metap/0000755000176200001440000000000014511006022011347 5ustar liggesusersmetap/NAMESPACE0000644000176200001440000000231614161101534012575 0ustar liggesusersexport(albatros) export(allmetap) export(invchisq) export(invt) export(logitp) export(meanp) export(meanz) export(maximump) export(minimump) export(plotp) export(schweder) export(sumlog) export(sump) export(sumz) export(truncated) export(two2one) export(votep) export(wilkinsonp) S3method(print,allmetap) S3method(print,invchisq) S3method(print,invt) S3method(print,logitp) S3method(print,meanp) S3method(print,meanz) S3method(print,sumlog) S3method(print,sump) S3method(print,sumz) S3method(print,votep) S3method(print,maximump) S3method(print,minimump) S3method(print,truncated) S3method(summary,truncated) S3method(plot,truncated) S3method(print,wilkinsonp) S3method(plot,metap) importFrom("graphics", "abline", "axis", "lines", "mtext", "plot", "text") importFrom("stats", "binom.test", "coef", "lm", "na.fail", "pbeta", "pchisq", "pnorm", "ppoints", "pt", "qbeta", "qchisq", "qnorm", "qqline", "qqplot", "qunif", "qt", "sd", "spline") importFrom("utils", "read.csv") importFrom("lattice", "xyplot") importFrom("Rdpack", "reprompt") importFrom("TFisher", "p.tpm", "stat.tpm") importFrom("mutoss", "ranktruncated") importFrom("qqconf", "qq_conf_plot") import("mathjaxr") metap/data/0000755000176200001440000000000014147446427012306 5ustar liggesusersmetap/data/dat.metap.rda0000644000176200001440000000632514147446376014664 0ustar liggesusersX XS {R.OJ&&;Oъ { NA tW@Ʃ(GDhtkDEوtt]y4.>t}@40CB3pL1↝cQƑ+kL]C刁zt]ouݧO!kmmgKs#>s꺡%@m-?6Y+ބ֠sooƇEIrQqj'7.(Ro} g?+(.SC=k%ÝiN&>h q5c?3L[\qTx4.‘wg9,-l =>)WwBkφWwfo; Y2OO` 4sW7CAG?+|,Dp9Fr=| ppgH{K"8CWnQqr* d/|aV39C?oqAE$A,JT+LתzF2Q8Yh,S)"Ler 1:1 bt!3ɻoJt(1Qjs\41VG.bt(>V!?ubFT(2:efJXI䶉*,_*cWC@4c/;GzM3sy99ɀ Zܿ~m̽4EPsU~P3Rq?|br/| LZ\I%:%FGqJQXSמށ"'D|NOp9<yp4ڛ y\nv\Nzsͧ nv6gחJ.\ Lgn|~.uVD!жpL/.uMj(Ӭ9]5Cfޗ&~ȭc!p2Id_{jKVƏ{Us/g{$n N@'i <_xz]?9i0>!FJWr(Җ5'mt!miC:tI Sf@C~9}vv :ĥVw ؼ.;%mĞ%^,X% 2AF;ʿ-WiSTX(K*R_Gt[wZ]z2;sL $bY1Mf)ŒNȢ'TkQc/MP+EN`WOY[?uɥ)=uT&SH 3[,su(Z3:DR1sWR}q1jjzH(1)RYiz21hN_bpo;wZ9Cs-r$꥕c@>ʝrIk0g5eڤՔynwcmTyeCzmӜ=NL58?58KZS.;wM CFӅءqv?F{iܟׁhGFip@q *fub<;fG{XhM>c|6yLa(C{4v,`]|ؒЇi'aX6zi6iv=tC-pl~s"ؐ7&NjVX#QSHĢx,JCqL/8V+IQ"z4<w?'Y;i8ƨ5J<; dJVD7Cү XdfrcÓAyΏ,+۱kޚ@;&&8+0<+1ܮjQ*Ƽ_0Jgj2z^ h_\.zhZ+fti3{FmCUٮM6|Ν6;ormna<%|"ue_\qp|$8ْ:*[x(Aw ~2:zQo8_?[Pd eEM["9P޹bf 4 ۄIA`{ Y}M<<56Pwx{:f [?^N{k?i?ЁB"J^?̈́HQOK I8zXh<^})1SLjU6Db*k'e*~mzC%f q4e%1R QD(#?4 Dmetap/man/0000755000176200001440000000000014147427216012143 5ustar liggesusersmetap/man/sumlog.Rd0000644000176200001440000000374714137514426013752 0ustar liggesusers\name{sumlog} \alias{sumlog} \alias{Fisher's method} \alias{chi-square (2) method} \alias{print.sumlog} \title{Combine p-values by the sum of logs (Fisher's) method } \description{Combine \mjseqn{p}-values by the sum of logs method, also known as Fisher's method, and sometimes as the chi-square (2) method\loadmathjax} \usage{ sumlog(p, log.p = FALSE) \method{print}{sumlog}(x, ...) } \arguments{ \item{p}{\sigvec} \item{log.p}{\logp} \item{x}{An object of class \sQuote{\code{sumlog}}} \item{...}{Other arguments to be passed through} } \details{ The method relies on the fact that \mjdeqn{\sum_{i=1}^k - 2 \log p_i}{sum (-2 log p)} is a chi-squared with \mjeqn{2 k}{2 * k} df where \mjseqn{k} is the number of studies \insertCite{fisher25}{metap}. \insertNoCite{becker94}{metap} \insertNoCite{rosenthal78}{metap} \insertNoCite{sutton00}{metap} \ltle{two} \plotmethod \nocancel } \value{ An object of class \sQuote{\code{sumlog}} and \sQuote{\code{metap}}, a list with entries \item{chisq}{Value of chi-squared statistic} \item{df}{Associated degrees of freedom} \item{p}{Associated \mjseqn{p}-value} \item{validp}{The input vector with the illegal values removed} %% ... } \references{ \insertAllCited{} } \author{Michael Dewey} \seealso{ See also \code{\link{plotp}} } \examples{ data(dat.metap) teachexpect <- dat.metap$teachexpect sumlog(teachexpect) # chisq = 69.473, df = 38, p = 0.0014, from Becker beckerp <- dat.metap$beckerp sumlog(beckerp) # chisq = 18.533, df = 10, sig rosenthal <- dat.metap$rosenthal sumlog(rosenthal$p) # chisq = 22.97, df = 10, p = 0.006 one sided cholest <- dat.metap$cholest$p sumlog(cholest) # chisq = 58.62, df = 68, p = 0.78 validity <- dat.metap$validity$p sumlog(validity) # chisq = 159.82, df = 40, p = 2.91 * 10^{-16} sumlog(c(0.0001, 0.0001, 0.9999, 0.9999)) # is significant all.equal(exp(sumlog(validity, log.p = TRUE)$p), sumlog(validity)$p) } % Add one or more standard keywords, see file 'KEYWORDS' in the % R documentation directory. \keyword{ htest } metap/man/dat.metap.Rd0000644000176200001440000001233014147451375014311 0ustar liggesusers\name{dat.metap} \alias{dat.metap} \alias{beckerp} \alias{cholest} \alias{edgington} \alias{naep} \alias{mourning} \alias{rosenthal} \alias{teachexpect} \alias{validity} \docType{data} \title{Example data} \description{ The package contains the following datasets: \code{beckerp}, \code{cholest}, \code{edgington}, \code{mourning}, \code{naep}, \code{rosenthal}, \code{teachexpect}, \code{validity}, and \code{zhang}. \loadmathjax} \usage{data(dat.metap) } \format{A list with the following elements: \describe{ \item{\code{beckerp}}{ A vector of length 5 } \item{\code{cholest}}{ A data frame with 34 observations on the following 5 variables. \describe{ \item{\code{ntreat}}{A numeric vector of number treated} \item{\code{ncontrol}}{A numeric vector of number in the control group} \item{\code{dtreat}}{A numeric vector of number of deaths in the treated group} \item{\code{dcontrol}}{A numeric vector of number of deaths in the control group} \item{\code{p}}{a numeric vector of one sided \mjseqn{p} values} } A vector of length 34 } \item{\code{edgington}}{ A vector of length 7 } \item{\code{naep}}{A data frame with 34 observations on the following 2 variables. \describe{ \item{\code{state}}{a factor with levels \code{AL}, \code{AR}, \code{AZ}, \code{CA}, \code{CO}, \code{CT}, \code{DE}, \code{FL}, \code{GA}, \code{HI}, \code{IA}, \code{ID}, \code{IN}, \code{KY}, \code{LA}, \code{MD}, \code{MI}, \code{MN}, \code{NC}, \code{ND}, \code{NE}, \code{NH}, \code{NJ}, \code{NM}, \code{NY}, \code{OH}, \code{OK}, \code{PA}, \code{RI}, \code{TX}, \code{VA}, \code{WI}, \code{WV}, \code{WY},} \item{\code{p}}{a numeric vector} }} \item{\code{mourning}}{ A data frame with 9 observations on the following 3 variables. \describe{ \item{\code{stance}}{a factor with levels \code{No stand}, \code{Opponent}, \code{Supporter}} \item{\code{grade}}{a factor with levels \code{G11-12}, \code{G7-8}, \code{G9-10}} \item{\code{p}}{a numeric vector} }} \item{\code{rosenthal}}{ A data frame with 5 observations on the following 3 variables. \describe{ \item{\code{t}}{A numeric vector of values of \mjseqn{t}} \item{\code{df}}{a numeric vector of degrees of freedom} \item{\code{p}}{a numeric vector of one sided \mjseqn{p} values} } } \item{\code{teachexpect}}{A vector of length 19 } \item{\code{validity}}{ A data frame with 20 observations on the following 3 variables \describe{ \item{\code{n}}{A numeric vector of sample sizes} \item{\code{r}}{a numeric vector of correlation coefficients} \item{\code{p}}{a numeric vector of one sided \mjseqn{p} values} } } \item{\code{zhang}}{ A data frame with 22 observations on the following 11 variables \describe{ \item{\code{study}}{Character, the study names} \item{\code{smd}}{numeric, the standardised mean difference} \item{\code{lo}}{numeric, the lower confidence limit} \item{\code{hi}}{numeric, the upper confidence limit} \item{\code{ntreat}}{numeric, the treated sample size} \item{\code{ncont}}{numeric, the control sample size} \item{\code{n}}{numeric, the total sample size} \item{\code{phase}}{factor, what phase the patients were in: acute, healing, healed} \item{\code{sd}}{numeric, the calculated standard deviation} \item{\code{z}}{numeric, the calculated z} \item{\code{p}}{numeric, the probability associated with z} } } } } \details{ \describe{ \item{\code{beckerp}}{Hypothetical \mjseqn{p} values from \insertCite{becker94;textual}{metap}} \item{\code{cholest}}{\if{html}{\eqn{}}\mjseqn{p} values from trials of interventions for lowering cholesterol lowering from \insertCite{sutton00;textual}{metap}} \item{\code{edgington}}{Hypothetical \mjseqn{p} values from \insertCite{edgington72a;textual}{metap}} \item{\code{mourning}}{Results from a study of mourning practices of Israeli youth following the assassination of Itzakh Rabin from \insertCite{benjamini00;textual}{metap}} \item{\code{naep}}{Results of mathematical achievment scores from the National Assessment of Educational Progress from \insertCite{benjamini00;textual}{metap}} \item{\code{rosenthal}}{Hypothetical example from \insertCite{rosenthal78;textual}{metap}} \item{\code{teachexpect}}{\if{html}{\eqn{}}\mjseqn{p}-values from studies of the effect of manipulating teacher expectancy on student IQ from \insertCite{becker94;textual}{metap}} \item{\code{validity}}{Data from studies of validity of student ratings of their instructors from \insertCite{becker94;textual}{metap} including correlations and sample sizes as well as \mjseqn{p}-values} \item{\code{zhang}}{Data from trials of exercise training for patients with cardiovascular disease from \insertCite{zhang16;textual}{metap} } } } \author{Michael Dewey} \note{The \mjseqn{p}-values in \code{cholest} have been re-calculated and are of higher accuracy than the ones given in the book.