.id, n.interval), "entry.status" = rep(lex$lex.Cst, n.interval), "exit.status" = new.Xst[valid]) ## Update breaks attribute and tranfer time.since attribute breaks.attr <- attr(lex, "breaks") breaks.attr[[time.scale]] <- sort(c(breaks.attr[[time.scale]], breaks)) attr(new.lex, "breaks") <- breaks.attr attr(new.lex, "time.since") <- attr(lex, "time.since") return(new.lex) } splitLexis <- function(lex, breaks, time.scale=1, tol= .Machine$double.eps^0.5) { ## Advise the uninformed user... if( inherits(lex,"stacked.Lexis") ) stop( "It makes no sense to time-split after stacking ---\n", "split your original Lexis object and stack that to get what you want.\n") ## Set temporary, unique, id variable lex$lex.tempid <- lex$lex.id lex$lex.id <- 1:nrow(lex) ## Save auxiliary data aux.data.names <- setdiff(names(lex), timeScales(lex)) aux.data.names <- aux.data.names[substr(aux.data.names,1,4) != "lex."] aux.data <- lex[, c("lex.id","lex.tempid", aux.data.names), drop=FALSE] ## Check for NAs in the timescale ts <- check.time.scale(lex, time.scale) ts.miss <- any(is.na(lex[,ts])) if( ts.miss ) { na.lex <- lex[ is.na(lex[,ts]),] lex <- lex[!is.na(lex[,ts]),] cat( "Note: NAs in the time-scale \"", ts, "\", you split on\n") } ## If states are factors convert to numeric while splitting factor.states <- is.factor( lex$lex.Cst ) if( factor.states ) { state.levels <- levels( lex$lex.Cst ) nstates <- nlevels( lex$lex.Cst ) lex$lex.Cst <- as.integer( lex$lex.Cst ) lex$lex.Xst <- as.integer( lex$lex.Xst ) } ## Split the data lex <- split.lexis.1D(lex, breaks, time.scale, tol) ## Reinstitute the factor levels if( factor.states ) { lex$lex.Cst <- factor( lex$lex.Cst, levels=1:nstates, labels=state.levels ) lex$lex.Xst <- factor( lex$lex.Xst, levels=1:nstates, labels=state.levels ) } ## Put the NA-rows back if( ts.miss ) lex <- rbind( lex, na.lex[,colnames(lex)] ) ## Save attributes lex.attr <- attributes(lex) ## Merge lex <- merge.data.frame(lex, aux.data, by="lex.id") ## Restore attributes attr(lex,"breaks") <- lex.attr$breaks attr(lex,"time.scales") <- lex.attr$time.scales attr(lex,"time.since") <- lex.attr$time.since class(lex) <- c("Lexis", "data.frame") ## Restore id variable lex$lex.id <- lex$lex.tempid lex$lex.tempid <- NULL return(lex) } Epi/R/apc.plot.R0000644000176200001440000001343113443412120013027 0ustar liggesusersplot.apc <- apc.plot <- function( x, r.txt="Rate", ... ) { if( !inherits( x, "apc" ) ) stop( "Argument must be an apc-object" ) # Determine the ranges of the horizontal axes a.lab = nice( x$Age[,1] ) cp.lab = nice( c(x$Per[,1],x$Coh[,1]), high=0.1 )[-1] # The necessary range of the two vertical axes r.rg <- range( x$Age[,-1] ) rr.rg <- range( rbind( x$Per[,-1], x$Coh[,-1] ) ) # Align the RR with the rates on an integer power of 10 rr.ref <- 10^floor( log10(r.rg[2])-log10(rr.rg[2]) ) # Find the tic-marks for the two vertical axes r.tic <- nice( r.rg, log=T, lpos=1:9 ) rr.tic <- nice( rr.rg, log=T, lpos=1:9 ) # Expand to cover it all r.tic <- sort( unique( c( r.tic, rr.tic*rr.ref ) ) ) rr.tic <- r.tic/rr.ref # Find the places for labels r.lab <- nice( r.tic, log=T, lpos=c(1,2,5) ) rr.lab <- nice( rr.tic, log=T, lpos=c(1,2,5) ) r.lab <- r.lab[ r.lab>min( r.tic) & r.labmin(rr.tic) & rr.lab% mutate(extime = dop + c(NA, diff(dop) * amt[-1] / amt[-length(amt)]) + grace) %>% ungroup() # generate 0 purchases in pzero where coverage expired before new purchase group_by(pdat, lex.id) %>% filter(extime < c(dop[-1],Inf)) %>% mutate(dop = extime, amt = 0) %>% select(lex.id, dop, amt) -> pzero # pzero has potentially become a grouped tibble so make it a data frame pzero <- as.data.frame(pzero) # append to original data frame pdat <- rbind(pdat[,names(pzero)], pzero) # reinstate the time-scale name names(pdat)[grep("dop",names(pdat))] <- tnam # sort by lex.id and time and coerce to data frame oo <- order(pdat$lex.id, pdat[,tnam, drop = TRUE]) pdat <- as.data.frame(pdat[oo,]) rownames(pdat) <- NULL pdat } #---------------------------------------------------------------------- # addDrug.Lexis addDrug.default <- addDrug.Lexis <- function(Lx, # Lexis object, should be timesplit pdat, # (named) list of data frames of drug purchaces amt = "amt", # name of amount variable in pdat apt = "apt", # name of amount per time variable in pdat # to be used if method = "dos" method = "ext", # extrapolation from times and amounts # "dos" is based on dosage, apt and amt # "fix" is using a fixed interval, maxt maxt = NULL, # vector of times covered by a single prescription, grace = 0, # vector of grace periods after final data tnam = setdiff(names(pdat[[1]]),c("lex.id", amt))[1], prefix = NULL, # character vector suffix = NULL, # character vector sepfix = "." # separator for pre- and suf-fixes ) { # utility functions na0 <- function(x) ifelse(is.na(x), 0, x) csum0 <- function(x) c(0, cumsum(na0(x)[-length(x)])) # binding variables qwzrx <- exnam <- tfc <- lex.id <- pur <- lex.dur <- xtime <- expos <- dospt <- NULL # don't bother about the warnings oldopts <- options(warn = -1) on.exit(options(oldopts)) # Save attributes to return with result lex.attr <- attributes(Lx) # time scale if (missing(tnam)) cat("NOTE: timescale taken as '", tnam, "'\n", sep = "") # construct names for the 0-expanded purchase data frames if not given if(is.null(names(pdat))) names(pdat) <- paste0('P', 1:length(pdat)) # prefix or suffix for variables ex, tf, ct, cd if(!(suff <- !is.null(prefix))) prefix <- names(pdat) if(!(pref <- !is.null(suffix))) suffix <- names(pdat) if(suff && pref) cat("NOTE: you are asking for *both* pre- and suffix\n") # if none specified use prefix pref <- pref | !suff # the renaming vector to be used later onam <- c("expos","tfex","ctime","cdos") shortnames <- substr(onam, 1, 2) # number of purchase files np <- length(pdat) # expand maxt and grace by recycling maxt <- rep(maxt , np)[1:np] grace <- rep(grace, np)[1:np] # Structure to hold the 0-expanded data sets pdat0 <- list() pall <- NULL # Define the 0 amount purchases at exposure end and collect times in pall for(i in 1:np) { pdat0[[i]] <- ins0(pdat[[i]], amt = amt, apt = apt, method = method, maxt = maxt[i], grace = grace[i], tnam = tnam, verbose = i == 1) pall <- rbind(pall, pdat0[[i]][,c("lex.id", tnam)]) } # order pall by id and time, remove duplicates and add a bogus variable oo <- order(pall$lex.id, pall[,tnam]) pall <- pall[oo,] pall <- pall[!duplicated(pall),] pall$qwzrx <- 0 # add the total purchase data in order to expand to all cut dates when # appending data from each drug Gx <- addCov.Lexis(Lx, pall, timescale = tnam) Gx <- select(Gx, -qwzrx, -exnam, -tfc) # remove tfc as time scale and keep Lexis attributes to resinstate later wh.tfc <- match("tfc", attr(Gx, "time.scales")) attr(Gx,"time.scales") <- Gsc <- attr(Gx, "time.scales")[-wh.tfc] attr(Gx,"time.since") <- Gsi <- attr(Gx, "time.since" )[-wh.tfc] class(Gx) <- Gcl <- c("Lexis", "data.frame") # put the expanded drug purchases in the Lexis object allnam <- NULL for(i in 1:np) { # renaming the variables with pre- and/or suffix rnam <- shortnames if(suff) rnam <- paste(rnam, suffix[i], sep = sepfix) if(pref) rnam <- paste(prefix[i], rnam, sep = sepfix) names(rnam) <- onam allnam <- c(allnam, rnam) # add the i'th drug exposure data file Gx <- addCov.Lexis(Gx, pdat0[[i]], timescale = tnam, exnam = "pur") # compute the exposure variables, drop unneeded variables and rename Gx <- ( group_by(Gx, lex.id, pur) %>% mutate(xtime = sum(lex.dur) + tfc[1], # total exposure time for this purchase dospt = amt / xtime ) # dose per time for this interval %>% group_by(lex.id) %>% mutate(expos = !is.na(amt) & amt>0, tfex = csum0(lex.dur * (cumsum(expos) > 0)), ctime = csum0(lex.dur * expos * (amt>0)) + na0(tfc[1]), cdos = csum0(lex.dur * expos * dospt) + na0(dospt[1]) * na0(tfc[1])) %>% select(-pur, -xtime, -dospt, -tfc, -amt) %>% plyr::rename(rnam) ) # reinstate as Lexis object attr(Gx,"time.scales") <- Gsc attr(Gx,"time.since") <- Gsi class(Gx) <- Gcl } return(Gx[,c(setdiff(names(Gx), allnam), allnam)]) } Epi/R/foreign.R0000644000176200001440000000346413763626440012766 0ustar liggesusers# The msdata method msdata <- function (obj, ...) UseMethod("msdata") msdata.Lexis <- function( obj, time.scale = timeScales(obj)[1], ... ) { tr.mat <- tmat(obj) # Essentially a msdata object is a stacked Lexis object with # other variable names tmp <- stack.Lexis(factorize.Lexis(obj)) lv <- c(match(timeScales(obj), names(tmp)), grep("lex\\.", names(tmp))) # The transitions that we refer to are extracted from lex.Tr: ss <- strsplit(as.character(tmp$lex.Tr), "->") # The resulting dataframe is created by renaming columns in the # stacked Lexis object data.frame( id = tmp$lex.id, from = sapply( ss, FUN=function(x) x[1] ), to = sapply( ss, FUN=function(x) x[2] ), trans = as.integer( tmp$lex.Tr ), Tstart = tmp[,time.scale], Tstop = tmp[,time.scale] + tmp$lex.dur, time = tmp$lex.dur, status = as.integer(tmp$lex.Fail), tmp[,-lv] ) } # The etm method etm <- function (data, ...) UseMethod("etm") etm.Lexis <- function( data, time.scale = timeScales(data)[1], cens.name = "cens", s = 0, t = "last", covariance = TRUE, delta.na = TRUE, ... ) { dfr <- data.frame( id = data$lex.id, from = as.character(data$lex.Cst), to = as.character(data$lex.Xst), entry = data[,time.scale], exit = data[,time.scale] + data$lex.dur, stringsAsFactors = FALSE ) dfr$to <- with( dfr, ifelse( from==to, cens.name, to ) ) etm::etm( data = dfr, state.names = levels(data$lex.Cst), tra = tmat(data, mode = "logical"), cens.name = cens.name, s = s, t = t, covariance = covariance, delta.na = delta.na ) } Epi/R/Life.lines.R0000644000176200001440000000555212531361077013317 0ustar liggesusersLife.lines <- function( entry.date = NA, exit.date = NA, birth.date = NA, entry.age = NA, exit.age = NA, risk.time = NA ) { # A function allowing any three of the arguments to be specified # and yet returns enty age and -time and exit age and -time. # Check if any variable is supplied with class if( conv <- any( inherits( entry.date, "Date" ), inherits( exit.date, "Date" ), inherits( birth.date, "Date" ), inherits( entry.age , "difftime" ), inherits( exit.age , "difftime" ), inherits( risk.time, "difftime" ) ) ) { # Convert "Date" and "difftime" to years if( inherits( entry.date, "Date" ) ) entry.date <- as.numeric( entry.date ) / 365.35 + 1970 if( inherits( exit.date, "Date" ) ) exit.date <- as.numeric( exit.date ) / 365.35 + 1970 if( inherits( birth.date, "Date" ) ) birth.date <- as.numeric( birth.date ) / 365.35 + 1970 if( inherits( entry.age , "difftime" ) ) entry.age <- as.numeric( entry.age ) / 365.35 if( inherits( exit.age , "difftime" ) ) exit.age <- as.numeric( exit.age ) / 365.35 if( inherits( risk.time, "difftime" ) ) risk.time <- as.numeric( risk.time ) / 365.35 # Convert to numeric class( entry.date ) <- "numeric" class( exit.date ) <- "numeric" class( birth.date ) <- "numeric" class( entry.age ) <- "numeric" class( exit.age ) <- "numeric" class( risk.time ) <- "numeric" } # Find out which three items are supplied. # wh <- (1:6)[!is.na( list( entry.date, entry.age, exit.date, exit.age, birth.date, risk.time ) )] # Matrix of relevant quantities. # LL <- rbind( entry.date, entry.age, exit.date, exit.age, birth.date, risk.time ) # Matrix giving the three constraints among the six quantities: # M <- rbind( c( -1, 1, 0, 0, 1, 0 ), c( 0, 0, -1, 1, 1, 0 ), c( 0, 1, 0, -1, 0, 1 ) ) # Now in principle we have that M %*% LL = 0. # Partitioning M=(A1|A2), t(LL)=(t(x1),t(x2)) # this gives A1 %*% x1 = -A2 %*% x2 # Check if there is sufficient information # if( qr( M[,-wh[1:3]] )$rank < 3 ) cat( "Insufficient information to display life lines" ) # Then do the calculation # A1 <- M[, wh[1:3]] A2 <- M[,-wh[1:3]] x1 <- LL[wh[1:3],] x2 <- -solve( A2 ) %*% A1 %*% x1 LL[-wh[1:3],] <- x2 LL <- data.frame( t(LL) ) attr( LL, "Date" ) <- conv # Convert to dates and difftimes if( conv ) { LL[,c(1,3,5)] <- ( LL[,c(1,3,5)] - 1970 ) * 365.25 LL[,c(2,4,6)] <- LL[,c(2,4,6)] * 365.25 class( LL[,1] ) <- class( LL[,3] ) <- class( LL[,5] ) <- "Date" class( LL[,2] ) <- class( LL[,4] ) <- class( LL[,6] ) <- "difftime" } LL } Epi/R/stack.Lexis.R0000644000176200001440000000377513763706532013533 0ustar liggesusers# Functions to facilitate analysis of multistate models # The stack method is already defined (in the utils package) # and hence imported in the NAMESPACE file stack.Lexis <- function(x, ...) { ## Function to stack obervations for survival analysis ## Make sure that lex.Cst and lex.Xst are factors with identical levels x <- factorize(x) ## Same covariates xx <- data.frame( cbind( x, lex.Tr="", lex.Fail=FALSE ) )[NULL,] tm <- tmat.Lexis( x ) for( fst in levels(factor(x$lex.Cst)) ) for( tst in levels(factor(x$lex.Xst)) ) if( !is.na(tm[fst,tst]) ) { tr = paste( fst, "->", tst , sep="" ) zz <- x[x$lex.Cst==fst,] xx <- rbind( xx, data.frame( zz, lex.Tr=tr, lex.Fail=(zz$lex.Xst==tst) ) ) } xx$lex.Tr <- factor(xx$lex.Tr) ## Reshuffle the variables wh.om <- match( "lex.Xst", names(xx) ) wh.rl <- match( c("lex.Tr","lex.Fail"), names(xx) ) xx <- xx[,c(1:wh.om,wh.rl,(wh.om+1):(wh.rl[1]-1))] attr(xx,"breaks") <- attr(x, "breaks") attr(xx,"time.scales") <- attr(x, "time.scales") class( xx ) <- c("stacked.Lexis","data.frame") xx } subset.stacked.Lexis <- function(x, ... ) { y <- subset.data.frame(x, ...) attr(y,"breaks") <- attr(x, "breaks") attr(y,"time.scales") <- attr(x, "time.scales") class(y) <- c("stacked.Lexis","data.frame") return(y) } transform.stacked.Lexis <- function(`_data`, ... ) { save.at <- attributes(`_data`) ## We can't use NextMethod here because of the special scoping rules ## used by transform.data.frame y <- base::transform.data.frame(`_data`, ...) save.at[["names"]] <- attr(y, "names") attributes(y) <- save.at y } # The tmat method tmat <- function (x, ...) UseMethod("tmat") tmat.Lexis <- function( x, Y=FALSE, mode="numeric", ... ) { zz <- table(x$lex.Cst,x$lex.Xst) class(zz) <- "matrix" if( Y ) { diag(zz) <- summary( x, simplify=FALSE )[[1]][1:nrow(zz),"Risk time:"] } else diag(zz) <- NA zz[zz==0] <- NA if( mode != "numeric" ) zz <- !is.na(zz) zz } Epi/R/ci.Crisk.R0000644000176200001440000001250414003542722012761 0ustar liggesusers# Simulate rates from a list of models, 0th simulation is the rates # based on the model estimates simrates <- function(mods, # named list of models - one for each cause nd, # prediction data frame nB = 1000, # number of simulated samples int = mean(diff(nd[,1]))) # time is first in column of nd # seed) not implemented yet { # from a list of models (mods) for nC cause-specific rates and a # common prediction frame, nd, we generate nB samples of predicted # rates. It is assumed that the nd refer to midpoints of intervals res <- NArray(list(time = rownames(nd), mod = names(mods), sim = 1:nB)) nT <- nrow(nd) # no of timepoints (interval midpoints) nC <- length(mods) # no. competing risks for(i in 1:nC) res[,i,] <- ci.lin(mods[[i]], nd, sample = nB) res <- exp(res) attr( res, "int" ) <- int res } # Compute nC+1 cumulative risks from nC rates mkprobs <- function(rtab, int) { # rtab is assumed to be a matrix with rates in (named) columns at int # equidistance assumed computed at times int/2, 3*int/2 etc. so rtab # is assumed nT x nC nT <- nrow(rtab) nC <- ncol(rtab) # integrated intensities at interval boundaries, so (1+nT) x nC Rtab <- rbind(0, apply(rtab, 2, cumsum)) * int # state probabilities at interval endpoints so (1+nT) x (1+nC) Pr <- Rtab[,c(1,1:nC)] * NA colnames(Pr)[1] <- "Surv" # Survival prob in first column # survival function (also the first column in Pr) Pr[,"Surv"] <- Sv <- exp(-apply(Rtab, 1, sum)) # convenience function to compute midpoints between points in a vector midpoint <- function(x) x[-1] - diff(x) / 2 # cumulative risks - note we are using the midvalue of the Sv, length nT for( i in 1:nC ) Pr[,i+1] <- c(0, cumsum(rtab[,i] * midpoint(Sv)) * int) Pr } # return first, mean and median and ci from simulated sample mnqt <- function(x, alpha = 0.05) { # extracts the relevant quantiles across the # simulated samples c(quantile(x, probs = c(0.5, alpha / 2, 1 - alpha / 2), na.rm = TRUE)) } # Here is the function we need to compute cumulative risks ci.Crisk <- function( mods, # list of models nd, # data frame of points where rates are to be computed int = mean(diff(nd[,1])), # interval length in nd nB = 1000, # no of parametic bootstrap samples perm = length(mods):0 + 1, # order of cumulation of states alpha = 0.05, # 1 minus confidence level sim.res = 'none') # seed = floor(runif(1, 1, 50000))) not implemented yet { if(missing(int)) cat("Times are assumed to be in the column", names(nd)[1], "at equal distances of", int, "\n") # First generate the simulated probabilities (T+1) x (C+1) x nB # contains the estimates as the first entry in the simulation dimension simrt <- simrates(mods = mods, nd = nd, nB = nB, int = int) # seed = seed) not implemented yet # if we want the simulation results for further processing attr(simrt, "int") <- int # the interval length needed with simrt if(substr(tolower(sim.res), 1, 1) == 'r') return(invisible(simrt)) # Array for the state probabilities probs <- NArray(list(time = 0:nrow(nd), cause = c("Surv", dimnames(simrt)[["mod"]]), sim = 1:nB)) # Compute the cumulative risks for(i in 1:nB) probs[,,i] <- mkprobs(simrt[,,i], int = int) attr(probs, "int") <- int # the interval length needed with probs if(substr(tolower(sim.res), 1, 1) == 'c') return(invisible(probs)) # otherwise we compute confidence intervals for selected statistics # 1. state (cumulative) probabilities Crisk <- sim2ci.Crisk(probs, alpha = alpha) # 2. stacked (cumulative) probabilities Srisk <- sim2ci.Srisk(probs, perm = perm, alpha = alpha) # 3. sojourn times in states Stime <- sim2ci.Stime(probs, alpha = alpha) # finally return in a list of useful quantities rlist <- list(Crisk = Crisk, Srisk = Srisk, Stime = Stime) attr(rlist, "int") <- int # the interval length used return(invisible(rlist)) } # 1. cumulative probabilities sim2ci.Crisk <- function(probs, alpha = 0.05) aperm(apply(probs, 1:2, mnqt, alpha), c(2,3,1)) # 2. stacked (cumulative) probabilities sim2ci.Srisk <- function(probs, perm = 1:dim(probs)[2], alpha = 0.05) { cprobs <- aperm(apply(probs[,perm,], c(1,3), cumsum), c(2,1,3)) cnam <- dimnames(cprobs)[["cause"]] for(i in 2:length(cnam)) dimnames(cprobs)[["cause"]][i] <- paste(cnam[1:i], collapse = "+") cpr <- aperm(apply(cprobs, 1:2, mnqt, alpha), c(2,3,1)) cpr[,-dim(cpr)[2],] } # 3. sojourn times in states sim2ci.Stime <- function(probs, int = attr(probs, "int"), alpha = 0.05) { # convenience function to compute midpoints between points in a vector midpoint <- function(x) x[-1] - diff(x) / 2 sojrn <- apply(probs, 2:3, function(x) cumsum(midpoint(x))) * int aperm(apply(sojrn, 1:2, mnqt, alpha), c(2,3,1)) } Epi/R/mod.Lexis.R0000644000176200001440000002067513743773377013214 0ustar liggesusersmodLexis <- function( Lx, nameLx, formula, from = preceding(Lx,to), to = absorbing(Lx), paired = FALSE, link = "log", scale = 1, verbose = TRUE, model, ... ) { # a common wrapper for glm and gam modeling of Lexis FU # is this a Lexis object ? if( !inherits(Lx,"Lexis") ) stop("The first argument must be a Lexis object.\n") # check that events are actual levels of lex.Xst if( is.numeric(to) ) to <- levels( Lx$lex.Xst )[to] wh <- match( to, levels(Lx$lex.Xst) ) if( any(is.na(wh)) ) stop("'to' must be a subset of: '", paste(levels(Lx$lex.Xst), collapse="','", sep=""), "'\n" ) # check that from are actual levels of lex.Cst if( is.numeric(from) ) from <- levels( Lx$lex.Cst )[from] wh <- match( from, levels(Lx$lex.Cst) ) if( any(is.na(wh)) ) stop("'from' must be a subset of: '", paste(levels(Lx$lex.Cst), collapse="','", sep=""), "'\n" ) # subset to these states Lx <- Lx[Lx$lex.Cst %in% from,] # first a small utility to show transitions as text: trt <- function( f, t ) paste( f, "->", t, sep="" ) # work out which transitions are modeled if( paired ) { if( length(from) != length(to) ) stop("If 'paired' is TRUE, from and to must have same length!\n") if( any(from==to) ) stop("If 'paired' is TRUE, entries in from and to must be different within pairs\n") trnam <- trt( from, to ) } else { tm <- tmat( Lx )[from,to,drop=FALSE] trnam <- outer( rownames(tm), colnames(tm), trt )[tm>0] trnam <- trnam[!is.na(trnam)] } # just for formatting the explanatory text onetr <- length( trnam )==1 trprn <- paste( trnam, collapse=", " ) # warn if a potentially silly model is defined if( any( (ts<-table(sapply( strsplit(trnam,"->"), function(x) x[1] )))>1 ) ) warning( "NOTE:\nMultiple transitions *from* state '",names(ts[ts>1]),"' - are you sure?", "\nThe analysis requested is effectively merging outcome states.", "\nYou may want analyses using a *stacked* dataset - see ?stack.Lexis\n" ) # Beginning of a new feature with a countmultiplier of the transitions # allowing tabular records to be merged to a Lexis object # --- not used subsequently in this function (yet) # if( !("lex.N" %in% names(Lx)) ) Lx$lex.N <- 1 # construct the model formula - note that we already made sure that # from and to are pairwise different if( length(formula) != 2 ) stop("formula must be a one-sided formula") form <- cbind( trt(Lx$lex.Cst,Lx$lex.Xst) %in% trnam, #*Lx$lex.N, Lx$lex.dur ) ~ 1 ## form <- cbind( (Lx$lex.Xst %in% to & ## Lx$lex.Xst != Lx$lex.Cst), #*Lx$lex.N, ## Lx$lex.dur ) ~ 1 form[3] <- formula[2] from <- levels( factor(Lx$lex.Cst) ) # only levels present in lex.Cst # Scaling Lx$lex.dur <- Lx$lex.dur/scale # Tell what we intend to and then do it if( verbose ){ cat( deparse(substitute(model)), " Poisson analysis of Lexis object ", nameLx, " with ", link, " link", ":\nRates for", if( onetr ) " the", " transition", if( !onetr ) "s", ": ", trprn, if( scale!=1 ) paste(", lex.dur (person-time) scaled by", scale ), "\n", sep="" ) } # Fit the model mod <- model( form, family = poisreg(link=link), data = Lx, ... ) # Add an explanatory attribute attr( mod, "Lexis" ) <- list( data=nameLx, trans=trnam, formula=form[-2], scale=scale ) mod } # Here are the actual functions of interest: ###################################################################### # the glm function glm.Lexis <- function( Lx, formula, from = preceding(Lx,to), to = absorbing(Lx), paired = FALSE, link = "log", scale = 1, verbose = TRUE, ... ) { # name of the supplied object nameLx <- deparse(substitute(Lx)) # sensible defaults if one of to and from is missing if( missing(from) & !missing(to) ) from <- preceding (Lx,to ) if( !missing(from) & missing(to) ) to <- succeeding(Lx,from) xx <- modLexis( Lx, nameLx, formula, from, to, paired = paired, link = link, scale = scale, verbose = verbose, model = stats::glm, ... ) class( xx ) <- c( "glm.lex", class(xx) ) xx } ###################################################################### # the gam function gam.Lexis <- function( Lx, formula, from = preceding(Lx,to), to = absorbing(Lx), paired = FALSE, link = "log", scale = 1, verbose = TRUE, ... ) { # name of the supplied object nameLx <- deparse(substitute(Lx)) # sensible defaults if one of the two is missing if( missing(from) & !missing(to) ) from <- preceding (Lx,to ) if( !missing(from) & missing(to) ) to <- succeeding(Lx,from) xx <- modLexis( Lx, nameLx, formula, from, to, paired = paired, link = link, scale = scale, verbose = verbose, model = mgcv::gam, ... ) class( xx ) <- c( "gam.lex", class(xx) ) xx } ###################################################################### # And here is the coxph counterpart: coxph.Lexis <- function( Lx, # Lexis object formula, # timescale ~ model from = preceding(Lx,to), # Exposure ('from' states) to = absorbing(Lx) , # Events ('to' states) paired = FALSE, verbose = TRUE, ... ) { # Lexis object ? if( !inherits(Lx,"Lexis") ) stop( "The first argument must be a Lexis object.\n") # sensible defaults if only one of to and from is missing if( missing(from) & !missing(to) ) from <- preceding (Lx,to ) if( !missing(from) & missing(to) ) to <- succeeding(Lx,from) # name of the dataset nameLx <- deparse(substitute(Lx)) # subset to the states we shall use Lx <- Lx[Lx$lex.Cst %in% from,] # work out which transitions are modeled # first a small utility for annotation trt <- function( f, t ) paste( f, "->", t, sep="" ) if( paired ) { if( length(from) != length(to) ) stop("If 'paired' is TRUE, from and to must have same length!\n") if( any(from==to) ) stop("If 'paired' is TRUE, entries in 'from' and 'to'", " must be pairwise different\n") trnam <- trt( from, to ) } else { tm <- tmat( Lx )[from,to,drop=FALSE] trnam <- outer( rownames(tm), colnames(tm), trt )[tm>0] trnam <- trnam[!is.na(trnam)] } # just for formatting explanatory text onetr <- length( trnam )==1 trprn <- paste( trnam, collapse=", " ) # warn if a potentially silly model is defined if( any( ts<-table(sapply( strsplit(trprn,"->"), function(x) x[1] ))>1 ) ) warning( "NOTE:\nMultiple transitions *from* state '",names(ts[ts>1]), "' - are you sure?", "\nThe analysis requested is effectively merging outcome states.", "\nYou may want analyses using a *stacked* dataset - see ?stack.Lexis\n" ) # Correct formula? if( length(formula) != 3 ) stop("'formula' must be a 2-sided formula, with the l.h.s. the timescale") # Is the l.h.s. a timescale? ts <- as.character( formula[2] ) if( !(ts %in% (tms<-timeScales(Lx))) ) stop( "l.h.s. of formula must be a timescale; one of:\n", tms, "\n" ) # What are the 'from' states actually present? from <- levels( factor(Lx$lex.Cst) ) # construct a Surv response object, and note that we want the possibility # of transitions to transient states, hence the lex.Xst != lex.Cst Sobj <- Surv( Lx[,ts], Lx[,ts]+Lx$lex.dur, trt( Lx$lex.Cst, Lx$lex.Xst ) %in% trnam ) # Lx$lex.Xst %in% to & # Lx$lex.Xst != Lx$lex.Cst ) # Tell what we intend to and then do it if( verbose ){ cat( "survival::coxph analysis of Lexis object ", nameLx, ":\nRates for", if( onetr ) " the", " transition", if( !onetr ) "s", " ", trprn, "\nBaseline timescale: ", ts, "\n", sep="" ) } mod <- coxph( as.formula( paste( "Sobj", as.character(formula[3]), sep="~") ), data = Lx, ... ) # Add an explanatory attribute attr( mod, "Lexis" ) <- list( data=nameLx, trans=trnam, formula=formula ) class( mod ) <- c( "coxph.lex", class(mod) ) mod } Epi/R/apc.fit.R0000644000176200001440000003335213452066255012655 0ustar liggesusersapc.fit <- function( data, A, P, D, Y, ref.c, ref.p, dist = c("poisson","binomial"), model = c("ns","bs","ls","factor"), dr.extr = "Y", parm = c("ACP","APC","AdCP","AdPC","Ad-P-C","Ad-C-P","AC-P","AP-C"), npar = c( A=5, P=5, C=5 ), scale = 1, alpha = 0.05, print.AOV = TRUE ) { dist <- match.arg(dist) model <- match.arg(model) drtyp <- deparse(substitute(dr.extr)) parm <- toupper(match.arg(parm)) has.data <- !missing( data ) has.pref <- !missing( ref.p ) has.cref <- !missing( ref.c ) if(has.data) { if (length(match(c("A", "P", "D", "Y"), names(data))) != 4) stop("Data frame ", deparse(substitute(data)), " has columns:\n", names(data), "\nmust have variables:\n", "A (age), P (period), D (cases) and Y (person-time)") data <- data[,c("A","P","D","Y")] data <- data[complete.cases(data),] A <- data$A P <- data$P D <- data$D Y <- data$Y } else { nm <- logical(4) nm[1] <- missing(A) nm[2] <- missing(P) nm[3] <- missing(D) nm[4] <- missing(Y) if (any(nm)) stop("Variable", if (sum(nm) > 1) "s", paste(c(" A", " P", " D", " Y")[nm], collapse = ","), " missing from input") if( diff(range( lv <- sapply( list(A = A, P = P, D = D, Y = Y), length) ) ) != 0 ) stop( "\nLengths of variables (", paste(paste(names(lv), lv, sep = ":"), collapse = ", "), ") are not the same." ) } # Utility to compute where the median amount y is on the x scale med <- function(x, y) { o <- order(x) a <- y[o] names(a) <- x[o] return( as.numeric(names(a[cumsum(a)/sum(a) > 0.5][1])) ) } # Set the reference points on the period and cohort scales p0 <- ifelse( has.pref, ref.p, med(P , D) ) c0 <- ifelse( has.cref, ref.c, med(P-A, D) ) # Number of parameters in the spline modeling if( is.list(npar) & length(npar)<3 ) stop("npar given as a list - should have length 3! \n") if( !is.list(npar) & length(npar)!=3 ) { npar <- rep(npar, 3)[1:3] names(npar) = c("A","P","C") cat("NOTE: npar is specified as:\n") ; print( npar ) } if( is.null(names(npar)) ) names(npar) <- c("A", "P", "C") # Labeling of confidence intervals lu <- paste(formatC( c(alpha/2, 1 - alpha/2) * 100, format = "f", digits = 1), "%", sep = "") if( is.list(model) ) { if (!all(sapply(model, is.function))) stop("'model' is a list, but not all elements are functions as they should be.") if ((lmod <- length(model)) < 3) stop("'model' is a list, with", lmod, "elements, it should have three.") if (is.null(names(model))) names(model) <- c("A", "P", "C") MA <- model[["A"]](A) MP <- model[["P"]](P) MC <- model[["C"]](P-A) Rp <- model[["P"]](p0) Rc <- model[["C"]](c0) } else { if (model == "factor") { MA <- model.matrix(~factor(A) - 1) MP <- model.matrix(~factor(P) - 1) MC <- model.matrix(~factor(P - A) - 1) Rp <- MP[abs(P - p0) == min(abs(P - p0)), , drop = FALSE][1, ] Rc <- MC[abs(P - A - c0) == min(abs(P - A - c0)), , drop = FALSE][1, ] } if (model == "ns") { # is npar a list knl <- is.list( npar ) # if scalar expand if( !knl & length(npar)==1 ) npar <- rep( npar, 3 ) # if no names, provide them if( is.null(names(npar)) ) names(npar) <- c("A","P","C") # if names too long or wrong case, rectify names( npar ) <- toupper( substr(names(npar),1,1) ) # if not a list make it one with the correct knots if( !knl ){ nkn <- npar eqp <- function(n) (1:n-0.5)/n npar <- list( A = quantile( rep( A,D), probs=eqp(nkn["A"]) ), P = quantile( rep(P ,D), probs=eqp(nkn["P"]) ), C = quantile( rep(P-A,D), probs=eqp(nkn["C"]) ) ) } MA <- Ns( A, knots = npar[["A"]] ) MP <- Ns(P , knots = npar[["P"]] ) MC <- Ns(P-A, knots = npar[["C"]] ) Rp <- ns(p0, knots = attr(MP,"knots"), Boundary.knots = attr(MP,"Boundary.knots")) Rc <- ns(c0, knots = attr(MC,"knots"), Boundary.knots = attr(MC,"Boundary.knots")) Knots <- list( Age = sort(c(attr(MA,"knots"), attr(MA,"Boundary.knots"))), Per = sort(c(attr(MP,"knots"), attr(MP,"Boundary.knots"))), Coh = sort(c(attr(MC,"knots"), attr(MC,"Boundary.knots")))) } if (model %in% c("bs", "ls")) { deg <- switch(model, ls = 1, bs = 3) knl <- is.list(npar) if (knl) nk <- sapply(npar, length) MA <- if (knl) bs(A, knots = npar[["A"]][-c(1,nk[1])], Boundary.knots = npar[["A"]][ c(1,nk[1])], degree = deg) else bs(A, df = npar[["A"]], degree = deg) MP <- if (knl) bs(P, knots = npar[["P"]][-c(1,nk[2])], Boundary.knots = npar[["P"]][ c(1,nk[2])], degree = deg) else bs(P, df = npar[["P"]], degree = deg) MC <- if (knl) bs(P - A, knots = npar[["C"]][-c(1, nk[3])], Boundary.knots = npar[["C"]][ c(1, nk[3])], degree = deg) else bs(P - A, df = npar[["C"]], degree = deg) Rp <- bs(p0, knots = attr(MP,"knots"), Boundary.knots = attr(MP,"Boundary.knots"), degree = attr(MP,"degree")) Rc <- bs(c0, knots = attr(MC,"knots"), Boundary.knots = attr(MC,"Boundary.knots"), degree = attr(MC,"degree")) Knots <- list(Age = sort(c(attr(MA,"knots"),attr(MA,"Boundary.knots"))), Per = sort(c(attr(MP,"knots"),attr(MP,"Boundary.knots"))), Coh = sort(c(attr(MC,"knots"),attr(MC,"Boundary.knots")))) } } if (tolower(substr(dist, 1, 2)) == "po") { m.APC <- glm(D ~ MA + I(P - p0) + MP + MC, offset = log(Y), family = poisson) Dist <- "Poisson with log(Y) offset" } is.bin <- FALSE if (is.bin <- tolower(substr(dist, 1, 3)) %in% c("bin")) { m.APC <- glm(cbind(D, Y - D) ~ MA + I(P - p0) + MP + MC, family = binomial) Dist <- "Binomial regression (logistic) of D/Y" } m.AP <- update(m.APC, . ~ . - MC) m.AC <- update(m.APC, . ~ . - MP) m.Ad <- update(m.AP, . ~ . - MP) m.A <- update(m.Ad, . ~ . - I(P - p0)) m.0 <- update(m.A, . ~ . - MA) AOV <- anova(m.A, m.Ad, m.AC, m.APC, m.AP, m.Ad, test = "Chisq") colnames(AOV)[1:4] <- c("Mod. df.","Mod. dev.", "Test df.","Test dev.") AOV <- abs(AOV) AOV <- cbind( Model = c("Age", "Age-drift", "Age-Cohort", "Age-Period-Cohort", "Age-Period", "Age-drift"), AOV, 'Test dev/df' = AOV[,"Test dev."]