} \references{ \insertAllCited{} } \examples{ data(dat.metap) } \keyword{datasets} metap/man/invt.Rd0000644000176200001440000000320514117643051013404 0ustar liggesusers\name{invt} \alias{invt} \alias{print.invt} \title{Combine p values using inverse t method} \description{Combine p values using the inverse t method\loadmathjax} \usage{ invt(p, k, data = NULL, subset = NULL, na.action = na.fail, log.p = FALSE) \method{print}{invt}(x, ...) } \arguments{ \item{p}{\sigvec} \item{k}{A vector of degrees of freedom to use, see details} \item{data}{Optional data frame containing variables} \item{subset}{Optional vector of logicals to specify a subset of the \mjseqn{p}-values} \item{na.action}{A function indicating what should happen when data contains NAs} \item{log.p}{\logp} \item{x}{An object of class \sQuote{\code{invt}}} \item{...}{Other arguments to be passed through} } \details{ Defined as \mjdeqn{\frac{\sum_{i=1}^n t_{k_i}(p_i)}% {\sqrt{\sum_{i=1}^n \frac{k_i}{k_i - 2}}}% > z(\alpha)% }{\sum t (p) /% \sqrt{\sum k / (k - 2)}% > z(\alpha)} If \code{k} is a single value it is used for all the \code{p} of which there are \code{n}. If any value of \mjseqn{k_i\le2} then the corresponding \mjseqn{p_i} is not included. \ltle{two} \plotmethod } \value{ An object of class \sQuote{\code{invt}} and \sQuote{\code{metap}}, a list with entries \item{z}{Value of z} \item{p}{Associated p-value} \item{validp}{The input vector with the illegal values removed} } \references{ \insertRef{becker94}{metap} } \author{Michael Dewey} \seealso{ See also \code{\link{plotp}} } \examples{ data(dat.metap) beckerp <- dat.metap$beckerp invt(beckerp, 50) all.equal(exp(invt(beckerp, 50, log.p = TRUE)$p), invt(beckerp, 50)$p) } \keyword{ htest } metap/man/truncated.Rd0000644000176200001440000000540414117606320014416 0ustar liggesusers\name{truncated} \alias{truncated} \alias{print.truncated} \alias{summary.truncated} \alias{plot.truncated} \title{Truncated product method routine} \description{Implements two procedures for truncated versions of Fisher's method\loadmathjax} \usage{ truncated(p, ptrunc = NULL, rtrunc = NULL, ...) \method{print}{truncated}(x, ...) \method{summary}{truncated}(object, ...) \method{plot}{truncated}(x, pparams = list(pchs = c(16, 1), pcols = c("black", "black")), ...) } \arguments{ \item{p}{\sigvec} \item{ptrunc}{Value of \mjseqn{p} to truncate at. See Details} \item{rtrunc}{Which rank \mjseqn{p} to truncate at. See Details} \item{x}{An object of class \sQuote{\code{truncated}}} \item{object}{An object of class \sQuote{\code{truncated}}} \item{\dots}{Other arguments to be passed through} \item{pparams}{A list containing a vector \code{pchs} of plotting symbols and a vector \code{pcols} of colours} } \details{Uses routines from TFisher to implement truncated Fisher \insertCite{zaykin07,zhang18}{metap} and from mutoss to implement rank-truncated Fisher \insertCite{dudbridge03}{metap} The print method prints the statistic and its associated \mjseqn{p}-value. The summary method also prints how many of the input values were actually used. The plot method provides an index plot of the \mjseqn{p}-values. By default used \mjseqn{p}-values are plotted with a black filled circle and those not used with a black unfilled circle. The colours and plotting symbols can be changed in \code{pparams}. The first element of each vector is for the used \mjseqn{p}-values and the second for the unused ones. } \value{An object of class \sQuote{\code{truncated}} a list with entries \item{p}{The resultant overall \mjseqn{p}-value} \item{stat}{The test statistic} \item{validp}{The input vector with illegal values removed} \item{ptrunc}{The \mjseqn{p}-value used for truncation} \item{trunc}{The rank value used for truncation} \item{n}{A vector containing \code{incl}, the number of valid values included, \code{excl}, the number of valid values not used} \item{method}{The method used} } \note{ Only one of \code{ptrunc} or \code{rtrunc} is returned as appropriate. If the function encounters an error it returns NA for the value of \code{p} and gives a warning message. The effect of specifying both \code{ptrunc} and \code{rtrunc} is undefined. } \references{ \insertAllCited{} } \author{ Michael Dewey } \seealso{ \code{\link{ranktruncated}}, \code{\link{stat.tpm}}, and \code{\link{p.tpm}} } \examples{ data(dat.metap) validity <- dat.metap$validity truncated(validity, ptrunc = 0.5) truncated(validity, rtrunc = 5) } \keyword{htest1} metap/man/schweder.Rd0000644000176200001440000000706414117606232014237 0ustar liggesusers\name{schweder} \alias{schweder} \title{Schweder and Spjotvoll plot} \description{Produces the plot suggested by Schweder and Spjotvoll to display a collection of \mjseqn{p}-values and also optionally draws the lowest slope line suggested by Benjamini and Hochberg\loadmathjax } \usage{ schweder(p, xlab = "Rank of p", ylab = "p", drawline = NULL, bh.lwd = 1, bh.lty = "solid", bh.col = "black", ls.control = list(frac = NULL), ls.lwd = 1, ls.lty = "dotted", ls.col = "black", ab.control = list(a = NULL, b = NULL), ab.lwd = 1, ab.lty = "dashed", ab.col = "black", ...) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{p}{A vector of \mjseqn{p}-values} \item{xlab}{Label for plot \mjseqn{x}-axis} \item{ylab}{Label for plot \mjseqn{y}-axis} \item{drawline}{Which line, if any, to draw. See Details} \item{bh.lwd}{Width of the lowest slope line} \item{bh.lty}{Line type of the lowest slope line} \item{bh.col}{Colour of the lowest slope line} \item{ls.control}{A list containing a named element \code{frac}. See Details} \item{ls.lwd}{Width of the least squares line} \item{ls.lty}{Line type of the least squares line} \item{ls.col}{Colour of the least squares line} \item{ab.control}{A list containing two elements \code{a} and \code{b}. See Details} \item{ab.lwd}{Width of the specified line} \item{ab.lty}{Line type of the specified line} \item{ab.col}{Colour of the specified line} \item{\dots}{Further parameters to be passed through to plot} } \details{After removing invalid \mjseqn{p}-values plots them. Any graphics parameters passed in \code{...} affect this part of the plot only. Note that the axes are chosen according to the scheme of Banjamini and Hochberg, Schweder and Spjotvoll used a different system. By setting \code{drawline} appropriately up to three lines may be drawn. If \code{drawline} includes the string \code{"bh"} the lowest slope line of Benjaimin and Hochberg is drawn. No further parameters are needed here but the characteristics of the line may be set: width, line type, and colour. If \code{drawline} includes the string \code{"ls"} a least squares line is drawn passing through the point \mjseqn{k+1, 1}. The parameter \code{frac} specified what fraction of the values be used for this and may need experimentation to obtain a suitable line. The characteristics of the line may be set: width, line type, and colour. If \code{drawline} includes the string \code{"ab"} a user specified line is drawn. The parameters \code{a} and \code{b} specify the intercept and slope. The characteristics of the line may be set: width, line type, and colour. } \value{ A list containing \item{p}{The values of \mjseqn{p} plotted} \item{bh.params}{A list containing at least items \code{a} and \code{b} the intercept and slope of the line drawn. This is only included if the lowest slope line was drawn} \item{ls.params}{A list containing at least items \code{a} and \code{b} the intercept and slope of the line drawn. This is only included if the least squares line was drawn} \item{ab.params}{A list containing at least items \code{a} and \code{b} the intercept and slope of the line drawn. This is only included if the user specified line was drawn} } \references{ \insertRef{becker94}{metap} \insertRef{benjamini00}{metap} \insertRef{schweder82}{metap} } \author{Michael Dewey} \examples{ data(dat.metap) teachexpect <- dat.metap$teachexpect schweder(teachexpect) } \keyword{ hplot } metap/man/allmetap.Rd0000644000176200001440000000277314142752336014241 0ustar liggesusers\name{allmetap} \alias{allmetap} \alias{print.allmetap} \title{Carry out all or some of the methods in the package} \description{Enables all or a selected number of the package methods to be executed on the same dataset\loadmathjax} \usage{ allmetap(p, method = NULL, log.p = FALSE) \method{print}{allmetap}(x, digits = 5, ...) } \arguments{ \item{p}{A vector of \mjseqn{p}-values} \item{method}{A vector of character containing names of methods or \sQuote{\code{all}}} \item{log.p}{Logical, are the \mjseqn{p}-values passed as logs?} \item{x}{An object of class \sQuote{\code{allmetap}}} \item{digits}{How many digits to print?} \item{...}{Other arguments to be passed through} } \details{The function uses each of the methods specified on the data-set in \code{p}. If method contains \sQuote{\code{all}} then this over--rides any specific method(s) named. } \value{Returns an object of class \sQuote{\code{allmetap}} and \sQuote{\code{data.frame}} containing columns \item{p}{The value of p returned} \item{valid}{The number of valid p values used for that method} \item{eponym}{The eponym, if any, for the method} The row names are the names of the methods used. If any of the methods cannot be applied to that data--set NA are returned for \code{p} and \code{valid}. } \author{Michael Dewey} \examples{ data(dat.metap) beckerp <- dat.metap$beckerp allmetap(beckerp, method = "all") allmetap(beckerp, method = c("sumz", "sumlog")) } \keyword{htest} metap/man/meanz.Rd0000644000176200001440000000341214117614262013540 0ustar liggesusers\name{meanz} \alias{meanz} \alias{print.meanz} \title{Combine p values using mean z method} \description{Combines p values using the mean of z method\loadmathjax} \usage{ meanz(p, log.p = FALSE) \method{print}{meanz}(x, ...) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{p}{\sigvec} \item{log.p}{\logp} \item{x}{An object of class \sQuote{\code{meanz}}} \item{...}{Other arguments to be passed through} } \details{ Let \mjdeqn{\bar{z} = \sum_{i=1}^k \frac{z(p_i)}{k}}{bar{z} = sum(z(p) / k)} and \mjdeqn{s_{\bar{z}} = \frac{s_z}{\sqrt{k}}}{s_{bar{z}} = s_z / sqrt k } Defined as \mjdeqn{% \frac{\bar{z}}{s_{\bar{z}}} > t_{k-1}(\alpha) }{((bar{z} / s_bar{z}) > t_{k-1}(alpha)} \lele{two} As can be seen if all the \mjseqn{p_i} are equal or close to equal this gives a \mjeqn{t=\pm\infty}{t=+-infty} leading to a returned value of 0 or 1. A set of \mjseqn{p} values with small variance will necessarily give a small \mjseqn{p} value which may be smaller than that for another set all of whose primary values are less than any in the first set. See examples for a demonstration. \plotmethod } \value{An object of class \sQuote{\code{meanz}} and \sQuote{\code{metap}}, a list with entries \item{z}{The value of the mean \mjseqn{z} statistic} \item{p}{The associated \mjseqn{p} value} \item{validp}{The input vector with illegal values removed} } \references{ \insertRef{becker94}{metap} } \author{Michael Dewey} \seealso{ See also \code{\link{plotp}} } \examples{ data(dat.metap) beckerp <- dat.metap$beckerp meanz(beckerp) meanz(c(0.1, 0.2)) # greater than next example meanz(c(0.3, 0.31)) # less than above all.equal(exp(meanz(beckerp, log.p = TRUE)$p), meanz(beckerp)$p) } \keyword{ htest } metap/man/sumz.Rd0000644000176200001440000000501414136254460013425 0ustar liggesusers\name{sumz} \alias{sumz} \alias{Stouffer's method} \alias{Sum of normals method} \alias{print.sumz} \title{Combine p-values using the sum of z (Stouffer's) method} \description{Combine \mjseqn{p}-values using the sum z method\loadmathjax} \usage{ sumz(p, weights = NULL, data = NULL, subset = NULL, na.action = na.fail, log.p = FALSE, log.input = FALSE) \method{print}{sumz}(x, ...) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{p}{\sigvec} \item{weights}{A vector of weights} \item{data}{Optional data frame containing variables} \item{subset}{Optional vector of logicals to specify a subset of the \mjseqn{p}-values} \item{na.action}{A function indicating what should happen when data contains NAs} \item{log.p}{\logp} \item{log.input}{\loginput} \item{x}{An object of class \sQuote{\code{sumz}}} \item{...}{Other arguments to be passed through} } \details{ Defined as \mjdeqn{\frac{\sum_{i=1}^k w_i z(p_i)}{\sqrt {\sum_{i=1}^k w_i ^ 2}}}{sum (w * z(p)) / sqrt(sum (w * w))} is a \mjseqn{z} where \mjseqn{k} is the number of studies and \mjseqn{w} are the weights \insertCite{stouffer49}{metap}. By default the weights are equal. In the absence of effect sizes (in which case a method for combining effect sizes would be more appropriate anyway) best results are believed to be obtained with weights proportional to the square root of the sample sizes \insertCite{zaykin11}{metap} \insertNoCite{becker94}{metap} \insertNoCite{rosenthal78}{metap} \ltlt{two} If the omitted \mjseqn{p} values had supplied weights a further warning is issued. \plotmethod } \value{An object of class \sQuote{\code{sumz}} and \sQuote{\code{metap}}, a list with entries \item{z}{Transformed sum of \mjseqn{z} values} \item{p}{Associated \mjseqn{p}-value} \item{validp}{The input vector with illegal values removed} \item{weights}{The weight vector corresponding to \code{validp}} } \references{ \insertAllCited{} } \author{Michael Dewey} \seealso{ See also \code{\link{plotp}} } \examples{ data(dat.metap) teachexpect <- dat.metap$teachexpect sumz(teachexpect) # z = 2.435, p = 0.0074, from Becker beckerp <- dat.metap$beckerp sumz(beckerp) # z = 1.53, NS, from Beckerp rosenthal <- dat.metap$rosenthal sumz(rosenthal$p) # 2.39, p = 0.009 sumz(p, df, rosenthal) # 3.01, p = 0.0013 validity <- dat.metap$validity$p sumz(validity) # z = 8.191, p = 1.25 * 10^{-16} all.equal(exp(sumz(validity, log.p = TRUE)$p), sumz(validity)$p) all.equal(sumz(log(validity), log.input = TRUE)$p, sumz(validity)$p) } \keyword{ htest } metap/man/meanp.Rd0000644000176200001440000000225414117604730013530 0ustar liggesusers\name{meanp} \alias{meanp} \alias{print.meanp} %- Also NEED an '\alias' for EACH other topic documented here. \title{Combine p values by the mean p method} \description{Combine \mjseqn{p} values by the mean p method\loadmathjax} \usage{ meanp(p) \method{print}{meanp}(x, ...) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{p}{\sigvec} \item{x}{An object of class \sQuote{\code{meanp}}} \item{...}{Other arguments to be passed through} } \details{ Defined as \mjdeqn{z = (0.5 - \bar{p}) \sqrt{12k}}{z = (0.5 - mean(p)) * sqrt(12k)} which is a standard normal and due to \insertCite{edgington72b;textual}{metap} \insertNoCite{becker94}{metap}\insertNoCite{rosenthal78}{metap} \lele{four} \plotmethod } \value{ An object of class \sQuote{\code{meanp}} and \sQuote{\code{metap}}, a list with entries \item{z}{Value of \mjseqn{z}} \item{p}{Associated \mjseqn{p}-value} \item{validp}{The input vector with illegal values removed} } \references{ \insertAllCited{} } \author{Michael Dewey} \seealso{ See also \code{\link{plotp}} } \examples{ data(dat.metap) rosenthal <- dat.metap$rosenthal meanp(rosenthal$p) # 2.17, p = 0.015 one tailed } \keyword{ htest } metap/man/albatros.Rd0000644000176200001440000001207714157360013014240 0ustar liggesusers\name{albatros} \alias{albatros} \alias{docontours} %- Also NEED an '\alias' for EACH other topic documented here. \title{Albatros plot} \description{Produces the albatros plot of Harrison et al\loadmathjax} \usage{ albatros(p, n, axes = list(xlimit = NULL, ylimit = NULL, lefttext = NULL, righttext = NULL), contours = list(type = NULL, contvals = NULL, ltys = NULL, contlabs = NULL), plotpars = list(yscale = NULL, pchs = NULL, cols = NULL), ...) docontours(conttype, xvals, contvals, xtrans, ytrans, xlims, ylims, ltys, contlabs) } \arguments{ \item{p}{A vector of \mjseqn{p} values} \item{n}{A vector of sample sizes} \item{axes}{A list containing \itemize{ \item \code{xlimit} a single value, the limit for the x-axis which is used symmetrically \item \code{ylimit} a vector of length 2, limits for the y-axis \item \code{lefttext} character, to label below plot \item \code{righttext} character, to label below plot } } \item{contours}{A list containing \itemize{ \item \code{type} what effect size to use, a character one of "corr", "or", "smd" \item \code{contvals} a vector, what values to draw the contours at \item \code{ltys} a vector, what line types to use } } \item{plotpars}{A list containing \itemize{ \item \code{yscale} Scaling for y-axis, See details \item \code{pchs} Symbols to be used \item \code{cols} Colours for points } } \item{\dots}{Arguments to be passed through to \code{plot}} \item{conttype}{Character: one of "smd", "or", "corr"} \item{xvals}{A vector of values to evaluate the contour} \item{contvals}{The values at which contours are drawn} \item{xtrans}{A function for transforming the x-axis} \item{ytrans}{A function for transforming the y-axis} \item{xlims}{The limits for the x-axis in plotting units} \item{ylims}{The limits for the y-axis in plottng units} \item{ltys}{A vector of line types for the contours} \item{contlabs}{Logical, draw the labels of the contours?