/AOV[,"Test df."], 'H0 ' = c("","zero drift ", "Coh eff|dr.", "Per eff|Coh", "Coh eff|Per", "Per eff|dr.") ) A.pt <- unique(A) A.pos <- match(A.pt, A) P.pt <- unique(P) P.pos <- match(P.pt, P) C.pt <- unique(P - A) C.pos <- match(C.pt, P - A) MA <- cbind(1, MA) # Determine the inner product (diagonal) for projection if (!mode(dr.extr) %in% c("character", "numeric")) stop("\"dr.extr\" must be of mode \"character\" or \"numeric\".\n") if (is.character(dr.extr)) { wt <- rep(1, length(D) ) drtyp <- "1-weights" if( toupper(substr(dr.extr, 1, 1)) %in% c("T","D") ) { wt <- D drtyp <- "D-weights" } else if( toupper(substr(dr.extr, 1, 1)) %in% c("L","R") ) { wt <- (Y^2)/D drtyp <- "Y^2/D-weights" } else if( toupper(substr(dr.extr, 1, 1)) %in% c("Y") ) { wt <- Y drtyp <- "Y-weights" } } if ( is.numeric(dr.extr) ) { if( length(dr.extr)==1 ) { wt <- D + dr.extr*Y drtyp <- paste("D+",dr.extr,"*Y weights",sep="") } if( length(dr.extr)==nrow(data) ) { wt <- dr.extr if( any(wt<0) ) stop("dr.extr must be non-negative") drtyp <- "extn-weights" } } Rp <- matrix(Rp, nrow = 1) Rc <- matrix(Rc, nrow = 1) xP <- Epi::detrend(rbind(Rp, MP), c(p0, P ), weight = c(0, wt)) xC <- Epi::detrend(rbind(Rc, MC), c(c0, P-A), weight = c(0, wt)) MPr <- xP[-1,,drop=FALSE] - has.pref * xP[rep(1, nrow(MP)),,drop=FALSE] MCr <- xC[-1,,drop=FALSE] - has.cref * xC[rep(1, nrow(MC)),,drop=FALSE] if (length(grep("-", parm)) == 0) { if (parm %in% c("ADPC", "ADCP", "APC", "ACP")) m.APC <- update(m.0, . ~ . - 1 + MA + I(P - p0) + MPr + MCr) drift <- rbind( ci.exp(m.APC, subset = "I\\(", alpha = alpha), ci.exp(m.Ad , subset = "I\\(", alpha = alpha) ) rownames(drift) <- c(paste("APC (",drtyp,")",sep=""), "A-d") if (parm == "ADCP") m.APC <- update(m.0, . ~ . - 1 + MA + I(P - A - c0) + MPr + MCr) if (parm == "APC") { MPr <- cbind(P - p0, MPr) m.APC <- update(m.0, . ~ . - 1 + MA + MPr + MCr) } if (parm == "ACP") { MCr <- cbind(P - A - c0, MCr) m.APC <- update(m.0, . ~ . - 1 + MA + MPr + MCr) } Age <- cbind(Age = A.pt, ci.exp(m.APC, subset = "MA", ctr.mat = MA[A.pos,,drop=FALSE], alpha = alpha))[order(A.pt),] Per <- cbind(Per = P.pt, ci.exp(m.APC, subset = "MPr", ctr.mat = MPr[P.pos,,drop=FALSE], alpha = alpha))[order(P.pt),] Coh <- cbind(Coh = C.pt, ci.exp(m.APC, subset = "MCr", ctr.mat = MCr[C.pos,,drop=FALSE], alpha = alpha))[order(C.pt),] colnames(Age)[-1] <- c("Rate", lu) colnames(Per)[-1] <- c("P-RR", lu) colnames(Coh)[-1] <- c("C-RR", lu) Type <- paste("ML of APC-model", Dist, ": (", parm, "):\n") Model <- m.APC } else { adc <- update(m.0, . ~ . - 1 + MA + I(P - A - c0)) adp <- update(m.0, . ~ . - 1 + MA + I(P - p0)) drift <- ci.exp(adc, subset = "I\\(") rownames(drift) <- "A-d" xP <- cbind(1, P - p0, MPr) xC <- cbind(1, P - A - c0, MCr) lP <- cbind(P - p0, MPr) lC <- cbind(P - A - c0, MCr) if (parm == "AD-C-P") { rc <- update(m.0, . ~ . - 1 + xC, offset = predict(adc, type = "link")) rp <- update(m.0, . ~ . - 1 + xP, offset = predict(adc, type = "link")) A.eff <- ci.exp(adc, subset = "MA", ctr.mat = MA[A.pos,], alpha = alpha) C.eff <- ci.exp( rc, subset = "xC", ctr.mat = xC[C.pos,], alpha = alpha) P.eff <- ci.exp( rp, subset = "xP", ctr.mat = xP[P.pos,], alpha = alpha) Model <- list( adc, rc, rp ) } else if (parm == "AD-P-C") { rp <- update(m.0, . ~ . - 1 + xP, offset = predict(adp,type = "link")) rc <- update(m.0, . ~ . - 1 + xC, offset = predict(rp,type = "link")) A.eff <- ci.exp(adp, subset = "MA", ctr.mat = MA[A.pos,], alpha = alpha) P.eff <- ci.exp(rp, subset = "xP", ctr.mat = xP[P.pos,], alpha = alpha) C.eff <- ci.exp(rc, subset = "xC", ctr.mat = xC[C.pos,], alpha = alpha) Model <- list( adp, rp, rc ) } else if (parm == "AC-P") { ac <- update(m.0, . ~ . - 1 + MA + lC) rp <- update(m.0, . ~ . - 1 + xP, offset = predict(ac,type = "link")) A.eff <- ci.exp(ac, subset = "MA", ctr.mat = MA[A.pos,], alpha = alpha) C.eff <- ci.exp(ac, subset = "lC", ctr.mat = lC[C.pos,], alpha = alpha) P.eff <- ci.exp(rp, subset = "xP", ctr.mat = xP[P.pos,], alpha = alpha) Model <- list( ac, rp ) } else if (parm == "AP-C") { ap <- update(m.0, . ~ . - 1 + MA + lP) rc <- update(m.0, . ~ . - 1 + xC, offset = predict(ap,type = "link")) A.eff <- ci.exp(ap, subset = "MA", ctr.mat = MA[A.pos,], alpha = alpha) P.eff <- ci.exp(ap, subset = "lP", ctr.mat = lP[P.pos,], alpha = alpha) C.eff <- ci.exp(rc, subset = "xC", ctr.mat = xC[C.pos,], alpha = alpha) Model <- list( ap, rc ) } Age <- cbind(Age = A.pt, A.eff)[order(A.pt),] Per <- cbind(Per = P.pt, P.eff)[order(P.pt),] Coh <- cbind(Cph = C.pt, C.eff)[order(C.pt),] colnames(Age)[-1] <- c("A.eff", lu) colnames(Per)[-1] <- c("P.eff", lu) colnames(Coh)[-1] <- c("C.eff", lu) Type <- paste("Sequential modelling", Dist, ": (", parm, "):\n") } # If the model was binomial we convert to probabilities o2p <- function(o) o/(1+o) if( is.bin ) Age[,-1] <- o2p(Age[,-1]) res <- list(Type = Type, Model = Model, Age = Age, Per = Per, Coh = Coh, Drift = drift, Ref = c(Per = if ( parm %in% c("APC","ADPC","Ad-P-C","AP-C") ) p0 else NA, Coh = if ( parm %in% c("ACP","ADCP","Ad-C-P","AC-P") ) c0 else NA ), Anova = AOV) # If a spline model is used, add a "Knots" component to the apc-object if (model %in% c("ns", "bs")) res <- c(res, list(Knots = Knots)) res$Age[, -1] <- res$Age[, -1] * scale if (print.AOV) { print(res$Type) print(res$Anova) } # Print warnings about reference points: if( !has.pref & parm %in% c("APC","ADPC") ) cat( "No reference period given; ", "reference period for age-effects is chosen as\n", "the median date of event: ", p0, ".\n" ) if( !has.cref & parm %in% c("ACP","ADCP") ) cat( "No reference cohort given; ", "reference cohort for age-effects is chosen as\n", "the median date of birth for persons with event: ", c0, ".\n" ) class(res) <- "apc" invisible(res) } Epi/R/apc.LCa.R0000644000176200001440000000354013471341545012525 0ustar liggesusers################################################################################### ### apc-LCa comparison apc.LCa <- function( data, # cohort reference for the interactions keep.models = FALSE, ... ) { models <- c("APa","ACa","APaC","APCa","APaCa" ) LCa.list <- list() length( LCa.list ) <- 5 names( LCa.list ) <- models for( mod in models ){ cat( mod, ":\n" ) LCa.list[[mod]] <- LCa.fit( data = data, model = mod, ... ) } APC <- apc.fit( data, npar = list( A=LCa.list[[2]]$knots$a.kn, P=LCa.list[[1]]$knots$p.kn, C=LCa.list[[1]]$knots$c.kn ) ) dev <- c( APC$Anova[c(2,5,3,4),"Mod. dev."], sapply( LCa.list, function(x) x$deviance ) ) df <- c( APC$Anova[c(2,5,3,4),"Mod. df."], sapply( LCa.list, function(x) x$df ) ) names(dev)[1:4] <- names(df)[1:4] <- gsub( "rift","", gsub("eriod","", gsub("ohort","", gsub( "-","", gsub( "ge", "", APC$Anova[c(2,5,3,4),"Model"]))))) if( keep.models ) return( list( dev = cbind( dev, df ), apc = APC, LCa = LCa.list ) ) else return( cbind( dev, df ) ) 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8Gt(>Rhyeyv N+t}[U?c_a&` <*0C0 #0 cR뵜sgT4,T}ghxyqҗ/K2DzHz[>p (6_ЏnhCPbgDԊ/?P{6KG|F5.5k$H+17(Y.)1[Rg*5"jDԈ)cf4iAq-_ -kzLZ;+#WFH:2i]@ A@Wq Fw^+֫wy5+jX/FxըRW׍)dqt{5tWJylJW:lZ;e^*3Ja;A9 9*efe>iZ endstream endobj startxref 548304 %%EOF Epi/inst/doc/flup.R0000644000176200001440000004611314003562715013612 0ustar liggesusers### R code from vignette source 'flup' ### Encoding: UTF-8 ################################################### ### code chunk number 1: flup.rnw:22-25 ################################################### options( width=90, SweaveHooks=list( fig=function() par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") ) ) ################################################### ### code chunk number 2: flup.rnw:137-139 ################################################### library(Epi) print( sessionInfo(), l=F ) ################################################### ### code chunk number 3: flup.rnw:148-157 ################################################### data( DMlate ) head( DMlate ) dmL <- Lexis( entry = list( per=dodm, age=dodm-dobth, tfD=0 ), exit = list( per=dox ), exit.status = factor( !is.na(dodth), labels=c("DM","Dead") ), data = DMlate ) timeScales(dmL) ################################################### ### code chunk number 4: flup.rnw:180-182 ################################################### str( dmL ) head( dmL )[,1:10] ################################################### ### code chunk number 5: flup.rnw:198-199 ################################################### summary.Lexis( dmL, timeScales=TRUE ) ################################################### ### code chunk number 6: dmL1 ################################################### plot( dmL ) ################################################### ### code chunk number 7: dmL2 ################################################### par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) plot( dmL, 1:2, lwd=1, col=c("blue","red")[dmL$sex], grid=TRUE, lty.grid=1, col.grid=gray(0.7), xlim=1960+c(0,60), xaxs="i", ylim= 40+c(0,60), yaxs="i", las=1 ) points( dmL, 1:2, pch=c(NA,3)[dmL$lex.Xst], col="lightgray", lwd=3, cex=0.3 ) points( dmL, 1:2, pch=c(NA,3)[dmL$lex.Xst], col=c("blue","red")[dmL$sex], lwd=1, cex=0.3 ) box(bty='o') ################################################### ### code chunk number 8: flup.rnw:255-258 ################################################### dmS1 <- splitLexis( dmL, "age", breaks=seq(0,100,5) ) summary( dmL ) summary( dmS1 ) ################################################### ### code chunk number 9: flup.rnw:268-271 ################################################### wh.id <- c(9,27,52,484) subset( dmL , lex.id %in% wh.id )[,1:10] subset( dmS1, lex.id %in% wh.id )[,1:10] ################################################### ### code chunk number 10: flup.rnw:277-279 ################################################### dmS2 <- splitLexis( dmS1, "tfD", breaks=c(0,1,2,5,10,20,30,40) ) subset( dmS2, lex.id %in% wh.id )[,1:10] ################################################### ### code chunk number 11: flup.rnw:284-290 ################################################### library( popEpi ) dmM <- splitMulti( dmL, age = seq(0,100,5), tfD = c(0,1,2,5,10,20,30,40), drop = FALSE ) summary( dmS2 ) summary( dmM ) ################################################### ### code chunk number 12: flup.rnw:301-304 ################################################### identical( dmS2, dmM ) class( dmS2 ) class( dmM ) ################################################### ### code chunk number 13: flup.rnw:334-344 ################################################### whc <- c(names(dmL)[1:7],"dodm","doins") # WHich Columns do we want to see? subset( dmL, lex.id %in% wh.id )[,whc] dmC <- cutLexis( data = dmL, cut = dmL$doins, timescale = "per", new.state = "Ins", new.scale = "tfI", precursor.states = "DM" ) whc <- c(names(dmL)[1:8],"doins") # WHich Columns do we want to see? subset( dmC, lex.id %in% wh.id )[,whc] ################################################### ### code chunk number 14: flup.rnw:362-369 ################################################### dmS2C <- cutLexis( data = dmS2, cut = dmS2$doins, timescale = "per", new.state = "Ins", new.scale = "tfI", precursor.states = "DM" ) subset( dmS2C, lex.id %in% wh.id )[,whc] ################################################### ### code chunk number 15: flup.rnw:393-394 ################################################### summary( dmS2C, timeScales=TRUE ) ################################################### ### code chunk number 16: box1 ################################################### boxes( dmC, boxpos=TRUE, scale.R=1000, show.BE=TRUE ) ################################################### ### code chunk number 17: flup.rnw:437-445 ################################################### timeBand( dmS2C, "age", "middle" )[1:10] # For nice printing and column labelling we use the data.frame() function: data.frame( dmS2C[,c("per","age","tfD","lex.dur")], mid.age=timeBand( dmS2C, "age", "middle" ), mid.t=timeBand( dmS2C, "tfD", "middle" ), left.t=timeBand( dmS2C, "tfD", "left" ), right.t=timeBand( dmS2C, "tfD", "right" ), fact.t=timeBand( dmS2C, "tfD", "factor" ) )[1:15,] ################################################### ### code chunk number 18: flup.rnw:481-482 ################################################### summary( (dmS2$age-dmS2$tfD) - (dmS2$dodm-dmS2$dobth) ) ################################################### ### code chunk number 19: flup.rnw:487-489 ################################################### summary( timeBand( dmS2, "age", "middle" ) - timeBand( dmS2, "tfD", "middle" ) - (dmS2$dodm-dmS2$dobth) ) ################################################### ### code chunk number 20: flup.rnw:594-596 ################################################### dmCs <- splitMulti( dmC, age = seq(0,110,1/4) ) summary( dmCs, t=T ) ################################################### ### code chunk number 21: flup.rnw:618-623 ################################################### ( a.kn <- with( subset( dmCs, lex.Xst=="Dead" ), quantile( age+lex.dur, (1:5-0.5)/5 ) ) ) ( i.kn <- c( 0, with( subset( dmCs, lex.Xst=="Dead" & lex.Cst=="Ins" ), quantile( tfI+lex.dur, (1:4)/5 ) ) ) ) ################################################### ### code chunk number 22: flup.rnw:639-644 ################################################### ma <- glm( (lex.Xst=="Dead") ~ Ns(age,knots=a.kn), family = poisson, offset = log(lex.dur), data = dmCs ) summary( ma ) ################################################### ### code chunk number 23: flup.rnw:663-666 ################################################### Ma <- glm( cbind(lex.Xst=="Dead",lex.dur) ~ Ns(age,knots=a.kn), family = poisreg, data = dmCs ) summary( Ma ) ################################################### ### code chunk number 24: flup.rnw:674-676 ################################################### Xa <- glm.Lexis( dmCs, from="DM", to="Dead", formula = ~ Ns(age,knots=a.kn) ) ################################################### ### code chunk number 25: flup.rnw:679-680 ################################################### attr( Xa, "Lexis" ) ################################################### ### code chunk number 26: flup.rnw:689-690 ################################################### xa <- glm.Lexis( dmCs, formula = ~ Ns(age,knots=a.kn) ) ################################################### ### code chunk number 27: flup.rnw:693-694 ################################################### c( deviance(ma), deviance(Ma), deviance(Xa), deviance(xa) ) ################################################### ### code chunk number 28: pr-a ################################################### nd <- data.frame( age=40:85, lex.dur=1000 ) pr.0 <- ci.pred( ma, newdata = nd ) # mortality per 100 PY pr.a <- ci.pred( Ma, newdata = nd )*1000 # mortality per 100 PY summary(pr.0/pr.a) matshade( nd$age, pr.a, plot=TRUE, type="l", lty=1, log="y", xlab="Age (years)", ylab="DM mortality per 1000 PY") ################################################### ### code chunk number 29: flup.rnw:741-745 ################################################### pm <- glm( cbind(lex.Xst=="Dead",lex.dur) ~ Ns(age,knots=a.kn) + lex.Cst + sex, family=poisreg, data = dmCs ) round( ci.exp( pm ), 3 ) ################################################### ### code chunk number 30: flup.rnw:759-763 ################################################### pm <- glm( cbind(lex.Xst=="Dead",lex.dur) ~ Ns(age,knots=a.kn) + Ns(tfI,knots=i.kn) + lex.Cst + sex, family=poisreg, data = tsNA20(dmCs) ) ################################################### ### code chunk number 31: flup.rnw:769-775 ################################################### Pm <- glm.Lexis( tsNA20(dmCs), form = ~ Ns(age,knots=a.kn) + Ns(tfI,knots=i.kn) + lex.Cst + sex ) c( deviance(Pm), deviance(pm) ) identical( model.matrix(Pm), model.matrix(pm) ) ################################################### ### code chunk number 32: flup.rnw:781-782 ################################################### round( ci.exp( Pm, subset="ex" ), 3 ) ################################################### ### code chunk number 33: ins-time ################################################### ndI <- data.frame( expand.grid( tfI=c(NA,seq(0,15,0.1)), ai=seq(40,80,10) ), sex="M", lex.Cst="Ins" ) ndI <- transform( ndI, age=ai+tfI ) head( ndI ) ndA <- data.frame( age= seq(40,100,0.1), tfI=0, lex.Cst="DM", sex="M" ) pri <- ci.pred( Pm, ndI ) * 1000 pra <- ci.pred( Pm, ndA ) * 1000 matshade( ndI$age, pri, plot=TRUE, las=1, xlab="Age (years)", ylab="DM mortality per 1000 PY", log="y", lty=1, col="blue" ) matshade( ndA$age, pra ) ################################################### ### code chunk number 34: flup.rnw:819-823 ################################################### library( survival ) cm <- coxph( Surv(age,age+lex.dur,lex.Xst=="Dead") ~ Ns(tfI,knots=i.kn) + lex.Cst + sex, data = tsNA20(dmCs) ) ################################################### ### code chunk number 35: flup.rnw:827-830 ################################################### Cm <- coxph.Lexis( tsNA20(dmCs), form= age ~ Ns(tfI,knots=i.kn) + lex.Cst + sex ) cbind( ci.exp( cm ), ci.exp( Cm ) ) ################################################### ### code chunk number 36: flup.rnw:839-842 ################################################### round( cbind( ci.exp( Pm ), rbind( matrix(NA,5,3), ci.exp( cm )[-6,] ) ), 3 ) ################################################### ### code chunk number 37: Ieff ################################################### nd <- data.frame( tfI=seq(0,15,,151), lex.Cst="Ins", sex="M" ) nr <- data.frame( tfI= 2 , lex.Cst="Ins", sex="M" ) ppr <- ci.exp( pm, list(nd,nr), xvars="age" ) cpr <- ci.exp( cm, list(nd,nr) ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( nd$tfI, cbind(ppr,cpr), plot=T, lty=c(1,2), log="y", xlab="Time since insulin (years)", ylab="Rate ratio") abline( h=1, lty=3 ) ################################################### ### code chunk number 38: IeffR ################################################### nd <- data.frame( tfI=seq(0,15,,151), lex.Cst="Ins", sex="M" ) nr <- data.frame( tfI= 0 , lex.Cst="DM" , sex="M" ) ppr <- ci.exp( pm, list(nd,nr), xvars="age" ) cpr <- ci.exp( cm, list(nd,nr) ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( nd$tfI, cbind(ppr,cpr), xlab="Time since insulin (years)", ylab="Rate ratio relative to non-Insulin", lty=c(1,2), log="y", plot=T ) ################################################### ### code chunk number 39: flup.rnw:948-953 ################################################### imx <- glm.Lexis( tsNA20(dmCs), formula = ~ Ns(age ,knots=a.kn) + Ns( tfI,knots=i.kn) + Ns(age-tfI,knots=a.kn) + lex.Cst + sex ) ################################################### ### code chunk number 40: flup.rnw:963-973 ################################################### Im <- glm.Lexis( tsNA20(dmCs), formula = ~ Ns(age ,knots=a.kn) + Ns( tfI,knots=i.kn) + Ns((age-tfI)*(lex.Cst=="Ins"),knots=a.kn) + lex.Cst + sex ) im <- glm.Lexis( tsNA20(dmCs), formula = ~ Ns(age ,knots=a.kn) + Ns( tfI,knots=i.kn) + lex.Cst:Ns(age-tfI,knots=a.kn) + lex.Cst + sex ) ################################################### ### code chunk number 41: flup.rnw:988-989 ################################################### anova( imx, Im, im, test='Chisq') ################################################### ### code chunk number 42: dur-int ################################################### pxi <- ci.pred( imx, ndI ) pxa <- ci.pred( imx, ndA ) pIi <- ci.pred( Im , ndI ) pIa <- ci.pred( Im , ndA ) pii <- ci.pred( im , ndI ) pia <- ci.pred( im , ndA ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( ndI$age, cbind( pxi, pIi, pii)*1000, plot=T, log="y", xlab="Age", ylab="Mortality per 1000 PY", lty=1, lwd=2, col=c("blue","forestgreen","red"), alpha=0.1 ) matshade( ndA$age, cbind( pxa, pIa, pia)*1000, lty=1, lwd=2, col=c("blue","forestgreen","red"), alpha=0.1 ) ################################################### ### code chunk number 43: dur-int-RR ################################################### ndR <- transform( ndI, tfI=0, lex.Cst="DM" ) cbind( head(ndI), head(ndR) ) Rxi <- ci.exp( imx, list(ndI,ndR) ) Rii <- ci.exp( im , list(ndI,ndR) ) RIi <- ci.exp( Im , list(ndI,ndR) ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( ndI$age, cbind( Rxi, RIi, Rii), plot=T, log="y", xlab="Age (years)", ylab="Rate ratio vs, non-Insulin", lty=1, lwd=2, col=c("blue","forestgreen","red"), alpha=0.1 ) abline( h=1 ) abline( h=ci.exp(imx,subset="lex.Cst")[,1], lty="25", col="blue" ) ################################################### ### code chunk number 44: splint ################################################### gm <- glm.Lexis( tsNA20(dmCs), formula = ~ Ns(age,knots=a.kn) + Ns(tfI,knots=i.kn) + lex.Cst:Ns(age,knots=a.kn):Ns(tfI,knots=i.kn) + lex.Cst + sex ) pgi <- ci.pred( gm, ndI ) pga <- ci.pred( gm, ndA ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( ndI$age, cbind( pgi, pii )*1000, plot=T, lty=c("solid","21"), lend="butt", lwd=2, log="y", xlab="Age (years)", ylab="Mortality rates per 1000 PY", alpha=c(0.2,0.1), col=c("black","red") ) matshade( ndA$age, cbind( pga, pia )*1000, lty=c("solid","21"), lend="butt", lwd=2, alpha=c(0.2,0.1), col=c("black","red") ) ################################################### ### code chunk number 45: RR-int ################################################### ndR <- transform( ndI, lex.Cst="DM", tfI=0 ) iRR <- ci.exp( im, ctr.mat=list(ndI,ndR) ) gRR <- ci.exp( gm, ctr.mat=list(ndI,ndR) ) par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1, bty="n" ) matshade( ndI$age, cbind(gRR,iRR), lty=1, log="y", plot=TRUE, xlab="Age (years)", ylab="Rate ratio: Ins vs. non-Ins", col=c("black","red") ) abline( h=1 ) ################################################### ### code chunk number 46: flup.rnw:1112-1125 ################################################### dmd <- glm.Lexis( dmCs, from="DM", to="Dead", formula = ~ Ns(age,knots=a.kn) + sex ) ind <- glm.Lexis( dmCs, from="Ins", to="Dead", formula = ~ Ns(age,knots=a.kn) + Ns(tfI,knots=i.kn) + Ns(age-tfI,knots=a.kn) + sex ) ini <- ci.pred( ind, ndI ) dmi <- ci.pred( dmd, ndI ) dma <- ci.pred( dmd, ndA ) ################################################### ### code chunk number 47: sep-mort ################################################### par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") matshade( ndI$age, ini*1000, plot=TRUE, log="y", xlab="Age (years)", ylab="Mortality rates per 1000 PY", lwd=2, col="red" ) matshade( ndA$age, dma*1000, lwd=2, col="black" ) ################################################### ### code chunk number 48: sep-HR ################################################### par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") matshade( ndI$age, ci.ratio(ini,dmi), plot=TRUE, log="y", xlab="Age (years)", ylab="RR insulin vs. no insulin", lwd=2, col="red" ) abline( h=1 ) ################################################### ### code chunk number 49: flup.rnw:1171-1179 ################################################### dmCs <- cutLexis( data = dmS2, cut = dmS2$doins, timescale = "per", new.state = "Ins", new.scale = "tfI", precursor.states = "DM", split.states = TRUE ) summary( dmCs ) ################################################### ### code chunk number 50: box4 ################################################### boxes( dmCs, boxpos=list(x=c(15,15,85,85), y=c(85,15,85,15)), scale.R=1000, show.BE=TRUE ) ################################################### ### code chunk number 51: flup.rnw:1209-1217 ################################################### dmM <- mcutLexis( dmL, timescale = "per", wh = c("doins","dooad"), new.states = c("Ins","OAD"), new.scales = c("tfI","tfO"), precursor.states = "DM", ties.resolve = TRUE ) summary( dmM, t=T ) ################################################### ### code chunk number 52: flup.rnw:1221-1226 ################################################### wh <- c(subset(dmM,lex.Cst=="Ins-OAD")$lex.id[1:2], subset(dmM,lex.Cst=="OAD-Ins")$lex.id[1:2]) options( width=110 ) print( subset( dmM, lex.id %in% wh )[,c('lex.id',names(dmM[1:8]),c("doins","dooad"))], digits=6, row.names=FALSE ) ################################################### ### code chunk number 53: mbox ################################################### boxes( dmM, boxpos=list(x=c(15,80,40,40,85,85), y=c(50,50,90,10,90,10)), scale.R=1000, show.BE=TRUE ) ################################################### ### code chunk number 54: mboxr ################################################### summary( dmMr <- Relevel( dmM, list('OAD+Ins'=5:6), first=FALSE) ) boxes( dmMr, boxpos=list(x=c(15,50,15,85,85), y=c(85,50,15,85,15)), scale.R=1000, show.BE=TRUE ) Epi/inst/doc/flup.pdf0000644000176200001440000342073214003562715014170 0ustar liggesusers%PDF-1.5 % 127 0 obj << /Length 792 /Filter /FlateDecode >> 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KC|ܞ&xN?}6̯k|C/O'W9~^= |mm#syl]7eRhpw' /`M,Wsbnv_a;Cl?0T֜wn7%6%8*%8\FZ >\fpsv=SؖںU%mӭgmJӯQF`5_e Uz"- xB`vd}l|zpW>y(}ŋ=߼?TLbYzyk96go_6/]hy4yq",G{wwO_w$ß*Z^<+n)؜ >!q,(:nIs-c)6 o"/Wfyqԉ;]ɳv [v%6iA![Nb#}HQ&P{sk%$JAڔb5d$~F=Hj~MbKЗ1vţ|;z*FS;*l` $;v y8R/,vF=ؔ{}zp?بbq qrq冬#q屷hEKy#y' ->p  ]E/G=Q,eeWmWӣ$vD.R˧&ysbԓ"ôk?/mMuyz} _SiHn7w+6^XS^!SOǸyuCa > stream xZ]s۶}c;Τvf$i{=~`(e_,Gmդ}HK`vX{'d AO#xuQh-"TZ:jiDi'"]iT'cl0 @VJ@6GSO3T@ĀaA0},Bb2y d t$7@Bee F:`+Ѱ \_=s(a"5ٳ,739 x֠ɦ;4<)@56b_~寗mՈKx!wՇF\eh~[#Uf=ob,U;w۪oI]| .y"h KtmF|@ * = Z,~ߴ_rR-ۑUM*?G^n%2:d^*L6@8'#i=o{+w _/ʺz6+>cNS^zGVZ9/+FŮJ⒗ֻ?0UFR գv#4D$mG@˻H=Eu v,z8r?@Ym!Lj̝\ޕ8,m㬿3G&oXߤaVGT<]wn;*@%(P.{ >jƥt/IըCgeFZX%NFk_7e%ⶩsiD6Vct6tl Ʃ%+Yڐ3INt ?:M9?W$Lv=jjs 5F9_VQ4_V)7A3M=T(y~YAe GCU.1&uy 'N}M\Ϧź7yk^(݃~$?2%#cNڣ  nu'jƇ[(XC(D[2#ت>|ٻDpY2nң1~ƍfa8hDN`>KS1DCܹZȺ5+ޞԡ/4ԡh?7.# cp;O=$߸~,FLMCdj5ȐF=Cz3f)#iWه JЦal2o9<Ǣؿۢ(}T'*WKtDg*0OI0 "jrNx{mBaڴJcsQgԏFL}No(a hcY¥]:^eVFM endstream endobj 303 0 obj << /Alternate /DeviceRGB /N 3 /Length 2596 /Filter /FlateDecode >> stream xwTSϽ7PkhRH H.*1 J"6DTpDQ2(C"QDqpId߼y͛~kg}ֺLX Xňg` lpBF|،l *?Y"1P\8=W%Oɘ4M0J"Y2Vs,[|e92<se'9`2&ctI@o|N6(.sSdl-c(2-yH_/XZ.$&\SM07#1ؙYrfYym";8980m-m(]v^DW~ emi]P`/u}q|^R,g+\Kk)/C_|Rax8t1C^7nfzDp 柇u$/ED˦L L[B@ٹЖX!@~(* {d+} G͋љς}WL$cGD2QZ4 E@@A(q`1D `'u46ptc48.`R0) @Rt CXCP%CBH@Rf[(t CQhz#0 Zl`O828.p|O×X ?:0FBx$ !i@ڐH[EE1PL ⢖V6QP>U(j MFkt,:.FW8c1L&ӎ9ƌaX: rbl1 {{{;}#tp8_\8"Ey.,X%%Gщ1-9ҀKl.oo/O$&'=JvMޞxǥ{=Vs\x ‰N柜>ucKz=s/ol|ϝ?y ^d]ps~:;/;]7|WpQoH!ɻVsnYs}ҽ~4] =>=:`;cܱ'?e~!ańD#G&}'/?^xI֓?+\wx20;5\ӯ_etWf^Qs-mw3+?~O~ endstream endobj 307 0 obj << /Length 2652 /Filter /FlateDecode >> stream xڽZo7BP@B-fI8Grp}pe[%9u܇oHΐ]r\> $H&&(\?9;zR)ESjrv1rXLu'gS5l/U)R~K2+\YZ54lp-gs鹽ӛCSL[aV2T}Le&ϗZM0/WMpwX.wfו#YUd ]*ʈљG/ΎImPd!,Gdsx=AN$/+QIoGe7]\b7"I][Y-[.`EtϨΨs߸G;kEonQV֒ޢ{7q2OA w{6V~&]e.tlqyZ}V[rX#uT=wvs ќ %@z *0 .|7a :`ExQ7X-9MRt;%eG**څ)Le6@nf~GZ : ^73]G˶e&lypt7hI6dA^!  ȗ /NS$)i?>jPNrCalK,75p(.@:aH_*QgټPzznnsw{3Ʋ $Q#n$]NOzw8ϟ٠αN8;"H[j̗ڪ$Y`!vUP0qVfYEʊڢ) ?7(6A^:(4|}l~Љ:j:GI~CC3_PNɽ-Y^l0Y\vKu~aNkK5ڗ** È!CE"[96 ,( 3ǎm6NjԻGS 1낰v}pJe*QQ=I[hT-ce%Fw\wQaLR1 ^>)J UlIGH+MDVr˦& \bUc2{+ǬxlF2U3\vMںj^~>^ Ľb`hhM~j#TSL|SLf)& wOLެ+Dk މx|-n]u3[Lvk~ ?"щ-L{o]#; ġʴ Rpi`hmLTJqq%)2=5ǡvN H1XD@@mhCPʸy7'{2lF7qxc<< u/#ݯ1Z 5xKr^jD|rza[3I\{ sK%'fՈ]SyN:vjTa'nSnԸfY ž$]q4)!e9WYToϼ잀'9/ae{{T|o$uJwi^RCtHlz5Bns;m> stream xڭWQs6 ~;y%k.K-ͺ[WaAۍm%~T$@I ׁ,:2.V*SAH< He|(j <[x(Q:ܕ0ng,fa_B>RfY_mV3k%Q9 d-s٤=GZ6va7<ұYil&Ɏ YBa^vYlZKe/O4iAVmni؎ q :^wuUVz=rd)K_(䶌K%LdU *m臕bF/jo;ݖ%#O59Zi`+UxbP~G{ *]BgVrj!}T!-²Ń~@[]mz|¦-wj00-E&i1t h, xW,4Nx3C# Z#wޯڥ3 uk|01k3;2 M -˹x8+3)wfpvN{,("SuCc8O<n^y4sK%9 #HtCLjk01^g@c 9;aM`CdNלmֹb?vi^i?iŃϋ@uq^> /ExtGState << /GS1 319 0 R /GS257 320 0 R >>/ColorSpace << /sRGB 321 0 R >>>> /Length 22217 /Filter /FlateDecode >> stream xK=IݷOsKn@H.ѐҠ  s~7Xepw{s|Wǯuo??/R?R/c}_뫷z}嫭]_j34~Z]6?~wie?}~vrޫ}?p$kWs/_wΏRw<~ǵywq{x1><W%_뻎|U?W(i6?~~he?~O|˳ܷ?;Z_y=}beڿ˾˗z߯_b_Q7t΅?_7_owޏg}&Y/?K?}ŭ|ߴ?u_ܶ|@i?_ s'U~ yY ~"kּb{Y*７U ~5g8VŗDzvSz<ǖ5%]W\QO8šqVa8WtiVɫ񽷥o?WOmpÌ+:}3V \eI^#/ʮXV kObȺ϶f\mOsջštq'){􍷵BkzJ5GX=zW:Eɷ`v~MXimF3mG kYj>3u?xiXݧ^߆>֊>W))wv[sɺ~7Wf]Mw{r-֎r{ o**wv/8Y|;9͝'lߑܦa?񙷙glCt"% δypEDY¯K$$jUnOw{)a^iik~g RA=rG}ϸ(~z^AgPإ/ST﷌\/y:¾xʨxlK/ӪʌǢ׬u>.x,:+Ԧ ||,5chGcՆ t6hci?~tṃ&n[[Q'Q8Xܶܧ"N>uH#6jW|p7Cܖ|Gx]K(:^+Un-r^1>b [\j܆?=nQz8+;}r~rqvP0&c| %6:v28%nc5۷ |D9q:/)oKNPa_W"*,pm]}oy63Rfn_yt5ސ2nYi0C;V 3߄"U?0WO|PIq> ed\fE.Mz;ˇYjvxy8)EWP̭"\i7- 3׽r|{&^^vMT('D)0=KQfFL-bML'{{[$2"UxK)DF1ofy*7=KMyYio+ɝ\r*O>Kr̽3>^ʽOiάd~߃ i0@/%Z*vq]43LP !BCǚA[5W([>ɟfM#6pwcQ"!ESJ%yg$(|Go}k0Ӯo_9jw}x9V.w`[N-{D[mʥ~vaxnYdE޵}ӷ;ߧ(io)^i`o=v.N/twקhGM2̯7:_m;:E_on ٝAWȲ޶G$~.΅hm赸Gt[/~_o,Fz(IDSѯ>X{ER-mϏL"rhقXmO~.XhFXi+8Pc*y޶2ێ㸺vaKa^6G&a+ڸpzXVt4|_ehc}v͟KVwY}v3gDy|o[\1Ѳ*:1:myۊdjLOv$~ڹ~KקaN;4*؞q gFk82OOT@;"Ϋe|?k(Q4y[A{"!:^X߷z9Mو;wǼ;Z&ohHb}}Fhf矌Kِο۞Ww:Eq6plf6D3[0wǵMqARؙQT}>EArVjjw`U:&~z,E3_: {F{gرz x?/?'e3}z?ƶtC~ <8+>/cFϓV|8)<5kWjϳH\9⼻mU_|nw8/u id_|^oyqk/xiD΂ /igS?wO&_7ğ8/mxs8ވ0H׫xdN_W"+ݟxg| I/a܏x*ʊoMcExRpNMn⿈0U _q<9h9GǣcWo}Ƴc8^s{ێv:ӃV?Z?7^4JgQ(w н|jA5Xq|qM7G|9_쇿W>to|3vz_桻lQ|6(tf Kt3w3:?w7{t3:ݑt3t3 =t3&w3y?w~^ztMKyV=Ӎrwv=&g7c߹s/sş e׃>6y݌r)g7vϨ^G֡5.z/{S#گOxgE>tk'^^34>5ڦ}z'9}n?98&ycDL1sL|cٽL͎i@Y\>3}L31դF~g7')Z9mOQQEN%lru9K9rK 92嶧~QneUG9J*GYM{:9J4#(GY+G;ΰM(G#(#Q8lր>SL>gtVv5Hv*ݛ5Z/ŴwG1rȚ0cX3r} w)fc}搜e[5ad4Bd>ք󆭜-&&쭿?yF&^՚cH'#bn٬ [9eylٲv1ϯ"[ߗIK?郶!#a/]#O2H[n#P^u}ao{zi>X> ڱulr}o`Žog{=/,|>|l}޶71Oo΍v}t}#Zvn/czLj]ח/s:r᤽l__N__V]jD#Si /~iwKקɀ/s:/C/S c[j8W~~:i[}]{2rKS0~|_!0}k(+i/۫YM;W=ۧp>vOڹP~k~>?uF߯ 9ykz?zy|?O7G<6'z^aǬEQ#^WfX^cٴJ%S,bY]mt>k=jzަ~Oa_oq \쿈GZGjDZ q_H_tı9?ΛpZ:Oz 7>p[Z_:ӭ}ixz$/I 5/z$5'z$<=jH=UHzk? 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jj52\"W2(ʻ2ܾ  L}`?`IE$ۧМVkƱ YP06鰼KZPqPw.MiP`A1+0hWlA}̠0` Zp fwkw+`( 7SWm4+;և`U/Uj͵KTT ,z[Z#s[,*c(Z N;YxZZ©Y6 nOh0ͭJ1âc:Vfng] 6s-|H R*`B6 iiwZx4-U,T"(Tr&U%EE`E^QABޔf0h@;2PoKUXt hl]Gl;X,~ZU6l7&i ,qS`ayI ,5W Xփ~06] ,Gh;#` QK]Ӹ3jї?