} } \details{Plots \mjseqn{n} against \mjseqn{p} and draws contours of constant effect size. \insertNoCite{harrison17}{metap} The \mjseqn{p} value scale on the x-axis is a logarithmic one but folded at the null value so that the extreme values represent small probabilities in each direction. The scale for the y-axis is user selectable. The original scale in the Stata version is \mjeqn{(\log_{10}n)^2}{log(n, base = 10) ^ 2} which is obtained by setting \code{yscale} to "classic" but it is also possible to use \mjeqn{\sqrt{n}}{sqrt(n)} which is the default or \mjseqn{n} by setting \code{yscale} to "n". If the dataset contains extreme values the plot may be uninformative and the \code{xlimit} and \code{ylimit} parameters my be helpful to clip the plot. If they are not specified the function tries to choose suitable values. For the contours if the \code{type} parameter in \code{contours} is NULL (the default) no contours will be plotted. The options available are \dQuote{smr} (Standardised mean difference) \dQuote{corr} (Correlation) \dQuote{or} (Odds ratio). The contours are labelled unless contlabs is set to \code{FALSE}. The function tries to position these so they are not obscured by the contour lines but if that is unsatisfactory then it is best to suppress them and position them manually or use a legend to identify line types. The \code{pch} parameter may either be a single value or a vector of the same length as \code{p}. It may contain anything which is legal as input to the parameter of the same name in the graphics library and will be used for the plotted points. The \code{cols} parameter works similarly. The values of \code{lefttext} and \code{righttext} are used to produce labels under the \mjseqn{x}-axis and are placed level with the label. By default they are not produced. The return values from the function may be useful if further annotations are required as they give the axis limits in plotting units. } \value{Returns A list containing \item{xlims}{The limits for the x-axis in plotting units} \item{ylims}{The limits for the y-axis in plotting units} } \references{ \insertAllCited{} } \author{Michael Dewey} \note{The docontours function is for internal use only} %% ~Make other sections like Warning with \section{Warning }{....} ~ \seealso{For plotting parameters see \code{\link{par}} } \examples{ data(dat.metap) validity <- dat.metap$validity fit.v <- albatros(validity$p, validity$n, contours = list(type = "corr", contvals = c(0.25, 0.5, 0.8), ltys = 1:3), axes = list(ylimit = c(1,200), lefttext = "Negative correlation", righttext = "Positive correlation"), main = "Validity") # fit.z <- albatros(dat.metap$zhang$p, dat.metap$zhang$n, contours = list(type = "smd", contvals = c(0.25, 0.5, 1), ltys = 1:3), plotpars = list(pchs = letters[unclass(dat.metap$zhang$phase)]), axes = list(lefttext = "Favours control", righttext = "Favours exercise"), main = "Zhang" ) } \keyword{hplot} metap/man/votep.Rd0000644000176200001440000000271114117606776013577 0ustar liggesusers\name{votep} \alias{votep} \alias{print.votep} \title{Combine p-values by the vote counting method} \description{ Combine \mjseqn{p}-values by the vote counting method\loadmathjax } \usage{ votep(p, alpha = 0.5) \method{print}{votep}(x, ...) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{p}{\sigvec} \item{alpha}{A value defining the significance value limits, see Details} \item{x}{An object of class \sQuote{\code{votep}}} \item{...}{Other arguments to be passed through} } \details{By default splits the \mjseqn{p}-values at 0.5 with those below counting as positive and those above counting as negative. However setting alpha allows specifying a neutral zone. In that case values between alpha and 1 - alpha will be assumed to be neutral and only those outside the zone counted as positive or negative. If the value of alpha is greater than unity it is assumed to be a percentage. \ltlt{two} \plotmethod } \value{An object of class \sQuote{\code{votep}} and \sQuote{\code{votep}}, a list with entries \item{p}{\mjseqn{p} value} \item{pos}{Number of positives} \item{neg}{Number of negatives} \item{alpha}{The cut--off significance value lying in the range 0 to 1} \item{validp}{The input vector with illegal values removed} } \references{ \insertRef{becker94}{metap} } \author{Michael Dewey} \seealso{ See also \code{\link{plotp}} } \examples{ data(dat.metap) beckerp <- dat.metap$beckerp votep(beckerp) } \keyword{ htest } metap/man/two2one.Rd0000644000176200001440000000255414117607465014040 0ustar liggesusers\name{two2one} \alias{two2one} %- Also NEED an '\alias' for EACH other topic documented here. \title{Convert two-sided p-values to one-sided} \description{Convert two-sided p-values to one-sided\loadmathjax} \usage{ two2one(p, two = NULL, invert = NULL) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{p}{A vector of p-values} \item{two}{A logical vector defining which \mjseqn{p}-values are two-sided and to be converted} \item{invert}{A logical vector defining which \mjseqn{p}-values are to be inverted} } \details{The \mjseqn{p}-values supplied to the other functions should be one-sided and all in the same direction. This convenience function will convert two-sided to one-sided and invert as necessary. By default it is assumed that all \mjseqn{p}-values are two-sided and the function converts them all to one-sided. Use \code{invert} to specify if some of the tests resulted in outcomes in the other direction. So for example a value of 0.05 will be converted to 0.025 unless \code{invert} is TRUE in which case it is converted to 0.975.} \value{A vector of one-sided \mjseqn{p}-values all in the correct direction } \author{Michael Dewey} \examples{ data(dat.metap) rosenthal <- dat.metap$rosenthal twop <- with(rosenthal, (pt(t, df))) two2one(twop, two = rep(FALSE, 5), invert = rep(TRUE, 5)) # restore to one-sided } \keyword{ manip } metap/man/macros/0000755000176200001440000000000013472726173013433 5ustar liggesusersmetap/man/macros/macros.Rd0000644000176200001440000000253014131333014015163 0ustar liggesusers\newcommand{\nocancel}{Inspection of the distribution of \mjseqn{p}-values is highly recommended as extreme values in opposite directions do not cancel out. See last example. This may not be what you want.} \newcommand{\plotmethod}{The plot method for class \sQuote{\code{metap}} calls \code{\link{plotp}} on the valid \eqn{p}-values.} \newcommand{\sigvec}{A vector of significance values} \newcommand{\ltle}{The values of \mjseqn{p_i} should be such that \mjseqn{0 < p_i\le 1} and a warning is given if that is not true. A warning is given if, possibly as a result of removing illegal values, fewer than #1 values remain and the return values are set to NA.} \newcommand{\ltlt}{The values of \mjseqn{p_i} should be such that \mjseqn{0 < p_i < 1} and a warning is given if that is not true. A warning is given if, possibly as a result of removing illegal values, fewer than #1 values remain and the return values are set to NA.} \newcommand{\lele}{The values of \mjseqn{p_i} should be such that \mjseqn{0\le p_i\le 1} and a warning is given if that is not true. A warning is given if, possibly as a result of removing illegal values, fewer than #1 values remain and the return values are set to NA.} \newcommand{\logp}{Logical, if TRUE result is returned as log(p)} \newcommand{\loginput}{Logical, if TRUE the input \mjseqn{p} values are assumed to be logged} metap/man/wilkinsonp.Rd0000644000176200001440000000616714136254503014634 0ustar liggesusers\name{wilkinsonp} \alias{wilkinsonp} \alias{maximump} \alias{minimump} \alias{Tippett's method} \alias{print.wilkinsonp} \alias{print.maximump} \alias{print.minimump} \title{Combine p-values using Wilkinson's method} \description{Combine \mjseqn{p}-values using Wilkinson's method\loadmathjax} \usage{ wilkinsonp(p, r = 1, alpha = 0.05, log.p = FALSE) maximump(p, alpha = 0.05, log.p = FALSE) minimump(p, alpha = 0.05, log.p = FALSE) \method{print}{wilkinsonp}(x, ...) \method{print}{maximump}(x, ...) \method{print}{minimump}(x, ...) } \arguments{ \item{p}{\sigvec} \item{r}{Use the \mjseqn{r}th smallest \mjseqn{p} value} \item{alpha}{The significance level} \item{log.p}{\logp} \item{x}{An object of class \sQuote{\code{wilkinsonp}} or of class \sQuote{\code{maximump}} or of class \sQuote{\code{minimump}}} \item{...}{Other arguments to be passed through} } \details{ Wilkinson \insertCite{wilkinson51}{metap} originally proposed his method in the context of simultaneous statistical inference: the probability of obtaining \mjseqn{r} or more significant statistics by chance in a group of \mjseqn{k}. The values are obtained from the Beta distribution, see \code{\link{pbeta}}. If \code{alpha} is greater than unity it is assumed to be a percentage. Either values greater than 0.5 (assumed to be confidence coefficient) or less than 0.5 are accepted. \lele{two} \code{maximump} and \code{minimump} each provide a wrapper for \code{wilkinsonp} for the special case when \mjeqn{r = \mathrm{length}(p)}{r = length(p)} or \mjseqn{r=1} respectively and each has its own print method. The method of minimum \mjseqn{p} is also known as Tippett's method \insertCite{tippett31}{metap}. \insertNoCite{becker94}{metap}\insertNoCite{birnbaum54}{metap} \plotmethod \nocancel } \value{An object of class \sQuote{\code{wilkinsonp}} and \sQuote{\code{metap}} or of class \sQuote{\code{maximump}} and \sQuote{\code{metap}} or of class \sQuote{\code{minimump}} and \sQuote{\code{metap}}, a list with entries \item{p}{The \mjseqn{p}-value resulting from the meta--analysis} \item{pr}{The \mjseqn{r}th smallest \mjseqn{p} value used} \item{r}{The value of \mjseqn{r}} \item{critp}{The critical value at which the \mjseqn{r}th value would have been significant for the chosen \code{alpha}} \item{validp}{The input vector with illegal values removed} %% ... } \references{ \insertAllCited{} } \note{The value of \code{critp} is always on the raw scale even if \code{log.p} has been set to TRUE} \author{Michael Dewey} \seealso{ See also \code{\link{plotp}} } \examples{ data(dat.metap) beckerp <- dat.metap$beckerp minimump(beckerp) # signif = FALSE, critp = 0.0102, minp = 0.016 teachexpect <- dat.metap$teachexpect minimump(teachexpect) # crit 0.0207, note Becker says minp = 0.0011 wilkinsonp(c(0.223, 0.223), r = 2) # Birnbaum, just signif validity <- dat.metap$validity$p minimump(validity) # minp = 0.00001, critp = 1.99 * 10^{-4} minimump(c(0.0001, 0.0001, 0.9999, 0.9999)) # is significant all.equal(exp(minimump(validity, log.p = TRUE)$p), minimump(validity)$p) all.equal(exp(maximump(validity, log.p = TRUE)$p), maximump(validity)$p) } \keyword{ htest } metap/man/sump.Rd0000644000176200001440000000343314117607162013416 0ustar liggesusers\name{sump} \alias{sump} \alias{Edgington's method} \alias{print.sump} \title{Combine p-values using the sum of p (Edgington's) method} \description{Combine \mjseqn{p}-values using the sum p method\loadmathjax} \usage{ sump(p) \method{print}{sump}(x, ...) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{p}{\sigvec} \item{x}{An object of class \sQuote{\code{sump}}} \item{...}{Other arguments to be passed through} } \details{ Defined as \mjdeqn{\frac{(\sum_{i=1}^k p_i)^k}{k!} - {k \choose 1}\frac{(\sum_{i=1}^k p_i - 1)^k}{k!} + {k \choose 2}\frac{(\sum_{i=1}^k p_i - 2)^k}{k!} ...}{% ((sum p) ^ k) / k! - (k-1)C(1) ((sum p - 1) ^ k) / k! + (k-2)C(2) ((sum p - 2) ^ k) / k! ...} where there are \mjseqn{k} studies and the series continues until the numerator becomes negative \insertCite{edgington72a}{metap}. Some authors use a simpler version \mjdeqn{\frac{(\sum_{i=1}^k p_i)^k}{k!}}{((sum p) ^ k) / k!} but this can be very conservative when \mjeqn{\sum_{i=1}^k p_i > 1}{sum p > 1}. There seems no particular need to use this method but it is returned as the value of \code{conservativep} for use in checking published values. \lele{two} A warning is given when the internal calculations are likely to have been subject to numerical error and an alternative method should be used to check the result. \plotmethod } \value{An object of class \sQuote{\code{sump}} and \sQuote{\code{metap}}, a list with entries \item{p}{The transformed sum of the \mjseqn{p}-values} \item{conservativep}{See details} \item{validp}{The input vector with illegal values removed} } \references{ \insertAllCited{} } \author{Michael Dewey} \seealso{ See also \code{\link{plotp}} } \examples{ data(dat.metap) edgington <- dat.metap$edgington sump(edgington) # p = 0.097 } \keyword{ htest } metap/man/metap-package.Rd0000644000176200001440000000214614147733606015137 0ustar liggesusers\name{metap-package} \alias{metap-package} \alias{metap} \docType{package} \title{\packageTitle{metap}} \description{\packageDescription{metap}} \details{ \packageIndices{metap} Provides a number of ways in which significance levels may be combined in a meta-analysis and includes most ot the methods in \insertCite{becker94;textual}{metap}. It includes a number of datasets taken from the literature. It also provides a display and an informal graphical test due to Schweder and Spjotvoll \insertCite{schweder82}{metap} and the lowest slope line of Benjamini and Hochberg \insertCite{benjamini00}{metap}. The albatros plot of Harrison et al \insertCite{harrison17}{metap} is also provided. Some further documentation and, possibly, a development version may be seen at \url{http://www.dewey.myzen.co.uk/meta/meta.html} } %\author{\packageAuthor{metap}} %\packageMaintainer{metap} \references{ \insertAllCited{} } \keyword{ package } \seealso{ The issue of meta-analysis of signficance levels is not completely unconnected with the topic of adjustment for multiple comparisons as in for example \code{\link{p.adjust}} } metap/man/logitp.Rd0000644000176200001440000000307614136254406013733 0ustar liggesusers\name{logitp} \alias{logitp} \alias{print.logitp} %- Also NEED an '\alias' for EACH other topic documented here. \title{Combine p values using logit method} \description{ Combine \mjseqn{p} values using logit method\loadmathjax } \usage{ logitp(p, log.p = FALSE) \method{print}{logitp}(x, ...) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{p}{\sigvec} \item{log.p}{\logp} \item{x}{An object of class \sQuote{\code{logitp}}} \item{...}{Other arguments to be passed through} } \details{ Defined as \mjdeqn{t = - \frac{\sum_{i=1}^k \log\frac{p_i}{1 - p_i}}{C}}{% t = - sum log(p / (1 - p)) / C} where \mjdeqn{C = \sqrt\frac{k \pi^2 (5 k + 2)}{3(5 k + 4)}}{C = sqrt((k pi^2 (5 k + 2)) / (3(5 k + 4)))} and \mjseqn{k} is the number of studies. \ltlt{two} \plotmethod } \value{ An object of class \sQuote{\code{logitp}} and \sQuote{\code{metap}}, a list with entries \item{t}{Value of Student's \mjseqn{t}} \item{df}{Associated degrees of freedom} \item{p}{Associated \mjseqn{p}-value} \item{validp}{The input vector with illegal values removed} } \references{ \insertRef{becker94}{metap} } \author{Michael Dewey} \seealso{ See also \code{\link{plotp}} } \examples{ data(dat.metap) teachexpect <- dat.metap$teachexpect logitp(teachexpect) # t = 2.763, df = 99, p = 0.0034, from Becker beckerp <- dat.metap$beckerp logitp(beckerp) # t = 1.62, df = 29, NS, from Becker validity <- dat.metap$validity$p logitp(validity) # t = 9.521, df = 104, p = 3.89 * 10^{-16} all.equal(exp(logitp(validity, log.p = TRUE)$p), logitp(validity)$p) } \keyword{ htest } metap/man/invchisq.Rd0000644000176200001440000000406414117642274014262 0ustar liggesusers\name{invchisq} \alias{invchisq} \alias{Lancaster's method} \alias{print.invchisq} \title{Combine p values using inverse chi squared method} \description{Combine \mjseqn{p}-values by the inverse chi-squared method, also known as Lancaster's method\loadmathjax } \usage{ invchisq(p, k, data = NULL, subset = NULL, na.action = na.fail, log.p = FALSE) \method{print}{invchisq}(x, ...) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{p}{\sigvec} \item{k}{A vector of degrees of freedom to use, see details} \item{data}{Optional data frame containing variables} \item{subset}{Optional vector of logicals to specify a subset of the \mjseqn{p}-values} \item{na.action}{A function indicating what should happen when data contains NAs} \item{log.p}{\logp} \item{x}{An object of class \sQuote{\code{invchisq}}} \item{...