+K`%[@;} ?h#F"L`Z|太fV|l,_rԢIsy1/[' x3F-)M7y,nKi_`|R"{S<~6.Cĉy}aY<R7飉<O~cU|Ň`B =8Z0F0hKgUC~7*b.6/>+m`p{x]57 :cV*U@@GN1uxJZ|q NYຢe*J[恢>Ron**7E -{",EQeA ˜QTbwZϊ,}r? ?qUQCQPQ5XVv ƁhH3m:[кT*ѺѺѺ%❩+?w endstream endobj startxref 924398 %%EOF Epi/inst/doc/simLexis.R0000644000176200001440000004201314003563040014424 0ustar liggesusers### R code from vignette source 'simLexis' ### Encoding: UTF-8 ################################################### ### code chunk number 1: simLexis.rnw:23-26 ################################################### options( width=90, SweaveHooks=list( fig=function() par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") ) ) ################################################### ### code chunk number 2: start ################################################### options( width=90 ) library( Epi ) print( sessionInfo(), l=F ) ################################################### ### code chunk number 3: Lexis ################################################### data(DMlate) dml <- Lexis( entry = list(Per=dodm, Age=dodm-dobth, DMdur=0 ), exit = list(Per=dox), exit.status = factor(!is.na(dodth),labels=c("DM","Dead")), data = DMlate ) ################################################### ### code chunk number 4: cut ################################################### dmi <- cutLexis( dml, cut = dml$doins, pre = "DM", new.state = "Ins", new.scale = "t.Ins", split.states = TRUE ) summary( dmi, timeScales=T ) ################################################### ### code chunk number 5: boxes ################################################### boxes( dmi, boxpos = list(x=c(20,20,80,80), y=c(80,20,80,20)), scale.R = 1000, show.BE = TRUE ) ################################################### ### code chunk number 6: split ################################################### Si <- splitLexis( dmi, seq(0,20,1/4), "DMdur" ) summary( Si ) print( subset( Si, lex.id==97 )[,1:10], digits=6 ) ################################################### ### code chunk number 7: knots ################################################### nk <- 5 ( ai.kn <- with( subset(Si,lex.Xst=="Ins" & lex.Cst!=lex.Xst ), quantile( Age+lex.dur , probs=(1:nk-0.5)/nk ) ) ) ( ad.kn <- with( subset(Si,lex.Xst=="Dead"), quantile( Age+lex.dur , probs=(1:nk-0.5)/nk ) ) ) ( di.kn <- with( subset(Si,lex.Xst=="Ins" & lex.Cst!=lex.Xst ), c(0,quantile( DMdur+lex.dur, probs=(1:(nk-1))/nk ) )) ) ( dd.kn <- with( subset(Si,lex.Xst=="Dead"), c(0,quantile( DMdur+lex.dur, probs=(1:(nk-1))/nk ) )) ) ( ti.kn <- with( subset(Si,lex.Xst=="Dead(Ins)"), c(0,quantile( t.Ins+lex.dur, probs=(1:(nk-1))/nk ) )) ) ################################################### ### code chunk number 8: Poisson ################################################### library( splines ) DM.Ins <- glm( (lex.Xst=="Ins") ~ Ns( Age , knots=ai.kn ) + Ns( DMdur, knots=di.kn ) + I(Per-2000) + sex, family=poisson, offset=log(lex.dur), data = subset(Si,lex.Cst=="DM") ) ci.exp( DM.Ins ) class( DM.Ins ) ################################################### ### code chunk number 9: simLexis.rnw:282-288 ################################################### DM.Ins <- glm.Lexis( Si, from = "DM", to = "Ins", formula = ~ Ns( Age , knots=ai.kn ) + Ns( DMdur, knots=di.kn ) + I(Per-2000) + sex ) ci.exp( DM.Ins ) class( DM.Ins ) ################################################### ### code chunk number 10: simLexis.rnw:293-302 ################################################### DM.Dead <- glm.Lexis( Si, from = "DM", to = "Dead", formula = ~ Ns( Age , knots=ad.kn ) + Ns( DMdur, knots=dd.kn ) + I(Per-2000) + sex ) Ins.Dead <- glm.Lexis( Si, from = "Ins", formula = ~ Ns( Age , knots=ad.kn ) + Ns( DMdur, knots=dd.kn ) + Ns( t.Ins, knots=ti.kn ) + I(Per-2000) + sex ) ################################################### ### code chunk number 11: prop-haz ################################################### All.Dead <- glm.Lexis( Si, to = c("Dead(Ins)","Dead"), formula = ~ Ns( Age , knots=ad.kn ) + Ns( DMdur, knots=dd.kn ) + lex.Cst + I(Per-2000) + sex ) round( ci.exp( All.Dead ), 3 ) ################################################### ### code chunk number 12: get-dev ################################################### what <- c("null.deviance","df.null","deviance","df.residual") ( rD <- unlist( DM.Dead[what] ) ) ( rI <- unlist( Ins.Dead[what] ) ) ( rA <- unlist( All.Dead[what] ) ) round( c( dd <- rA-(rI+rD), "pVal"=1-pchisq(dd[3],dd[4]+1) ), 3 ) ################################################### ### code chunk number 13: pr-array ################################################### pr.rates <- NArray( list( DMdur = seq(0,12,0.1), DMage = 4:7*10, r.Ins = c(NA,0,2,5), model = c("DM/Ins","All"), what = c("rate","lo","hi") ) ) str( pr.rates ) ################################################### ### code chunk number 14: mknd ################################################### nd <- data.frame( DMdur = as.numeric( dimnames(pr.rates)[[1]] ), lex.Cst = factor( 1, levels=1:4, labels=levels(Si$lex.Cst) ), sex = factor( 1, levels=1:2, labels=c("M","F")) ) ################################################### ### code chunk number 15: make-pred ################################################### for( ia in dimnames(pr.rates)[[2]] ) { dnew <- transform( nd, Age = as.numeric(ia)+DMdur, Per = 1998+DMdur ) pr.rates[,ia,1,"DM/Ins",] <- ci.pred( DM.Dead, newdata = dnew ) pr.rates[,ia,1,"All" ,] <- ci.pred( All.Dead, newdata = dnew ) for( ii in dimnames(pr.rates)[[3]][-1] ) { dnew = transform( dnew, lex.Cst = factor( 2, levels=1:4, labels=levels(Si$lex.Cst) ), t.Ins = ifelse( (DMdur-as.numeric(ii)) >= 0, DMdur-as.numeric(ii), NA ) ) pr.rates[,ia, ii ,"DM/Ins",] <- ci.pred( Ins.Dead, newdata = dnew ) pr.rates[,ia, ii ,"All" ,] <- ci.pred( All.Dead, newdata = dnew ) } } ################################################### ### code chunk number 16: mort-int ################################################### par( mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, las=1 ) plot( NA, xlim=c(40,82), ylim=c(5,300), bty="n", log="y", xlab="Age", ylab="Mortality rate per 1000 PY" ) abline( v=seq(40,80,5), h=outer(1:9,10^(0:2),"*"), col=gray(0.8) ) for( aa in 4:7*10 ) for( ii in 1:4 ) matshade( aa+as.numeric(dimnames(pr.rates)[[1]]), cbind( pr.rates[,paste(aa),ii,"DM/Ins",], pr.rates[,paste(aa),ii,"All" ,] )*1000, type="l", lty=1, lwd=2, col=c("red","limegreen") ) ################################################### ### code chunk number 17: Tr ################################################### Tr <- list( "DM" = list( "Ins" = DM.Ins, "Dead" = DM.Dead ), "Ins" = list( "Dead(Ins)" = Ins.Dead ) ) ################################################### ### code chunk number 18: make-ini ################################################### str( ini <- Si[NULL,1:9] ) ################################################### ### code chunk number 19: ini-fill ################################################### ini[1:2,"lex.id"] <- 1:2 ini[1:2,"lex.Cst"] <- "DM" ini[1:2,"Per"] <- 1995 ini[1:2,"Age"] <- 60 ini[1:2,"DMdur"] <- 5 ini[1:2,"sex"] <- c("M","F") ini ################################################### ### code chunk number 20: simL ################################################### set.seed( 52381764 ) Nsim <- 5000 system.time( simL <- simLexis( Tr, ini, t.range = 12, N = Nsim ) ) ################################################### ### code chunk number 21: sum-simL ################################################### summary( simL, by="sex" ) ################################################### ### code chunk number 22: Tr.p-simP ################################################### Tr.p <- list( "DM" = list( "Ins" = DM.Ins, "Dead" = All.Dead ), "Ins" = list( "Dead(Ins)" = All.Dead ) ) system.time( simP <- simLexis( Tr.p, ini, t.range = 12, N = Nsim ) ) summary( simP, by="sex" ) ################################################### ### code chunk number 23: Cox-dur ################################################### library( survival ) Cox.Dead <- coxph( Surv( DMdur, DMdur+lex.dur, lex.Xst %in% c("Dead(Ins)","Dead")) ~ Ns( Age-DMdur, knots=ad.kn ) + I(lex.Cst=="Ins") + I(Per-2000) + sex, data = Si ) round( ci.exp( Cox.Dead ), 3 ) ################################################### ### code chunk number 24: TR.c ################################################### Tr.c <- list( "DM" = list( "Ins" = Tr$DM$Ins, "Dead" = Cox.Dead ), "Ins" = list( "Dead(Ins)" = Cox.Dead ) ) system.time( simC <- simLexis( Tr.c, ini, t.range = 12, N = Nsim ) ) summary( simC, by="sex" ) ################################################### ### code chunk number 25: nState ################################################### system.time( nSt <- nState( subset(simL,sex=="M"), at=seq(0,11,0.2), from=1995, time.scale="Per" ) ) nSt[1:10,] ################################################### ### code chunk number 26: pstate0 ################################################### pM <- pState( nSt, perm=c(1,2,4,3) ) head( pM ) par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) plot( pM ) plot( pM, border="black", col="transparent", lwd=3 ) text( rep(as.numeric(rownames(pM)[nrow(pM)-1]),ncol(pM)), pM[nrow(pM),]-diff(c(0,pM[nrow(pM),]))/5, colnames( pM ), adj=1 ) box( col="white", lwd=3 ) box() ################################################### ### code chunk number 27: pstatex ################################################### clr <- c("limegreen","orange") # expand with a lighter version of the two chosen colors clx <- c( clr, rgb( t( col2rgb( clr[2:1] )*2 + rep(255,3) ) / 3, max=255 ) ) par( mfrow=c(1,2), las=1, mar=c(3,3,4,2), mgp=c(3,1,0)/1.6 ) # Men plot( pM, col=clx, xlab="Date of FU" ) lines( as.numeric(rownames(pM)), pM[,2], lwd=3 ) mtext( "60 year old male, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) mtext( "Survival curve", side=3, line=1.5, adj=0 ) mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) axis( side=4 ) axis( side=4, at=1:19/20, labels=FALSE ) axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) # Women pF <- pState( nState( subset(simL,sex=="F"), at=seq(0,11,0.2), from=1995, time.scale="Per" ), perm=c(1,2,4,3) ) plot( pF, col=clx, xlab="Date of FU" ) lines( as.numeric(rownames(pF)), pF[,2], lwd=3 ) mtext( "60 year old female, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) mtext( "Survival curve", side=3, line=1.5, adj=0 ) mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) axis( side=4 ) axis( side=4, at=1:19/20, labels=FALSE ) axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) ################################################### ### code chunk number 28: pstatey ################################################### par( mfrow=c(1,2), las=1, mar=c(3,3,4,2), mgp=c(3,1,0)/1.6 ) # Men pM <- pState( nState( subset(simL,sex=="M"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) plot( pM, col=clx, xlab="Age" ) lines( as.numeric(rownames(pM)), pM[,2], lwd=3 ) mtext( "60 year old male, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) mtext( "Survival curve", side=3, line=1.5, adj=0 ) mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) axis( side=4 ) axis( side=4, at=1:19/20, labels=FALSE ) axis( side=4, at=1:19/20, labels=FALSE, tcl=-0.4 ) axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) # Women pF <- pState( nState( subset(simL,sex=="F"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) plot( pF, col=clx, xlab="Age" ) lines( as.numeric(rownames(pF)), pF[,2], lwd=3 ) mtext( "60 year old female, diagnosed 1990, aged 55", side=3, line=2.5, adj=0, col=gray(0.6) ) mtext( "Survival curve", side=3, line=1.5, adj=0 ) mtext( "DM, no insulin DM, Insulin", side=3, line=0.5, adj=0, col=clr[2] ) mtext( "DM, no insulin", side=3, line=0.5, adj=0, col=clr[1] ) axis( side=4 ) axis( side=4, at=1:9/10, labels=FALSE ) axis( side=4, at=1:19/20, labels=FALSE, tcl=-0.4 ) axis( side=4, at=1:99/100, labels=FALSE, tcl=-0.3 ) ################################################### ### code chunk number 29: comp-0 ################################################### PrM <- pState( nState( subset(simP,sex=="M"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) PrF <- pState( nState( subset(simP,sex=="F"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) CoxM <- pState( nState( subset(simC,sex=="M"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) CoxF <- pState( nState( subset(simC,sex=="F"), at=seq(0,11,0.2), from=60, time.scale="Age" ), perm=c(1,2,4,3) ) par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6 ) plot( pM, border="black", col="transparent", lwd=3 ) lines( PrM, border="blue" , col="transparent", lwd=3 ) lines( CoxM, border="red" , col="transparent", lwd=3 ) text( 60.5, 0.05, "M" ) box( lwd=5, col="white" ) ; box( lwd=2, col="black" ) plot( pF, border="black", col="transparent", lwd=3 ) lines( PrF, border="blue" , col="transparent", lwd=3 ) lines( CoxF, border="red" , col="transparent", lwd=3 ) text( 60.5, 0.05, "F" ) box( lwd=5, col="white" ) ; box( lwd=2, col="black" ) ################################################### ### code chunk number 30: CHANGE1 (eval = FALSE) ################################################### ## source( "../R/simLexis.R", keep.source=TRUE ) ################################################### ### code chunk number 31: CHANGE2 ################################################### simX <- Epi:::simX sim1 <- Epi:::sim1 lint <- Epi:::lint get.next <- Epi:::get.next chop.lex <- Epi:::chop.lex ################################################### ### code chunk number 32: simLexis.rnw:972-975 ################################################### cbind( attr( ini, "time.scales" ), attr( ini, "time.since" ) ) ################################################### ### code chunk number 33: simLexis.rnw:1000-1001 ################################################### simLexis ################################################### ### code chunk number 34: simLexis.rnw:1018-1019 ################################################### simX ################################################### ### code chunk number 35: simLexis.rnw:1031-1032 ################################################### sim1 ################################################### ### code chunk number 36: simLexis.rnw:1044-1045 ################################################### lint ################################################### ### code chunk number 37: simLexis.rnw:1055-1056 ################################################### get.next ################################################### ### code chunk number 38: simLexis.rnw:1065-1066 ################################################### chop.lex ################################################### ### code chunk number 39: simLexis.rnw:1083-1084 ################################################### nState ################################################### ### code chunk number 40: simLexis.rnw:1093-1094 ################################################### pState ################################################### ### code chunk number 41: simLexis.rnw:1098-1100 ################################################### plot.pState lines.pState Epi/inst/doc/crisk.R0000644000176200001440000002347414003562633013763 0ustar liggesusers### R code from vignette source 'crisk' ### Encoding: UTF-8 ################################################### ### code chunk number 1: crisk.rnw:24-27 ################################################### options( width=90, SweaveHooks=list( fig=function() par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") ) ) ################################################### ### code chunk number 2: crisk.rnw:83-100 ################################################### library(Epi) library(popEpi) data(DMlate) Ldm <- Lexis(entry = list( per = dodm, age = dodm-dobth, tfd = 0 ), exit = list( per = dox ), exit.status = factor( !is.na(dodth), labels = c("DM","Dead") ), data = DMlate ) summary(Ldm, t = T) Mdm <- mcutLexis( Ldm, wh = c('dooad','doins'), new.states = c('OAD','Ins'), precursor = 'DM', seq.states = FALSE, ties = TRUE ) summary( Mdm ) ################################################### ### code chunk number 3: crisk.rnw:105-107 ################################################### Sdm <- splitMulti(factorize(subset(Mdm, lex.Cst == "DM")), tfd = seq(0, 20, 1/12)) ################################################### ### code chunk number 4: boxes5 ################################################### boxes(Mdm, boxpos = list(x = c(15, 50, 15, 85, 85), y = c(85, 50, 15, 85, 15)), scale.R = 100, show.BE = TRUE) ################################################### ### code chunk number 5: boxes4 ################################################### boxes( Relevel(Sdm, c(1, 4, 2, 3)), boxpos = list(x = c(15, 85, 80, 15), y = c(85, 85, 20, 15)), scale.R = 100, show.BE = TRUE ) ################################################### ### code chunk number 6: crisk.rnw:139-142 ################################################### mD <- gam.Lexis(Sdm, ~ s(tfd, k = 5), to = 'Dead') mO <- gam.Lexis(Sdm, ~ s(tfd, k = 5), to = 'OAD' ) mI <- gam.Lexis(Sdm, ~ s(tfd, k = 5), to = 'Ins' ) ################################################### ### code chunk number 7: crisk.rnw:155-160 ################################################### int <- 1/100 nd <- data.frame( tfd = seq(int,10,int)-int/2 ) # not the same as the split, # and totally unrelated to it rownames(nd) <- nd$tfd str(nd) ################################################### ### code chunk number 8: rates ################################################### matshade(nd$tfd, cbind(ci.pred(mD, nd), ci.pred(mI, nd), ci.pred(mO, nd))*1000, ylim = c(0.02,500), yaxt = "n", ylab = "Rates per 1000 PY", xlab = "Time since DM diagnosis (years)", col = c("black","red","blue"), log = "y", lwd = 3, plot = TRUE) axis(side = 2, at = ll<-outer(c(1,2,5),-2:3,function(x,y) x*10^y), labels = formatC(ll,digits = 4), las = 1) axis(side = 2, at = ll<-outer(c(1.5,2:9),-2:3,function(x,y) x*10^y), labels = NA, tcl = -0.3) text(0, 0.5*0.6^c(1,2,0), c("Dead","Ins","OAD"), col = c("black","red","blue"), adj = 0) ################################################### ### code chunk number 9: crisk.rnw:194-209 ################################################### # rates at midpoints lD <- ci.pred( mD, nd )[,1] lI <- ci.pred( mI, nd )[,1] lO <- ci.pred( mO, nd )[,1] # cumulative rates and survival fuction at right border of the intervals LD <- cumsum(lD) * int LI <- cumsum(lI) * int LO <- cumsum(lO) * int Sv <- exp( -LD - LI - LO ) # but when integrating to get the cumulative risks we use the average # of the survival function at the two endpoints (adding 1 as the first) mp <- function(x) x - diff(c(1, x)) / 2 rD <- cumsum(lD * mp(Sv)) * int rI <- cumsum(lI * mp(Sv)) * int rO <- cumsum(lO * mp(Sv)) * int ################################################### ### code chunk number 10: crisk.rnw:214-218 ################################################### summary(rD + rI +rO + Sv) oo <- options(digits = 20) cbind(summary(Sv + rD + rI + rO)) options(oo) ################################################### ### code chunk number 11: stack ################################################### zz <- mat2pol(cbind(rD,rI,rO,Sv), x = nd$tfd, xlim = c(0,10), xaxs = "i", yaxs = "i", las = 1, xlab = "Time since DM diagnosis (years)", ylab = "Probability", col = c("black","red","blue","forestgreen") ) mm <- t(apply(zz,1,mid<-function(x) x[-1]-diff(x)/2)) text( 9, mm[900,], c("Dead","Ins","OAD","DM"), col = "white" ) box(col = "white",lwd = 3) ################################################### ### code chunk number 12: crisk.rnw:278-280 ################################################### head(cbind(ci.pred(mI,nd), ci.exp(mI,nd) )) head(cbind(ci.pred(mI,nd), exp(ci.lin(mI,nd)[,c(1,5:6)]))) ################################################### ### code chunk number 13: crisk.rnw:285-287 ################################################### str(ci.lin(mI, nd, sample = 4)) head(cbind(ci.pred(mI,nd), exp(ci.lin(mI, nd, sample = 4)))) ################################################### ### code chunk number 14: crisk.rnw:319-321 (eval = FALSE) ################################################### ## setwd("/home/bendix/stat/R/examples") ## source('ci.Crisk.R', echo=TRUE, max=10000) ################################################### ### code chunk number 15: crisk.rnw:326-334 ################################################### system.time( res <- ci.Crisk(list(OAD = mO, Ins = mI, Dead = mD), nd = data.frame(tfd = (1:1000-0.5)/100), nB = 1000, perm = 4:1)) str(res) ################################################### ### code chunk number 16: crisk.rnw:364-372 ################################################### system.time( rsm <- ci.Crisk(list(OAD = mO, Ins = mI, Dead = mD), nd = data.frame(tfd = (1:1000-0.5)/100), nB = 2000, sim.res = 'rates')) str(rsm) ################################################### ### code chunk number 17: crisk.rnw:379-387 ################################################### system.time( csm <- ci.Crisk(list(OAD = mO, Ins = mI, Dead = mD), nd = data.frame(tfd = (1:1000-0.5)/100), nB = 2000, sim.res = 'crisk')) str(csm) ################################################### ### code chunk number 18: crisk.rnw:406-408 ################################################### Brates <- aperm(apply(rsm, 1:2, Epi:::mnqt), c(2,3,1)) str(Brates) ################################################### ### code chunk number 19: rates-ci ################################################### matshade(nd$tfd, cbind(ci.pred(mD, nd), ci.pred(mI, nd), ci.pred(mO, nd))*1000, ylim = c(0.1,500), yaxt = "n", ylab = "Rates per 1000 PY", xlab = "Time since DM diagnosis (years)", col = c("black","red","blue"), log = "y", lwd = 3, plot = TRUE) matlines(nd$tfd, cbind(Brates[,"Dead",], Brates[,"Ins" ,], Brates[,"OAD" ,])*1000, col = c("white","black","black"), lty = 3, lwd=c(3,1,1)) axis(side = 2, at = ll<-outer(c(1,2,5),-2:3,function(x,y) x*10^y), labels = formatC(ll,digits = 4), las = 1) axis(side = 2, at = ll<-outer(c(1.5,2:9),-2:3,function(x,y) x*10^y), labels = NA, tcl = -0.3) text(0, 0.5*0.6^c(1,2,0), c("Dead","Ins","OAD"), col = c("black","red","blue"), adj = 0) ################################################### ### code chunk number 20: crates ################################################### matshade(c(0,nd$tfd+1/200), cbind(res$Crisk[,"Dead",], res$Crisk[,"Ins" ,], res$Crisk[,"OAD" ,]), plot = TRUE, xlim = c(0,10), xaxs = "i", yaxs = "i", las = 1, xlab = "Time since DM diagnosis (years)", ylab = "Cumulative probability", col = c("black","red","blue")) text(8, 0.3 + c(1,0,2)/25, c("Dead","Ins","OAD"), col = c("black","red","blue"), adj = 0) ################################################### ### code chunk number 21: crisk.rnw:467-469 ################################################### str(res$Crisk) str(res$Srisk) ################################################### ### code chunk number 22: stack-ci ################################################### zz <- mat2pol(res$Crisk[,c("Dead","Ins","OAD","Surv"),1], x = as.numeric(dimnames(res$Crisk)[[1]])/100, xlim = c(0,10), xaxs = "i", yaxs = "i", las = 1, xlab = "Time since DM diagnosis (years)", ylab = "Probability", col = c("black","red","blue","forestgreen") ) mm <- t(apply(zz, 1, mid<-function(x) x[-1] - diff(x) / 2)) text( 9, mm[900,], c("Dead","Ins","OAD","DM"), col = "white" ) matshade(as.numeric(dimnames(res$Srisk)[[1]])/100, cbind(res$Srisk[,1,], res$Srisk[,2,], res$Srisk[,3,]), col = 'transparent', col.shade = "white", alpha = 0.3) ################################################### ### code chunk number 23: crisk.rnw:503-504 ################################################### str(res$Stime) ################################################### ### code chunk number 24: crisk.rnw:507-510 ################################################### s510 <- res$Stime[1:2*500,,] dimnames(s510)[[1]] <- c(" 5 yr","10 yr") round(ftable(s510, row.vars=1:2), 2) Epi/inst/doc/yll.R0000644000176200001440000001611014003563064013434 0ustar liggesusers### R code from vignette source 'yll' ### Encoding: UTF-8 ################################################### ### code chunk number 1: yll.rnw:21-24 ################################################### options( width=90, SweaveHooks=list( fig=function() par(mar=c(3,3,1,1),mgp=c(3,1,0)/1.6,las=1,bty="n") ) ) ################################################### ### code chunk number 2: states ################################################### library( Epi ) TM <- matrix(NA,4,4) rownames(TM) <- colnames(TM) <- c("Well","DM","Dead","Dead(DM)") TM[1,2:3] <- TM[2,4] <- 1 zz <- boxes( TM, boxpos=list(x=c(20,80,20,80),y=c(80,80,20,20)), wm=1.5, hm=4 ) ################################################### ### code chunk number 3: states ################################################### zz$Arrowtext <- c( expression(lambda), expression(mu[W]), expression(mu[D][M]) ) boxes( zz ) ################################################### ### code chunk number 4: yll.rnw:265-266 ################################################### data( DMepi ) ################################################### ### code chunk number 5: yll.rnw:271-273 ################################################### str( DMepi ) head( DMepi ) ################################################### ### code chunk number 6: yll.rnw:293-297 ################################################### DMepi <- transform( subset( DMepi, A>30 ), D.T = D.nD + D.DM, Y.T = Y.nD + Y.DM ) head(DMepi) ################################################### ### code chunk number 7: yll.rnw:303-329 ################################################### # Knots used in all models ( a.kn <- seq(40,95,,6) ) ( p.kn <- seq(1997,2015,,4) ) ( c.kn <- seq(1910,1976,,6) ) # Check the number of events between knots ae <- xtabs( cbind(D.nD,D.DM,X) ~ cut(A,c(30,a.kn,Inf)) + sex, data=DMepi ) ftable( addmargins(ae,1), col.vars=3:2 ) pe <- xtabs( cbind(D.nD,D.DM,X) ~ cut(P,c(1990,p.kn,Inf)) + sex, data=DMepi ) ftable( addmargins(pe,1), col.vars=3:2 ) ce <- xtabs( cbind(D.nD,D.DM,X) ~ cut(P-A,c(-Inf,c.kn,Inf)) + sex, data=DMepi ) ftable( addmargins(ce,1), col.vars=3:2 ) # Fit an APC-model for all transitions, seperately for men and women mW.m <- glm( D.nD ~ -1 + Ns(A ,knots=a.kn,int=TRUE) + Ns( P,knots=p.kn,ref=2005) + Ns(P-A,knots=c.kn,ref=1950), offset = log(Y.nD), family = poisson, data = subset( DMepi, sex=="M" ) ) mD.m <- update( mW.m, D.DM ~ . , offset=log(Y.DM) ) mT.m <- update( mW.m, D.T ~ . , offset=log(Y.T ) ) lW.m <- update( mW.m, X ~ . ) # Model for women mW.f <- update( mW.m, data = subset( DMepi, sex=="F" ) ) mD.f <- update( mD.m, data = subset( DMepi, sex=="F" ) ) mT.f <- update( mT.m, data = subset( DMepi, sex=="F" ) ) lW.f <- update( lW.m, data = subset( DMepi, sex=="F" ) ) ################################################### ### code chunk number 8: yll.rnw:336-373 ################################################### a.ref <- 30:90 p.ref <- 1996:2016 aYLL <- NArray( list( type = c("Imm","Tot","Sus"), sex = levels( DMepi$sex ), age = a.ref, date = p.ref ) ) str( aYLL ) system.time( for( ip in p.ref ) { nd <- data.frame( A = seq(30,90,0.2)+0.1, P = ip, Y.nD = 1, Y.DM = 1, Y.T = 1 ) muW.m <- ci.pred( mW.m, nd )[,1] muD.m <- ci.pred( mD.m, nd )[,1] muT.m <- ci.pred( mT.m, nd )[,1] lam.m <- ci.pred( lW.m, nd )[,1] muW.f <- ci.pred( mW.f, nd )[,1] muD.f <- ci.pred( mD.f, nd )[,1] muT.f <- ci.pred( mT.f, nd )[,1] lam.f <- ci.pred( lW.f, nd )[,1] aYLL["Imm","M",,paste(ip)] <- yll( int=0.2, muW.m, muD.m, lam=NULL, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Imm","F",,paste(ip)] <- yll( int=0.2, muW.f, muD.f, lam=NULL, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Tot","M",,paste(ip)] <- yll( int=0.2, muT.m, muD.m, lam=NULL, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Tot","F",,paste(ip)] <- yll( int=0.2, muT.f, muD.f, lam=NULL, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Sus","M",,paste(ip)] <- yll( int=0.2, muW.m, muD.m, lam=lam.m, A=a.ref, age.in=30, note=FALSE )[-1] aYLL["Sus","F",,paste(ip)] <- yll( int=0.2, muW.f, muD.f, lam=lam.f, A=a.ref, age.in=30, note=FALSE )[-1] } ) round( ftable( aYLL[,,seq(1,61,10),], col.vars=c(3,2) ), 1 ) ################################################### ### code chunk number 9: imm ################################################### plyll <- function(wh){ par( mfrow=c(1,2), mar=c(3,3,1,1), mgp=c(3,1,0)/1.6, bty="n", las=1 ) matplot( a.ref, aYLL[wh,"M",,], type="l", lty=1, col="blue", lwd=1:2, ylim=c(0,12), xlab="Age", ylab="Years lost to DM", yaxs="i" ) abline(v=50,h=1:10,col=gray(0.7)) text( 90, 11, "Men", col="blue", adj=1 ) text( 40, aYLL[wh,"M","40","1996"], "1996", adj=c(0,0), col="blue" ) text( 43, aYLL[wh,"M","44","2016"], "2016", adj=c(1,1), col="blue" ) matplot( a.ref, aYLL[wh,"F",,], type="l", lty=1, col="red", lwd=1:2, ylim=c(0,12), xlab="Age", ylab="Years lost to DM", yaxs="i" ) abline(v=50,h=1:10,col=gray(0.7)) text( 90, 11, "Women", col="red", adj=1 ) text( 40, aYLL[wh,"F","40","1996"], "1996", adj=c(0,0), col="red" ) text( 43, aYLL[wh,"F","44","2016"], "2016", adj=c(1,1), col="red" ) } plyll("Imm") ################################################### ### code chunk number 10: tot ################################################### plyll("Tot") ################################################### ### code chunk number 11: sus ################################################### plyll("Sus") ################################################### ### code chunk number 12: CHANGE1 (eval = FALSE) ################################################### ## source( "../R/erl.R", keep.source=TRUE ) ################################################### ### code chunk number 13: CHANGE2 ################################################### surv1 <- Epi::surv1 surv2 <- Epi::surv2 erl1 <- Epi::erl1 erl <- Epi::erl yll <- Epi::yll ################################################### ### code chunk number 14: yll.rnw:484-485 ################################################### surv1 ################################################### ### code chunk number 15: yll.rnw:489-490 ################################################### erl1 ################################################### ### code chunk number 16: yll.rnw:497-498 ################################################### surv2 ################################################### ### code chunk number 17: yll.rnw:502-503 ################################################### erl ################################################### ### code chunk number 18: yll.rnw:507-508 ################################################### yll Epi/inst/doc/yll.pdf0000644000176200001440000107322114003563064014013 0ustar liggesusers%PDF-1.5 % 79 0 obj << /Length 789 /Filter /FlateDecode >> stream xڅTn0+x*$ E$Sa; j}qI,,o dsVˬf +:Z3&Tjmmp~EfT|/:|CUKfOSUI[cYv޾W\+:ιc?" np6vK+fil7g/o.a'DXIgS36pVXyPfٷSdBs\SZw6wLō5#,U) i) 'BQ%6Hx{vH:Bi. ? n?5MSN|A6ӆOP󭯑)Q} p2oߘcU uUŸ㺦7U,Y_ ` S|#2/*В:[RTrTv!" 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    Vignettes for the Epi package

    Other Epi package related stuff

    • \pkg{Epi} has grown out of the course 'Statistical Practise in Epidemiology with R', abbreviated SPE.
    • The website for the Epi package.
    • A list of reports and published papers using the Lexis machinery is here.