}{Other arguments to be passed through} } \details{ Defined as \mjdeqn{\sum_{i=1}^n \chi^2_{k_i}(p_i) > \chi^2_{\sum{k_i}}(\alpha)}{\sum \chi^2_k(p) > \chi^2_\sum{k}(\alpha)} If \code{k} is a single value it is used for all the \code{p} of which there are \code{n}. If any value of \mjseqn{k_i\le0} then the corresponding \mjseqn{p_i} is not included. \ltle{two} \plotmethod \nocancel } \value{ An object of class \sQuote{\code{invchisq}} and \sQuote{\code{metap}}, a list with entries \item{chisq}{Value of chi-squared statistic} \item{df}{Associated degrees of freedom} \item{p}{Associated p-value} \item{validp}{The input vector with the illegal values removed} } \references{ \insertRef{becker94}{metap} \insertRef{lancaster49}{metap} } \author{ Michael Dewey } \seealso{ See also \code{\link{sumlog}} and \code{\link{plotp}} } \examples{ data(dat.metap) beckerp <- dat.metap$beckerp invchisq(beckerp, 2) # same as sumlog invchisq(c(0.999, 0.999, 0.001, 0.001), 4) all.equal(exp(invchisq(beckerp, 2, log.p = TRUE)$p), invchisq(beckerp, 2)$p) } % Add one or more standard keywords, see file 'KEYWORDS' in the % R documentation directory. \keyword{ htest } metap/man/plotp.Rd0000644000176200001440000000271114210141406013552 0ustar liggesusers\name{plotp} \alias{plotp} \title{Q-Q plot of p-values} \description{ Produces a Q--Q plot of the p-values supplied\loadmathjax } \usage{ plotp(pvals, plotversion = "qqconf", ...) } \arguments{ \item{pvals}{A vector of \mjseqn{p}--values} \item{plotversion}{Whether to use the qqconf version or the original} \item{\dots}{Other parameters to pass through to \code{qqplot} and \code{qqline} } } \details{After eliminating out of range \mjseqn{p}--values and missing values produces a Q--Q plot. If the package \code{qqconf} is unavailable or \code{plotversion} is set other than "qqconf" then the plot uses the function from base graphics. The line shown is through the quantiles (by default the 0.25 and 0.75). If the package \code{qqconf} is available then the plot uses that package's function and as well as the Q--Q plot produces a confidence region. Parameters can be passed to \code{qq_conf_plot} to exert further control over the plot. If \code{plotversion} is set to "qqconf" but package \code{qqconf} is not available then a warning is given and no plot is produced. } \value{ Invisibly returns a list consisting of \item{validp}{The valid \mjseqn{p}--values} } \author{Michael Dewey} \seealso{ \code{\link{qqplot}} and \code{\link{qqline}} for the original plot and \code{\link{qq_conf_plot}} for the new version. } \examples{ data(dat.metap) cholest <- dat.metap$cholest$p plotp(cholest) } \keyword{hplot} metap/DESCRIPTION0000644000176200001440000000204214511006022013053 0ustar liggesusersPackage: metap Type: Package Title: Meta-Analysis of Significance Values Version: 1.9 Date: 2023-10-05 Authors@R: person("Michael", "Dewey", role = c("aut", "cre"), email = "lists@dewey.myzen.co.uk", comment = c(ORCID = "0000-0002-7522-3677") ) Description: The canonical way to perform meta-analysis involves using effect sizes. When they are not available this package provides a number of methods for meta-analysis of significance values including the methods of Edgington, Fisher, Lancaster, Stouffer, Tippett, and Wilkinson; a number of data-sets to replicate published results; and routines for graphical display. 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ݝXE4t 1z  =ߪ8dep7>/~A^p/ ]C~K6^V y^V$./+Wҽlܕe͵aL^D~32qwՔw*RUzw?.zf7P/kB׈UwO`$dtyy&Cm0-3%t PLw6Q m;F#rPw_Ib.?4[{[CXQ}0;֐|5l_J1 Mnz#O@2j.dsP)٠c e}X :YJNX#Y,K }ӳ:yM-zTȟMko `bv3g&'8VȵfTDG1⨶Czn0IlZ bpjkGqh7Ν߰m)P /a=pȼ!ǖWH+zz3࢖JEkm$߾]Aǥ?j)u۽i(>7i|mnÅMzZ͍v|M֪vY &_ޯLqЯ]$Ù;uѾ8W8qVne:>M/ zP_=T,4C1I2}GT?Z{1o/Q/i,OWF4-D@%Ğ5CH/#YQ ُٝF:lde݀GlUS[xD9q3dP)p`9tU;t{-MucK@JH"/K=F.SF9!}W:3S0i4T^h䑺sB{U=6̠s3$/,C1 ;7)hT_.[^ % e*µ,hE.zz</^H_zyh|%Ћ_L@IROmU5 i}?H0T|D asvx~Ly_Sj*+Nܰ~} .wlŵ]1B\R.>>qÏ]A\Y2 d|{ZA\(,s~&w9^#vp{{X >򺅏Zu`zzZ]\kcT[ mk}T.OQi_=d K9lX"#4mՋ@@QVӫ Dy4>4YF'V[jFn_??rO(7b[EU,MكLe3|O]/T mBw"j#.]QeWJ/^ѻ7+^|WN{gǗ WIJPtwvߤ@0zjMn*)X Hwsk4A0iƻJMi9 uU1۝`+=Zo:vF/:VӨ(Zmv3MCe}G;̏uUqAZq metap/vignettes/0000755000176200001440000000000014510765336013402 5ustar liggesusersmetap/vignettes/compare.Rnw0000644000176200001440000005756614136254755015545 0ustar liggesusers\documentclass[12pt]{article} \usepackage{amsmath,amssymb} %\usepackage{mydef2} \usepackage[round]{natbib} \usepackage{parskip,url} \usepackage{graphicx,subfig} \setlength{\topmargin}{0cm} \addtolength{\textheight}{2cm} %\lhead{} %\input{title} %\VignetteIndexEntry{Comparison of methods in the metap package} \title{Comparison of methods in the \pkg{metap} package} \author{Michael Dewey} \newcommand{\pkg}[1]{\texttt{#1}} \newcommand{\func}[1]{\texttt{#1}} \newcommand{\code}[1]{\texttt{#1}} \newcommand{\codefont}{\footnotesize} \newcommand{\mygraph}[3]{% \begin{figure}[htbp] \includegraphics[height=6cm,width=10cm]{compare-#1} \caption{#2} \label{#3} \end{figure} } % in mypdf fourth parameter needs [] \newcommand{\mypdf}[4]{% \begin{figure}[htbp] \includegraphics#4{#1.pdf} \caption{#2} \label{#3} \end{figure} } \newcommand{\twograph}[8]{% \begin{figure}[htbp] \subfloat[#2\label{#3}]{\includegraphics[height=6cm,width=7cm]{compare-#1}}% \subfloat[#5\label{#6}]{\includegraphics[height=6cm,width=7cm]{compare-#4}} \caption{#7} \label{#8} \end{figure} } \begin{document} \maketitle \section{Introduction} \subsection{What is this document for?} This document describes some methods for the meta--analysis of $p$--values (significance values) contained in the package \pkg{metap} and contains comments on the performance of the various algorithms under a small number of different scenarios with hints on the choice of method. \subsection{Notation} The $k$ studies give rise to $p$--values, $p_i,\;i = 1, \dots, k$. These are assumed to be independent. We shall also need the ordered $p$--values: $p_{[1]} \le p_{[2]}, \dots, \le p_{[k]}$ and weights $w_i,\;i = 1, \dots, k$. Logarithms are natural. A function for combining $p$--values is denoted $g$. The size of the test is $\alpha$. We may also need $k$ degrees of freedom, $\nu_i$. The methods are referred to by the name of the function in \func{metap}. Table \ref{funcs} shows other descriptions of each method. \begin{table}[htbp] \begin{tabular}{lll} Function name & \multicolumn{2}{c}{Description(s)} \\[1ex] & \multicolumn{1}{c}{Eponym} \\ \func{invchisq} & Lancaster's method & Inverse chi square \\ \func{invt} & & Inverse t \\ \func{logitp} & & Logistic\\ \func{meanp} \\ \func{meanz} \\ \func{maximump} \\ \func{minimump} & Tippett's method \\ \func{sumlog} & Fisher's method & Chi square (2 df)\\ \func{sump} & Edgington's method & Uniform\\ \func{sumz} & Stouffer's method & Normal\\ \func{truncated} & Truncated Fisher\\ \func{truncated} & & rank--truncated\\ \func{votep} \\ \func{wilkinsonp} & Wilkinson's method \\ \end{tabular} \caption{Methods considered in this document} \label{funcs} \end{table} \section{Theoretical results} There have been various attempts to clarify the problem and to discuss optimality of the methods. A detailed account was provided by \citet{liptak58}. \citet{birnbaum54} considered the property of admissibility. A method is admissible if when it rejects $H_0$ for a set of $p_i$ it will also reject $H_0$ for $P^*_i$ where $p^*_i \le p_i$ for all $i$. He considered that Fisher's and Tippett's method were admissible. See also \citet{owen09}. He also points out the problem is poorly specified. This may account for the number of methods available and their differing behaviour. The null hypothesis $H_0$ is well defined, that all $p_i$ have a uniform distribution on the unit interval. There are two classes of alternative hypothesis \begin{itemize} \item $H_A$: all $p_i$ have the same (unknown) non--uniform, non--increasing density, \item $H_B$: at least one $p_i$ has an (unknown) non--uniform, non--increasing density. \end{itemize} If all the tests being combined come from what are basically replicates then $H_A$ is appropriate whereas if they are of different kinds of test or different conditions then $H_B$ is appropriate. Note that Birnbaum specifically considers the possibility that the tests being combined may be very different for instance some tests of means, some of variances, and so on. \section{The methods} \subsection{Comparison scenarios} To provide a standard of comparison we shall use the following two situations. Some authors have also used the case of exactly two $p_i$. \begin{description} %\subsubsection{What if all $p_i = p$?\label{twopisection}} \item[What if all $p_i = p$?]\label{twopisection} Perhaps surprisingly there are substantial differences here as we shall see when we look at each method. We shall describe how the returned value varies with $p$ and $k$. %\subsubsection{Cancellation} \item[Cancellation] When the collection of primary studies contains a number of values significant in both directions the methods can give very different results. If the intention of the synthesis is to examine a directional hypothesis one would want a method where these cancelled out. The decision between methods should be made on theoretical grounds of course. We shall use the following four values as our example. \end{description} {\codefont <<>>= cancel <- c(0.001, 0.001, 0.999, 0.999) @ } <>= library(metap) data(dat.metap) validity <- dat.metap$validity$p genvec <- function(pvals, kvals, fun, name) { ps <- length(pvals) ks <- length(kvals) temp <- matrix(-1, nrow = ps, ncol = ks) for(i in 1:ps) for(j in 1:ks) { temp[i, j] <- fun(rep(pvals[i], kvals[j]))$p } temp2 <- as.vector(temp) res <- data.frame(method = rep(name, length(temp2)), p = rep(pvals, ks), k = rep(kvals, each = ps), g = temp2 ) res } @ \subsection{Methods using transformation of the $p$--values} One class of methods relies on transforming the $p$--values first. \begin{table}[htbp] \begin{tabular}{lll} Function name & Definition & Critical value \\[1ex] \func{invchisq} & $\sum_{i=1}^k \chi^2_{\nu_i}(p_i)$ & $\chi^2_{\sum{\nu_i}}(\alpha)$ \\[1ex] \func{invt} & $\frac{\sum_{i=1}^k t_{\nu_i}(p_i)}% {\sqrt{\sum_{i=1}^k \frac{\nu_i}{\nu_i - 2}}}$ & $z(\alpha)$ \\[1ex] \func{logitp} & $\frac{\sum_{i=1}^k \log\frac{p}{1 - p}}{C}$ & $t_{5k+4}$ \\ & where $C = \sqrt\frac{k \pi^2 (5 k + 2)}{3(5 k + 4)}$ & \\[1ex] \func{meanz} & $\frac{\bar{z}}{s_{\bar{z}}}$ & $t_{k-1}(\alpha)$ \\ & where $\bar{z} = \sum_{i=1}^k \frac{z(p_i)}{k}$ \\ & and $s_{\bar{z}} = \frac{s_z}{\sqrt{k}}$ & \\[1ex] \func{sumlog} & $\sum_{i=1}^{k} - 2 \log p_i$ & $\chi_{2k}(\alpha)$ \\[1ex] \func{sumz} & $\frac{\sum_{i=1}^k z(p_i)}{\sqrt{k}}$ & $z(\alpha)$\\ \end{tabular} \caption{Definitions of methods using transformation of the $p$ values} \label{transdefs} \end{table} <>= kvals <- c(4, 5, 6, 8, 10, 15, 20) pvals <- c(0.2, 0.3, 0.3679, 0.4, 0.5, 0.6) dat <- rbind( genvec(pvals, kvals, logitp, "logitp"), genvec(pvals, kvals, meanz, "meanz"), genvec(pvals, kvals, sumlog, "sumlog"), genvec(pvals, kvals, sumz, "sumz") ) @ <>= lattice::xyplot(g ~ k | method, groups = p, type = "l", data = dat, auto.key = list(space = "left", lines = TRUE, title = "p"), ylab = "g(p)" ) @ \subsubsection{The method of summation of logs, Fisher's method} See Table \ref{transdefs} for the definition. This works because $- 2 \log p_i$ is a $\chi^2_2$ and the sum of $\chi^2$ is itself a $\chi^2$ with degrees of freedom equal to the sum of the degrees of freedom of the individual $\chi^2$. Of course the sum of the log of the $p_i$ is also the log of the product of the $p_i$. Fisher's method \citep{fisher25} is provided in \func{sumlog}. <>= set.seed(18122019) temp <- matrix(runif(10000), nrow = 100) fisher <- apply(temp, 1, function(x) sumlog(x)$p) lanc4 <- apply(temp, 1, function(x) invchisq(x, 4)$p) lanc16 <- apply(temp, 1, function(x) invchisq(x, 16)$p) lanc256 <- apply(temp, 1, function(x) invchisq(x, 256)$p) banda <- function(x, y) { res <- data.frame(sum = x + y, diff = (x - y)) res } dat <- data.frame(rbind(banda(fisher, lanc4), banda(fisher, lanc16), banda(fisher, lanc256), banda(lanc4, lanc16), banda(lanc4, lanc256), banda(lanc16, lanc256) ), name = factor(c(rep("FL4", 100), rep("FL16", 100), rep("FL256", 100), rep("L4L16", 100), rep("L4L256", 100), rep("L16L256", 100)), levels = c("FL4", "FL16", "FL256", "L4L16", "L4L256", "L16L256") ) ) @ <>= lattice::xyplot(diff ~ sum | name, data = dat, panel = function(x, y, ...) { lattice::panel.xyplot(x, y, ...) lattice::panel.abline(h = mean(y), lty = 2) lattice::panel.abline(h = mean(y) + 1.96 * sd(y), lty = 3) lattice::panel.abline(h = mean(y) - 1.96 * sd(y), lty = 3) } ) @ <>= stouff <- apply(temp, 1, function(x) sumz(x)$p) invt4 <- apply(temp, 1, function(x) invt(x, 4)$p) invt16 <- apply(temp, 1, function(x) invt(x, 16)$p) invt256 <- apply(temp, 1, function(x) invt(x, 256)$p) banda <- function(x, y) { res <- data.frame(sum = x + y, diff = (x - y)) res } dat <- data.frame(rbind(banda(stouff, invt4), banda(stouff, invt16), banda(stouff, invt256), banda(invt4, invt16), banda(invt4, invt256), banda(invt16, invt256) ), name = factor(c(rep("St4", 100), rep("St16", 100), rep("St256", 100), rep("t4t16", 100), rep("t4t256", 100), rep("t16t256", 100)), levels = c("St4", "St16", "St256", "t4t16", "t4t256", "t16t256") ) ) @ <>= lattice::xyplot(diff ~ sum | name, data = dat, panel = function(x, y, ...) { lattice::panel.xyplot(x, y, ...) lattice::panel.abline(h = mean(y), lty = 2) lattice::panel.abline(h = mean(y) + 1.96 * sd(y), lty = 3) lattice::panel.abline(h = mean(y) - 1.96 * sd(y), lty = 3) } ) @ As can be seen in Figure \ref{equalp} when all the $p_i=p$ \func{sumlog} returns a value which decreases with $k$ when $p<0.32$, increases with $k$ when $p>0.37$, and in between increases with $k$ and then decreases. Some detailed algebra provided in a post to https://stats.stackexchange.com/questions/243003 by Christoph Hanck suggests that the breakpoint is $e^{-1} = 0.3679$. Where the $p_i$ are less than this then for a sufficiently large $k$ (several hundred) the result will be significant and not if above that. Over the range of $k$ we are plotting this bound is not yet closely approached. \mygraph{transeqp}{Behaviour of the methods using transformed $p$ values for $k$ values of $p=p_i$}{equalp} \subsubsection{Inverse $\chi^2$ Lancaster's method} It would of course be possible to generalise Fisher's method to use transformation to $\chi^2$ with any other number of degrees of freedom rather than 2. \citet{lancaster61} suggests that this is highly correlated with \func{sumlog}. Lancaster's method is provided in \func{invchisq}. In fact the resemblance to \func{sumlog} becomes less as the number of degrees of freedom increases. Figure \ref{fishlanc} shows for a small number of selected degrees of freedom how it compares to Fisher's method. \twograph{fishlanc}{Fisher's method and Lancaster's method}{fishlanc}{stouffinvt}{Stouffer's method and inverse $t$}{stouffinvt}{Sum and difference plots of Fisher v Lancaster and Stouffer v inverse $t$}{compfishstouff} \subsubsection{The method of summation of $z$ values, Stouffer's method} The method of summation of $z$ values is provided in \func{sumz} \citep{stouffer49}. See Table \ref{transdefs} for the definition. As can be seen in Figure \ref{equalp} it returns a value for our $p_i=p$ example which decreases with $k$ when $p$ below 0.5 and increases above. A weighted version of Stouffer's method is available %\begin{equation} $\frac{\sum_{i=1}^k w_i z(p_i)}{\sqrt {\sum_{i=1}^k w_i ^ 2}}$ %\end{equation} where $w_i$ are the weights. In the absence of effect sizes (in which case a method using effect sizes would be more appropriate anyway) best results are believed to be obtained with weights proportional to the square root of the sample sizes \citep{zaykin11} following \citet{liptak58}. \subsubsection{Mean of normals method} There is also a method closely related to Stouffer's using the mean of normals provided in \func{meanz} also defined in Table \ref{transdefs} which has very similar properties except that when all the $p_i$ are equal it either gives 0 or 1 as can be seen in Figure \ref{equalp}. <<>>= meanz(c(0.3, 0.31))$p meanz(c(0.1, 0.2))$p @ The method of \func{meanz} also has the unusual property that a set of $p$--values which are all less than those in another set can still give rise to a larger overall $p$. See example above. This is the only method considered here which has this property so if it is a desirable one then that is the only method to consider. \subsubsection{The inverse $t$ method} A closely related method is the inverse $t$ method. See Table \ref{transdefs} for the definition. This method is provided in \func{invt}. As is clear from the definition this method tends to Stouffer's method as $\nu_i \to \infty$. Figure \ref{stouffinvt} shows this for selected degrees of freedom. \subsubsection{The method of summation of logits} See Table \ref{transdefs} for the definition. This method is provided in \func{logitp}. The constant $C$ was arrived at by equating skewness and kurtosis with that of the $t$--distribution \citep{loughin04}. As can be seen in Figure \ref{equalp} this method returns a value for our $p_i=p$ example which decreases with $k$ when $p$ below 0.5 and increases above. \subsubsection{Examples for methods using transformations of the $p$ values} <>= log10p <- function(x) { res <- round(-log(x, base = 10), 2) res } @ \begin{table}[htbp] \begin{tabular}{lll} Function name & \multicolumn{1}{c}{validity} & \multicolumn{1}{c}{cancel} \\ & \multicolumn{1}{c}{value expressed} \\ & \multicolumn{1}{c}{as $-\log_{10}p$} \\[1ex] \func{logitp} & \Sexpr{log10p(logitp(validity)$p)} & \Sexpr{logitp(cancel)$p} \\ \func{meanz} & \Sexpr{log10p(meanz(validity)$p)} & \Sexpr{meanz(cancel)$p} \\ \func{sumlog} & \Sexpr{log10p(sumlog(validity)$p)} & \Sexpr{round(sumlog(cancel)$p, 5)} \\ \func{sumz} & \Sexpr{log10p(sumz(validity)$p)} & \Sexpr{sumz(cancel)$p}\\ \end{tabular} \caption{Examples of methods using transformation of the $p$ values} \label{transexamples} \end{table} Using the same example dataset which we have already plotted and our cancellation dataset we have the values in Table \ref{transexamples}. As can be seen all the methods cancel except for \func{sumlog}. The agreement for the validity dataset is close except for \func{meanz} whoch gives a value several orders of magnitude greater than the other three. Lancaster's method and inverse $t$ are not shown as they are both infinite families of possible methods and in any event are similar to Fisher's method and Stouffer's method respectively. \subsection{Methods using untransformed $p$--values} \begin{table}[htbp] \begin{tabular}{lll} Function name & Definition & Critical value \\[1ex] \func{meanp} & $\bar p = \frac{\sum_{i=1}^k p_i}{k}$ \\ & $z = (0.5 - \bar{p}) \sqrt{12k}$ & $z(\alpha)$ \\ \func{minimump} & $p_{[1]}$ & $1 - (1 - \alpha)^{\frac{1}{k}}$ \\ \func{maximump} & $p_{[k]}$ & $\alpha^k$ \\ \func{wilkinsonp} & $p_{[r]}$ & $\sum_{s=r}^k {k \choose s}\alpha^s (1 - \alpha)^{k-s}$\\[1ex] \func{sump} & $\frac{(S)^k}{k!