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DMߦv9=]yױ띁a]5ن w6=BEH;}u>\C-S(>tzwWxx)nYQ_dʘR`QQt:x=߃Nf_]' :R7"7uI)kfOApn@a0!G=zWw_j ͥ endstream endobj 464 0 obj << /Type /XRef /Index [0 465] /Size 465 /W [1 3 1] /Root 462 0 R /Info 463 0 R /ID [<68364C7D7E1DF602FDAF0EE30B02264E> <68364C7D7E1DF602FDAF0EE30B02264E>] /Length 1131 /Filter /FlateDecode >> stream x%O]UｼЏHj jp?S (jЃS *^@Bkś5粄k})pu)ʕ$*ep UpunMplmp ;{.,d\u`fԈvj$*isuok,| n**irETAWD=g;;Ɣfs#n%Q ADA/4E)n4*#Qh1.(SQ!v{3y$64N$z܃]5HbwG M2[0HoE2HY Mff3IN7{MW$9qlJ$'-O#Rqކ$Ad(m>c-f#H-vyUE^1{{u( ҾH]<`$i<ț}3^|-IhBHg|@[}(2g4V+dG_jP*@%ș/4MaCIZ7{:5ՃFHyA_˨h< Oھ:7}um@`/ ;΁CC{6!GOڴFOLӾ/ʛs`jip̛w?ח_KUV̿U.ol[= 2.8.0 passes package metadata to citation(). if(!exists("meta") || is.null(meta)) meta <- packageDescription("Epi") year <- sub("-.*", "", meta$Date) note <- sprintf("R package version %s", meta$Version) citEntry(entry = "Manual", title = "{Epi}: A Package for Statistical Analysis in Epidemiology", author = personList(as.person("Bendix Carstensen"), as.person("Martyn Plummer"), as.person("Esa Laara"), as.person("Michael Hills")), year = year, note = note, url = "https://CRAN.R-project.org/package=Epi", textVersion = paste("Bendix Carstensen, Martyn Plummer, Esa Laara, Michael Hills", sprintf("(%s).", year), "Epi: A Package for Statistical Analysis in Epidemiology.", paste(note, ".", sep = ""), "URL https://CRAN.R-project.org/package=Epi") ) citEntry(entry = "Article", title = "{Lexis}: An {R} Class for Epidemiological Studies with Long-Term Follow-Up", author = personList(as.person("Martyn Plummer"), as.person("Bendix Carstensen")), journal = "Journal of Statistical Software", year = "2011", volume = "38", number = "5", pages = "1--12", url = "https://www.jstatsoft.org/v38/i05/", textVersion = paste("Martyn Plummer, Bendix Carstensen (2011).", "Lexis: An R Class for Epidemiological Studies with Long-Term Follow-Up.", "Journal of Statistical Software, 38(5), 1-12.", "URL https://www.jstatsoft.org/v38/i05/."), header = "If you use Lexis objects/diagrams, please also cite:" ) citEntry(entry = "Article", title = "Using {Lexis} Objects for Multi-State Models in {R}", author = personList(as.person("Bendix Carstensen"), as.person("Martyn Plummer")), journal = "Journal of Statistical Software", year = "2011", volume = "38", number = "6", pages = "1--18", url = "https://www.jstatsoft.org/v38/i06/", textVersion = paste("Bendix Carstensen, Martyn Plummer (2011).", "Using Lexis Objects for Multi-State Models in R.", "Journal of Statistical Software, 38(6), 1-18.", "URL https://www.jstatsoft.org/v38/i06/."), header = "For use of Lexis objects in multi-state models, please also cite:" ) Epi/CHANGES0000644000176200001440000011427514016476407012005 0ustar liggesusersChanges in 2.44 o addCov.Lexis now always return a data.frame o New function: addDrug.Lexis adding drug exposure variables from files with drug exposure information to a Lexis object. Changes in 2.43 o a bug in addCov.Lexis ignored clinical mesurements prior to start of follow-up. This lead to a major redesign of addCov.Lexis by taing advatage of rcutLexis. It lost the add.scales argument, but time since clinical measurement is returned as a timescale by default. o ci.Crisk added. Computes simulation-based confidence intervals for cumulative risks in a competing risks situation. o sortLexis, orderLexis and order.Lexis added; order/sort of a Lexis object by (lex.id,time). o precursor.states now defaults to transient(Lx) for cutLexis, mcutLexis and rcutLexis, so precursor.states is no longer a required argument. o mcutLexis reported wrong number of ties resolved; fixed o Bug in mcutLexis accidentally omitting new states as precursor states o Bug in boxes.Lexis causing text in boxes always to be printed in bold font is fixed. Default font is changed to 1 instead of 2 o factorize.Lexis now only turns lex.Cst and lex.Xst into factors with the same set of levels. o Relevel.Lexis now behaves like Relevel, specifically: a character vector as second argument (ref=) will cause a reordering of levels of lex.Cst and lex.Xst, earlier it would merely cause a renaming of states, which could cause undetected rubbish. Changes in 2.42 o Extra line feed in output from coxph.Lexis to make output nicer o function 'rcutLexis' added allowing multiple transitions per person to be specified for cuts, including recurrences. Only keeps track of most recently occupied state, not history. Changes in 2.41 o A bug in addCov.Lexis messing up states due to unexpected sort order of a merge, has been rectified. o the ccwc function could select invalid controls when there was only one eligible non-case, due to the documented behaviour of sample for vectors of length 1. Changes in 2.40 o plotCIF and stackedCIF have been modified to comply with changes in survival (Esa Laara) Changes in 2.39 o mat2pol added: function that takes a set of curves represented as columns in a matrix (mat) and plots then as stacked polygons (pol) o the argument formula for glm.Lexis, gam.Lexis and coxph.Lexis is moved up to be the second argument, making simple specification of models for two-state (survival) models easier o addCov.Lexis was not exported as a proper method for Lexis, due to a mis-named argument in the definition. o addCov.Lexis produced erroneous results because of mistaken sorting order variables o A new function harm generating a basis of harmonic functions o Cleanup of documentation for Relevel o ci.lin argument ctr.mat now allows a list of 4 data frames to compute differences of differences of predictions. Useful for some interaction models o Bug in notes from ccwc corrected (MP) o Minor editorial changes in annotation of output from coxph.Lexis o The by= argument to summary.Lexis crashed the function if the Lexis object was a data.table. Now fixed. o Documentation of boxes.MS slightly amended. Changes in 2.38 o Minor editorial changes in urls in documentation files o The poisreg family now works with anova o Superfluous 'names' attributes on all variables in data sets bdendo and bdendo11 have been removed. Documentation for both now in the same file. bdendo11.Rd removed. Changes in 2.37 o ci.surv added to facilitate calculation of survival function from a smooth parametric model o Bug in apc.LCa - wrong labeling of resulting list element has been rectified. Changes in 2.36 o Lexis gains a 'notes' argument allowing to silence notes o Documentation of bootLexis upadated and groomed o Description of units of measurement in diet dataset corrected o Problems with default reference period/cohort in apc.fit fixed o apc.lines gains an argument shade= enabling shaded confidence limits of estimated curves. o Scaling of the trend internally in projection.ip to avoid numerical problems in solve() o Default vertical scaling of the box size in boxes.MS increased a bit Changes in 2.35 o Major re-write of vignette of follow-up data o glm.Lexis example updated o Lexis now gives a note and not a warning when dropping persons with no follow-up time o Epi.Rd included as man page, allowing easy access to the index via ?Epi. o simLexis updated to cope with poisreg family in modeling input o timeSince function added to tell which time scales are defined as time since entry to a state. Allows for a slightly more compact output from summary.Lexis, when timeScales=TRUE. o such timescales are NA before entry. In modeling we may want these to be 0, hence the model tsNA20 (timescale NAs to zero), that does this for such time scales. And optionally for all. o improved readbility of error message from ci.lin Changes in 2.34 o cleanup of ci.lin to exploit the (post 3.5.0) behaviour of coef/vcov which are now in sync o apc.fit nomenclature for drift extraction has been changed from "weighted" to "Y" in concert with BxCs recent paper. Changes in 2.33 o Fixed bug in gen.exp causing a crash when purchase dates were indestinguishable from FU-dates by match() but not by %in%. o Previously, apc.fit with dist="bin" returned odds in the Age component. Now returns probabilities. o Argument names and -order have been changed for glm.Lexis, gam.Lexis and coxph.Lexis, they are now x, from, to and formula. o Utility functions to describe state characteristics and relationships have been added: absorbing(), transient(), preceding(), succeeding(), before() and after() Changes in 2.32 o gen.exp: time since drug cessation was only computed for latest cessation, not for intermittent ones. Rectified and expanded set of result variables that keep track of patients' status are added. gen.exp also gains an argument, rm.dose, indicating whether doses purchased should be counted if time-allocation of purchases are limited by the push.max argument. Several disjoint FU-periods for persons are now allowed. o The changed functionality of vcov() returning 0s for aliased parameters (instead of omitting them) is now used and hence ci.lin is simplified. o A small utility in.span(A,x) checks if the vector x is in the column span of the matrix A. At the same time thinCol to remove linearly dependent columns from a matrix is now a function of its own. It was previously buried inside detrend, but the functions decurve and detrend needed it. Changes in 2.31 o A new link function, poisreg, added for (event,time) response data, courtesy of Martyn Plummer o Functions glm.Lexis, gam.Lexis and coxph.Lexis fitting models using Lexis objects have been added. The two former use the poisreg family. Slightly experimental still. o Bug in LCa.fit rectified, non-needed elements of npar can now be omitted, previously all 5 named items of the list were required. o matshade now allow NAs in x or y coordinates, causing separate shaded areas to be drawn. Changes in 2.30 o A function decurve added; it removes not only a linear trend but also a quadratic term from a designmatrix. Belongs in the realm of APC models. o Small changes in pc.lines, and addition of pc.matshade to make shaded confidence limits in APC plots Changes in 2.29 o ci.lin with a list of two prediction frames as argument to ctr.mat now also honors the vcov and sample arguments. Also expanded to accept a single data frame to mimick ci.pred and extending this to honor arguments vcov and sample. This facility ignores the offset, though. o matshade gains an argument plot that starts a new plot. Defauts to is.null(dev.list()), so if no plot frame is open one will be made. Changes in 2.28 o Added function matshade() that plots shaded confidence bands. o Epi:::ci.dfr (called from ci.lin) redesigned so that it actually works in most cases. Changes in 2.27 o Documentation of LCa.fit improved - really disturbing typos rectified. o Ns groomed to have knots= have precedence over df=, o Code of ci.dfr groomed, gam objects are now also accommodated when using the list(dfrx,dfrr) version of the ctr.mat argument. Bug causing a crash with splines fixed, however not elegantly. Changes in 2.26 o ci.lin did not honour a reference data frame of 1 row as promised. Fixed. Changes in 2.25 o N2Y now also completes the Lexis triangles in the last age-category by fitting the sum to the average of the two prevalent numbers. o ci.lin(vcov=TRUE) now returns a list whose first element is named 'coef' (previously 'est') and which is a vector (previously a 1-column matrix). Old performance was illogical. ci.lin also now accepts a list of two prediction dataframes as the ctr.mat argument. On the basis of these it computes the row-wise difference (RR for ci.exp). o bootLexis for bootstrapping persons from a Lexis object added. nid.Lexis (and nid.default) counting the number of persons in a Lexis object added as utility. o Dataset BrCa used for illustration of the Crowther and Lambert paper added together with a vignette using the data to illustrate a subset of the analyses as in the paper, plus some extra. o Relevel had a minor bug producing warnings where none were needed. Changes in 2.24 o Bug in Relevel functionality when using a 2-column structure for grouping levels fixed. Now also transfers ungrouped levels to the result as new levels. o Substantial update of the vignette on follow-up data with Epi. o Documentation groomed. Changes in 2.22 o vcov() use in ci.lin() updated to work with the new definition of vcov. o Relevel now also accepts a two-column structure as input --- basically a list of what each factor level should be mapped to. o A few changes and groomings of the vignettes Changes in 2.21 o minor changes in documentation of LCa.fit o the addScales argument to addCov.Lexis now implemented, along with small changes in the naming of the examination types in the absence of given ones. Changes in 2.20 o Vignettes now pre-build on order to keep source o Enhanced options for seq.states= argument to mcutLexis() allowing the last seen event determine the state. Inspired by a vigette in the survival package describing the feature. Changes in 2.19 o Typos in documentation of LCa.fit fixed o Bug in knot calculation in LCa.fit fixed. Meaningless models emerged if explicit knots were supplied for cohort effects. Prior to 2.19 only supplying *number* of knots for effects would give meaningful models if a cohort effect were included (with or without age-interaction). WISH: gen.exp has now got a wrapper, genExp.Lexis, explicitly using the Lexis structure. Changes in 2.18 o addCov.Lexis was fundamentally flawed, re-written, argument names and order changed too. o Documentation links between addCov.Lexis and gen.exp are introduced. Changes in 2.16 o Function addCov.Lexis added. Allows addition of covariates (clinical mesurements) taken at a particular time to be added to a Lexis object. Changes in 2.15 o typo in stackedCIF code corrected (caused a crash with ony one group) Changes in 2.14 o plotCIF, stackedCIF plotting Nelson-Aalen-Johansen estimators of cumulative risks added, courtesy Esa Lr o Convenice wrappers for grep to select elements: fgrep, ngrep, lgrep1. o A bug in Ns has been fixed, thanks to Lars J Diaz (DK) and Stephen Wade (AUS). o surv1, surv2, yll, erl: NAs in input rates are now changed to 0 (with a warning) instead of crashing the function. o documentation of ci.cum groomed. Changes in 2.12 o New function ci.ratio to compute RR with CIs from independent estimates of rates Changes in 2.11 o Small errors in calculation of knots in the simLexis macro corrected o A severe bug in mcutLexis which caused omission of certain cuts has been fixed. Changes in 2.10 o Bug in lls() caused a crash when objects had funny names (such as '[.Lexis'). Fixed. Changes in 2.9 o Grooming of code and documentation for mcutLexis. Changes in 2.8 o A function, mcutLexis, to cut at several different event times, preserving intermediat event histories has been added. o Errors in the erl.Rd corrected: Description of the argument "immune" was wrong, as were the description of the timepoints where rates were supposed given. o Inaccuracies in the vignette for simLexis patched. o lls() now also lists the size of objects o For illustrative purposes the DMepi dataset has been included Changes in 2.7 o '[.Lexis' redefined to comply with data.table as used from popEpi Changes in 2.6 o Added function erl computing Expected Residual Lifetime in an illness-death model added, together with companions surv1, surv2, erl1 and yll (Years of Life Lost). Changes in 2.5 o Argument "timeScales" added to summary.Lexis, printing names of timescales and which of them (if any) are defined as time since enty into a state. o rm.tr added; removes transitions from a Lexis object o boxes.MS no longer isssues a warning when show.BE is set to TRUE. o LCa.fit rewritten and expanded to encompass both age-period and age-cohort multiplicative interactions. o APC.LCa added, fits all possible Lee-Carter type models and APC-models. boxes.APC.LCa plots the relationship between models including the residual deviances, and optionally places boxes to provide overview of best fitting models. Changes in 2.4 o Ns updated with the possibility of clamping effects to have 0 slope beyond the outer knots, see argument "fixsl". Changes in 2.3 o Cplot (usually called from rateplot) now checks if age- and period-groupings are of the same length, and tells you if they are not, instead of just plotting (almost) nothing. o Grooming of LCa functions, and in particular the documentation. o Update of apc.fit so that also Y^2/D (the observed information about the rate) and Y (person-time) is allowed as weight when defining the inner product inducing orthogonality between linear and non-linear effects. Changes in 2.2 o LCa.fit added: Fits Lee-Carter models with smooth age and time effects to rate-data. print, summary, plot and predict methods also supplied. Changes in 2.1 o The show.BE="nz" feature in boxes.Lexis is now documented o "[.Lexis" is now exported and works... Changes in 2.0 o cbind, rbind and "[" methods for Lexis objects have been added o Consequential fixes in simLexis Changes in 1.1.72 o Improved man page for N2Y Changes in 1.1.71 o Bug from calling lme4::vcov from within ci.lin fixed Changes in 1.1.70 o Bug in calling lme4::fixef from within ci.lin fixed o ci.lin with sample=TRUE now samples from the posterior of the parameter vector and then transforms this by the contrast matrix (earlier the sampling was from the posterior of the ctr.mat transformed parameters). Changes in 1.1.69 o ci.cum now has an argument ci.Exp (defaults to FALSE) that computes the ci of the cum.haz on the log-scale. This is useful if you want to transform c.i.s to the survival scale and want the c.i.s for the survival function to stay inside [0,1]. o ci.pred updated to automatically use the inverse link for transformation of results. Also now only accepts glm objects. o Ns now have arguents ref= and detrend=. ref= allows a reference value to be specified (where the Ns is 0); this is independent of the supplied data. detrend= projects the columns of Ns() on the orthogonal of the variable supplied; this is strongly dependent on the data. Changes in 1.1.68 o ci.lin has been groomed to use internally (newly, from 1.1.68) defined methods COEF and VCOV to extract coefficients and variance-covariances of these from different types of objects. Changes in 1.1.67 o The simLexis vignette has been groomed a bit o The function ci.pred (a wrapper for predict.glm) added Changes in 1.1.66 o A crr.Lexis method has been added to simplify the use of the Fine-Gray model when data are set up in a Lexis object. o ci.lin and ci.exp now recognises crr objects. o A wrapper, ci.pred, for predict.glm has been added, it returns predictions with confidence intervals. Changes in 1.1.65 o Despite the note, dropped rows from construction of a Lexis objects were not put in the "dropped" attribute. Changes in 1.1.64 o Fixed the sim-Lexis vignette Changes in 1.1.64 o Added function ZArray, which generates an array of 0s just as NArray generates an array of NAs. o Updated code to avoid "::" and ":::" as far as possible, as well as "<<-". Hence excluded records from construction of a Lexis object is now put in an attribute "dropped" of the Lexis object. Changes in 1.1.62 o Bug fix in the example code for boxes.Lexis Changes in 1.1.61 o ci.lin updated to recognize objects of class "lmerMod" from lmer. Changes in 1.1.60 o Documentation for DMlate updated. Changes in 1.1.59 o boxes.Lexis updated so that also no. of beginners and enders are properly formatted if larger than 999 Changes in 1.1.57 o boxes.Lexis updated with arguments show.BE and BE.pre, allowing annotation of boxes by the *number* of persons strating and ending in different states. Changes in 1.1.57 o simLexis substantially updated and groomed to accept Cox-models for transitions too. Example in the documentation and vignette is expanded accordingly. Changes in 1.1.56 o Typos in documentation corrected. o When records with too short follow-up are encountered by Lexis, they are dropped from the resulting object, but they will be availabe in the object drop.sh in the global environment. o The col and border arguments to plot.pState were not repeated automatically, so needed fixing. o More elaborate warning and error-messages if initiators in absorbing states are handed to simLexis. Changes in 1.1.55 o Documentation of clogistic is clarified w.r.t. likelihood contributions of matched sets. Changes in 1.1.54 o apc.fit updated to use the Ns wrapper, and automatically use knots located so that the marginal number of events is the same between knots. o plot.apc and lines.apc defined as methods for apc objects. They are just wrappers for apc.plot and apc.lines. o gen.exp example slightly modified to give better output. Changes in 1.1.53 o Population figures in N.dk, M.dk and Y.dk updated Changes in 1.1.52 o col.txt argument to plotEst was not working properly. Fixed o txt argument to plotEst can now be an expression vector allowing sub- and superscripts and mathematical expressions. o Relevel did not issue warning or error when a given level was being specified as member of more than one new level. It now stops with an error. o The convenience wrappers Ns (for ns) and NArray (for array) have been added Changes in 1.1.51 o boxes.Lexis fixed so that rates could be computed from matrix input to. Changes in 1.1.50 o Calculation of p-values in ci.lin has been modified, thyanks to Krista Fischer. Changes in 1.1.49 o Default of "border" argument to plot.pState changed to "transparent" Changes in 1.1.48 o Slight tidying of code in apc.fit. Automatic determination of reference points for period and cohort fixed to produce median correctly. Changes in 1.1.47 o Bug in simLexis (specifically in Epi:::simX) where factor levels were wrongly used, is now corrected. Versions earlier are likely to produce wrong state allocation in simulated dataset and not crash. Changes in 1.1.46 o lex.id handling in simLexis changed, allows for easier simulation in chunks which may be necessary to avoid memory problems. Changes in 1.1.45 o simLexis introduced. Allows simulation from multiple timescale mulitste models. Accompanying utilities supplied too: pr.Lexis, prev and plot.prev. Changes in 1.1.44 o A number of dead links in the documentation have been resurrected. o attach() purged from Lexis.diagram, Lexis.lines and ccwc. o Bug in computing AUC in ROC fixed, thanks to Karl Ove Hufthammer. Documentation clarified with respect to definition of test. o Bug fix to remove warning when more than one variable name was supplied in the by= argument of summary.Lexis. Changes in 1.1.43 o N2Y fixed so that local variable bindings are recognized (M. Plummer) o summary.Lexis expanded with the argument by=, allowing a summary by a factor. Also, the default behaviour is now to return only the transition summary, and only optionally the transition rates; giverned by the Rates= argument Changes in 1.1.42 o Bug that caused a crash of ROC when vaiables in the "form" argument were only in the "data" argument data frame and not in the global environmant. Now fixed thanks to Ben Barnes of the Robert Koch Institute, German Center for Cancer Registry Data Changes in 1.1.41 o boxes.Lexis now returns an object of class MS, which easily allows plotting of slightly modified multistate displays using the new command boxes.MS. The facility in boxes.Lexis to produce weedy code for the same purpose has been removed. o boxes.Lexis now allows to show *both* number of transitions *and* rates between the states. o stack.Lexis now takes the Lexis attributes "time.scales" and "breaks" across from the Lexis object to the stacked.Lexis object. Changes in 1.1.40 o subset, transform and Relevel methods have been added for objects of type stacked.Lexis. Changes in 1.1.39 o effx has been expanded with an extra argument eff=, which defaults to NULL, allows "RR" for relative risk for binary data, and "RD" for rate differences for failure data. Also logical response is admitted for binomial and failure responses. o factorize and Relevel are now synonyms. Methods for Relevel are Relevel.default, Relevel.factor, Relevel.Lexis, for factorise only the factorize.default and factorize.Lexis exist. o A mistake in estimating sequential residuals in apc.fit() has been corrected. The wrong model (adc instead of rc, in the case parm == "AD-C-P") was used for the basis of residuals. Thanks to Shih-Yung Su from Taiwan. o as.Date.cal.yr is added, even though it was removed earlier: cal.yr is a class for date variables and the conversion function should be around. o A bug in ci.pd causing calculations to go wrong if vectors were supplied as input. Correction thanks to Patrick Rymer. o A bug in factorize.Lexis is fixed. Now appropriately groups factor levels in the state factors lex.Cst and lex.Xst. Relevel.Lexis is defined as an alias for factorize.Lexis. Thus the functins Relevel() and factorize() are now identical. Changes in 1.1.36 o A bug in boxes.Lexis causing arrow-coloring to go out of sync fixed o Array problems in stat.table fixed Changes in 1.1.35 o none. Just compiled for the archive with R 2.15.0 Changes in 1.1.34 o plotEst now has an arguments col.txt and font.txt which allows the use of different colors and fonts for the annotation of the estimates. Models likely to be multiplicative incurs a logarithmic x-axis in the plot. o ci.exp introduced - a wrapper for ci.lin, getting the exponentiated parameters with CIs. o A bug causing unintended reordering of levels using boxes.Lexis is fixed. o Method etm for Lexis objects included. This just takes a Lexis object, and fishes out the relevant information to be able to call the function etm from the etm package (empirical transition matrix). This function is now physically defined in the file(s) foreign.Lexis.R(d). Changes in 1.1.32 o gen.exp was re-written and simplified. o Small cosmetic changes to the code for N2Y Changes in 1.1.31 o The extractor functions entry, exit, status and dur have now an argument by.id=FALSE. If set to TRUE, only one record per lex.id is returned and the resulting object has lex.id as (row)names attribute. Changes in 1.1.30 o DMlate expanded with the column dooad o Documentation for as.Date.cal.yr fixed o Bug in gen.exp fixed (It was assuming a data frame called dfr existed was wrong, but not spotted by the example because in the example one actually did exist!) Changes in 1.1.29 o New function gen.exp for generating time-varying exposure variables from drug purchase records. Changes in 1.1.28 o splitLexis now allows NAs in the timescale on which you split. Records with NAs are simply left untouched, but a warning is printed. o A bug in boxes.Lexis preventing rates to be printed was issued. Changes in 1.1.27 o A few typos corrected o Functions a.lines, a.points, cp.lines and cp.points added to facilitate plotting points and curves from APC-models. o apc.fit did not return the reference cohort/period if it was not supplied in a model with explicit drift. Changes in 1.1.26 o A new function N2Y added which computes person-years in Lexis triangles from population prevalence data. o Demographic example data from Denmark added: N.dk - population size at 1 Jan Y.dk - risk time in Lexis triangles M.dk - mortality data B.dk - births in Denmark 1902 ff. Changes in 1.1.25 o Added sd() function to stat.table() o tmat.Lexis has an argument Y=FALSE which if set to TRUE will return the person-years in the diagonal. o boxes() now explicitly defined with methods boxes.Lexis and boxes.matrix that explicitly call boxes.default (which is the function doing the work (almost identical to the former boxes.Lexis). Changes in 1.1.24 o countLexis did not take the "timescales" and "breaks" attribute across to the resulting Lexis object. Changes in 1.1.23 o A missing defualt value for new.scale in doCutLexis caused a crash o A missing default value for new.scale in doCutLexis caused a crash when using the count=TRUE argument to cutLexis. Changes in 1.1.23 o ci.lin and ci.cum now have a sample= argument that causes return of a sample from the normal distribution with mean equal to the estimates and variance equal to the estimated variance of the estimates. To be used to do "parametric bootstrap" of complicated functions of the parameters, such as state occupancy probabilities from multistate models. o ci.lin now supports objects of class mipo (Multiple Imputation Pooled Objects --- see the mice package). o tabplot removed --- it was a proper subset of the mosaicplot from the graphics package Changes in 1.1.22 o A bug in boxes.Lexis prevented the use of ht= and wd= arguments to set boxes to a prespecified size. The scaling of these is now also clarified in the man file for boxes.Lexis. Changes in 1.1.21 o Specifying period of cohort effects with only two parameters caused apc.fit to crash. Fixed by adding a few ",drop=FALSE" in subsetting of matrices. o Since as.Date.cal.yr was not used anywhere, it has been removed from the package. o A function Wald added to do Wald test of several parameters or linear combinations of them. It is a small extension on top of ci.lin. Changes in 1.1.20 o CITATION file added. Changes in 1.1.19 o ci.lin amended by an argument subint= allowing to select subsets of parameters matching several strings. Changes in 1.1.18 o boxes.Lexis has been made a bit more versatile for production of box-diagrams from multistate models. Changes in 1.1.17 o A comma was missing in the code-output from boxes.Lexis o mstate.Lexis function changed name to msdata.Lexis, according to the change in convention in the mstate package. Code simplified as it is now using the functionality in stack.Lexis. o A factorize.Lexis function has been added, it basically changes the variables lex.Cst and lex.Xst to factors with same set of levels. A useful facility when we want boxes.Lexis to work. Changes in 1.1.16 o boxes.Lexis now resets the graphical parameters (par()) on exit. o plot.Lexis now has a default Lexis object as argument, allowing use of the function to plot empty Lexis diagrams without setting up a Lexis object first. The bogus object has timescales c("Date","Age") but 0 follow-up time. Changes in 1.1.14 o ci.lin now has an argument df to allow for t-quantiles in ci calculations. o lls() function revised to give nicer (left justified) output. Changes in 1.1.13 o ci.lin now supports objects of class clogistic. o utility function ci.mat() added --- earlier defined inside ci.lin and ci.cum, but also useful on its own. o lls() and clear() added, to ease overview and clearing of workspace (and attachments!) o apc.frame now sets the option "apc.frame.par" with the offset and scaling of calendar time part of the apc frame. This is recognised now by apc.lines automatically. o Function pc.points, pc.lines, pc.matlines, pc.matpoints added to ease plotting the calendar time region of an apc frame; live off the option "apc.frame.par". Changes in 1.1.12 o Added function clogistic for conditional logistic regression. Changes in 1.1.9 o A function PY.ann.Lexis is added. It writes the length of (pieces of) lifelines in a Lexis digram produced by plot.Lexis. o plot.Lexis now sets an option "Lexis.time.scale" which is queried by lines.Lexis and points.Lexis, so that time.scale is only needed in plot.Lexis. Changes in 1.1.8 o apc.fit had a bug in the specification of knots when using the argument model="bs". Fixed. Changes in 1.1.7 o boxes.Lexis has been further enhanced with the facility to plot rates instead of no. transitions on the arrows if required. The code has been tidied a bit too. o The man file for boxes.Lexis and subsidiaries have been renamed to MS.boxes.Rd Changes in 1.1.5 o boxes.Lexis have been enhanced to accommodate two-way transitions between states. Annotation by number of transitions has been improved to accommodate this too by always putting the number on the left side of the arrow. Changes in 1.1.3 o ci.lin() and ci.cum() have been expanded to accept objects of class "MIresult" from the mitools package (Esa Lr). o The boxes.Lexis() now gives a more versatile piece of code, which computes the text widths and heights. Changes in 1.1.2 o cutLexis crashed if new.state=TRUE and new.scale=FALSE were specified. Fixed. Changes in 1.1.1 o Functions stack.Lexis, tmat.Lexis and mstate.Lexis have been added to facilitate practical multistate modeling. The two latter provides an interface to the mstate package. o Functions tbox, dbox, fillarr, boxarr and boxes.Lexis added to facilitate drawing of multistate box diagrams. Changes in 1.1.0 o Two new datasets DMrand and DMlate with random samples from the Danish National diabetes register. The examples from these illustrate most of the recently added multistate stuff. o Minor bug in check.time.scale was fixed (misplaced parentheses in the argument to any(), causing a warning). o cutLexis introduces a new timescale "time since event", which has missing values for any follow-up time prior to event. Hence requires that the Lexis plotting functions explicitly discards the units with missing on timescales in use. Accomplished by the new function valid.times. o cutLexis now places the new states after the precursor states and before the other ones in the factors lex.Cst and lex.Xst. o splitLexis uses the first timescale by default. Which in particular means that in the case of only one time scale it is not necessary to specify it, so this has become acceptable now. o Vignettes has been updated. o Example for ci.cum has been fixed to be compatible with the new survival package as of 2.9.0 as announced. o apc.fit fitted the wrong model when using parm="AC-P". Fixed o The axis scaling of apc.plot has been improved. o apc.frame now by default plots a reference line for RR=1, this may be switched off by the (newly introduced) parameter "ref.line=FALSE". Changes in 1.0.10 o Fixed parse errors in documentation. Changes in 1.0.9 o Thanks to Mike Murphy, Professor of Demography, Department of Social Policy, London School of Economics, a bug causing a crash of apc.fit if only one row in the model matrix corresponds to the reference level was fixed. o Also thanks to Mike Murphy, a much more efficient calculation of median period and cohort is now used. o apc.fit expanded with an argument allowing logistic regression model instead of a Poisson model only. Changes in 1.0.8 o tab.Lexis removed and replaced by summary.Lexis which gives a better summary of the transitions and transition rates. o A bug in ci.pd (confidence interval for probability difference) has been fixed. Changes in 1.0.7 o Stat.table data= argument fixed. Changes in 1.0.6 o Lexis now converts character values of entry/exit.status to factors for lex.Cst and lex.Xst. And produces a warning if the entry.state is defaulted to the first level of exit.state (i.e. when exit.state is given as charcter or factor). o splitLexis gave wrong results for factor states. cutLexis gave wrong results for character states. Fixed by letting Lexis coerce character mode entry.status and exit.status to factors for lex.Cst and lex.Xst. In split.lexis.1D was the problem with the factor states, they were coerced to numeric when stuffed into the new.Xst matrix. Now states are turned to numeric before the call to split.lexis.1D and the factor attributes re-instituted after the split. o Added transform method for Lexis objects. Changes in 1.0.5 o Typos in documentation of APC functions corrected. o cutLexis updated to handle various instances by MP. A few BxC additions to MP's code: - cutLexis2 is renamed cutLexis. BxC's old cutLexis killed. - count=FALSE as argument to cutLexis, just calls countLexis if TRUE. - cutLexis no longer returns the working column lex.cut - cutLexis was missing the attributes "time.scales" and "breaks". Added. - cut= is allowed, simplifying cut of split Lexis objects. - documentation accordingly altered. o splitLexis amended so that lex.Xst is returned as a factor if lex.Cst is a factor. splitLexis crashed if lex.Cst and lex.Xst were factors. o Lexis now allows omission of entry.status --- if exit.status is numeric/logical/factor, entry.status (and hence lex.Cst) will be set to 0/FALSE/first level. o Lexis made sure that lex.Cst and lex.Xst have the same class. If they are factors, the set of levels is taken to be the union. Changes in 1.0.1 o cutLexis now works properly - no it did not! o cutLexis now accepts a (smaller) dataframe with cutpoints and states as input. Changes in 0.9.6 o Bugfix in timeBand, crashed when type="factor" was chosen. levels was given as 0:(lengh(breaks)+1), changed to 0:lengh(breaks) Changes in 0.9.5 o The Lexis definition now assumes that entry is 0 if only one of exit or duration are given as a one-component list. o tab.Lexis is now properly working as a method for Lexis objects. Changes in 0.9.4 o The lex.-variables in Lexis objects are now called lex.dur, lex.Cst, lex.Xst, lex.id (duration, Current state, eXit state and identification) o An extra option states= added to Lexis. If used the state variables are returned as factors. o The utility function deltat.Lexis() has been renamed to dur(). o state() now returns a dataframe of both (entry,exit) states a default. The reason for this is that lex.Cst and lex.Xst may be factors (which actually would be the logical thing to have by default, but it is not enforced only allowed). o entry() and exit() now by default returns matrices with entry and exit times on all timescales. If only one timescale is requested, they return a 1-column matrix. o A minor typo in stat.table corrected: in the definition of the quantile function prob=probs changed to probs=probs. o cutLexis() bugs corrected. Now works with split data too, but requires specification of censoring states --- i.e. states that will be replaced by the new state obtained at the cut date. Changes in 0.9.3 (since 0.9.0) o New function cutLexis() to allow cutting of follow-up time at a specific date for each person, where a new state is assumed. o New function tab.Lexis() which tabulates records as well as events and person-years from a Lexis object. o splitLexis got state information wrong if breaks were not unique. Fixed. Changes in 0.9.0 o effx and effx.match updated following Tartu 2007 to avoid attaching the data, and to correct the parsing of the list of control variables. Changes in 0.8.0 o A new function Lexis() to define follow-up on multiple timescales has been added. An object of class Lexis is defined and a number of utilities for the class are available. Time-splititng is now done by splitLexis(). o The old Lexis function for time-splitting has been renamed to W.Lexis for backward compatibility. o The function epi.eff() has been replaced by effx() and effx.match(). Changes 0.7.2 to 0.7.3 o Icens is now able to handle a constant underlying rate. (A bug in expand.data was fixed). Changes 0.7.0 to 0.7.2 o Bugs in ROC fixed, and the functionality of the grid option slightly chnaged. Changes 0.6.1 to 0.7.0 o Function Icens() for estimation of rates from intervalcensored follow-up data by Martyn Plummer added. o Function epi.eff by Michael Hills is added. Estimates effects in various epidemiological study types. Changes 0.6.0 to 0.6.1 o Coding errors in thoro dataset corrected. Only concerning dates and status for livercancer diagnosis. o Lexis.lines now allows col.life, lwd.life, pch.fail, col.fail and cex.fail to have the same length as the data, i.e. to produce individualized lines and points. As Lexis.diagram calls Lexis.lines, this facility is also available through Lexis.diagram. Changes from 0.4 to 0.6 o ci.pd() amended to support the Agresti-Caffo method for confidence intervals for difference between proportions. Newcombes method 10 is still used in twoby2. o apc.fit() added. Fits age-period-cohort models with a range of possibilities for parametrizations. o Functions for time-splitting at arbitrary times and at recurrent failures have been added: isec(), icut(), fcut1(), fcut() and ex1(). Eventually they will be superseded by new facilities in Lexis. o Function apc.plot() to make a plot of an apc fit is added. It is just a wrapper for apc.frame() and apc.lines(), with suitable computation of the paramters supplied to apc.frame. o Lexis.lines(): pch.fail and col.fail expandS to vectors of length two if only one value is given. o ci.cum() aimed at computing cumulative hazard functions from parametric functions for hazards. o Problem in print.floated() with printing of objects of class "floated" fixed. o Problem in ci.lin when subset did not match any factor names and diff=T was given the function crashed. Fixed, and documentation updated. o cal.yr produces objects of class c("cal.yr","numeric"). Functions as.Date.numeric and as.Date.cal.yr added.

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