}% - {k \choose 1}\frac{(S - 1)^k}{k!}% + {k \choose 2}\frac{(S - 2)^k}{k!} - \dots$ & $\alpha$ \\ & where $S = \sum_{i=1}^k p_i$ \\ \end{tabular} \caption{Definitions of methods not using transformation of the $p$ values, % the series for \func{sump} continues until the term in in the numerator $(S-i)$ becomes negative} \label{untransdefs} \end{table} <>= kvals <- c(4, 5, 6, 8, 10, 15, 20) pvals <- c(0.2, 0.3, 0.3679, 0.4, 0.5, 0.6) dat <- rbind( genvec(pvals, kvals, meanp, "meanp"), genvec(pvals, kvals, maximump, "maximump"), genvec(pvals, kvals, minimump, "minimump"), genvec(pvals, kvals, sump, "sump"), genvec(pvals, kvals, votep, "votep") ) @ <>= lattice::xyplot(g ~ k | method, groups = p, type = "l", data = dat, auto.key = list(space = "left", lines = TRUE, title = "p"), ylab = "g(p)" ) @ \mygraph{untranseqp}{Behaviour of the methods using untransformed $p$ values for $k$ values of $p=p_i$}{unequalp} \subsubsection{The method of minimum $p$, maximum $p$, and Wilkinson's method} The methods of minimum $p$ \citep{tippett31}, maximum $p$ and Wilkinson \citep{wilkinson51} are defined in Table \ref{untransdefs}. Wilkinson's method depends on which value (the $r$th) of $p_{[i]}$ is selected. % p is pbeta(p[r], r, k+1-r) % critical p is qbeta(alpha, r, k+1-r) Wilkinson's method is provided in \func{wilkinsonp} and a convenience function \func{minimump} with its own \code{print} method is provided for the minimum $p$ method ($r=1$). It is also possible to use the method for the maximum $p$ (that is $r=k$) and a convenience function \func{maximump} is provided for that purpose. As can be seen in Figure \ref{unequalp} these methods return a value for our $p_i=p$ example which always increases with $k$ which is true for \func{minimump} and which always decreases with $k$ which is true for \func{maximump} \subsubsection{The method of summation of $p$--values, Edgington's method\label{sump}} Defined in Table \ref{untransdefs} \citep{edgington72a}. This method is provided in \func{sump}. As can be seen in Figure \ref{unequalp} this method returns a value for our $p_i=p$ example which decreases with $k$ when $p$ below 0.5 and increases above. Some authors use a simpler version, $\frac{(\sum p)^k}{k!}$, for instance \citet{rosenthal78} in the text although compare his Table 4. This can be very conservative when $\sum p > 1$ There seems no particular need to use this method but it is returned by \func{sump} as the value of \code{conservativep} for use in checking published values. Note also that there can be numerical problems for extreme values of $S$ and in that case recourse might be made to \func{meanp} which has similar properties. \subsubsection{The mean $p$ method} Defined in Table \ref{untransdefs}. Although this method is attributed to Edgington \citep{edgington72b} when the phrase Edgington's method is used it refers to the method of summation of $p$--values described above in Section \ref{sump}. As can be seen in Figure \ref{unequalp} this method returns a value for our $p_i=p$ example which decreases with $k$ when $p$ below 0.5 and increases above. Not surprisingly this method gives very similar results to Edington's other method implemented in \func{sump} and since it does not have the numerical problems of that method it might perhaps be preferred. \subsubsection{Examples for methods using untransformed $p$--values} Using the same example dataset which we have already plotted and our cancellation dataset we have the values in Table \ref{untransexamples}. As can be seen \func{meanp} and \func{sump} cancel but the other two do not. Agreement here is not so good especially for the maximum p method. Wilkinson's method not shown as it depends on the value of $r$. \begin{table}[htbp] \begin{tabular}{lrl} Function name & \multicolumn{1}{c}{validity} & \multicolumn{1}{c}{cancel} \\ & \multicolumn{1}{c}{value expressed} \\ & \multicolumn{1}{c}{as $-\log_{10}p$} \\[1ex] \\[1ex] \func{minimump} & \Sexpr{log10p(minimump(validity)$p)} & \Sexpr{round(minimump(cancel)$p, 5)} \\ \func{maximump} & \Sexpr{log10p(maximump(validity)$p)} & \Sexpr{round(maximump(cancel)$p, 5)} \\ \func{meanp} & \Sexpr{log10p(meanp(validity)$p)} & \Sexpr{meanp(cancel)$p}\\ \func{sump} & \Sexpr{log10p(sump(validity)$p)} & \Sexpr{sump(cancel)$p} \\ \end{tabular} \caption{Examples for methods using the untransformed $p$ values} \label{untransexamples} \end{table} \subsection{Other methods} \subsubsection{The method of vote--counting} A simple way of looking at the problem is vote counting. Strictly speaking this is not a method which combines $p$--values in the same sense as the other methods. If most of the studies have produced results in favour of the alternative hypothesis irrespective of whether any of them is individually significant then that might be regarded as evidence for that alternative. The numbers for and against may be compared with what would be expected under the null using the binomial distribution. A variation on this would allow for a neutral zone of studies which are considered neither for nor against. For instance one might only count studies which have reached some conventional level of statistical significance in the two different directions. This method returns a value for our $p_i=p$ example which is 1 for $p$ values above 0.5 and otherwise invariant with $p$ but decreases with $k$. This method does cancel significant values in both directions. \begin{table}[htbp] \begin{tabular}{lll} Function name & validity & cancel \\[1ex] \func{votep} & \Sexpr{round(votep(validity)$p, 6)} & \Sexpr{round(votep(cancel)$p, 5)} \\ \end{tabular} \caption{Examples for vote counting} \label{votepexamples} \end{table} \subsubsection{Methods not using all $p$--values} If there is a hypothesis that the signal will be concentrated in only a few $p$--values then alternative methods are available in \func{truncated}. This is a wrapper to two packages available on CRAN: \pkg{TFisher} which provides the truncated Fisher method \citep{zaykin07,zhang18} and \pkg{mutoss} which provides the rank--truncated Fisher method \citep{dudbridge03}. Note that Table \ref{truncatedexamples} only shows results for the validity data--set as, since the methods explicitly only consider results in one direction the cancellation issue does not arise. \begin{table}[htbp] \begin{tabular}{lll} Function name & truncated at $p$ = 0.5 & truncated at rank = 5 \\[1ex] \func{truncated} & \Sexpr{log10p(truncated(validity, ptrunc = 0.5)$p)} & \Sexpr{log10p(truncated(validity, rtrunc = 5)$p)} \\ \end{tabular} \caption{Examples for truncated using the validity data--set expressed as $-\log_{10}p$} \label{truncatedexamples} \end{table} These methods are appropriate for the situation where it is known that many of the $p$--values are noise and there will only be a few signals. \section{Loughin's recommendations} In his simulation study \citet{loughin04} carried out extensive comparisons. Note that he did not consider all the methods implemented here. These omissions are not too important for our purposes. The methods implemented here as \func{invchisq}, \func{invt}, \func{meanp} and \func{meanz} are all very similar to ones which he did study. The truncation methods appeared about the same time as his work but in any case are fundamentally different. Vote counting is arguably not a method of the same sort. As Loghin points out the first thing to consider is whether large $p$--values should cancel small ones. If this is not desired then the only methods to consider are those in \func{sumlog} (Fisher), \func{minimump} (Tippett) and \func{maximump}. \mypdf{struct}{Loughin's recommendations based on structure}{struct}{[height=6cm,width=8cm]} He bases his recommendations on criteria of structure and the arrangement of evidence against $H_0$. Figure \ref{struct} shows a summary of his recommendations about the structure of the evidence. \mypdf{strength}{Loughin's recommendations based on where the strength of the evidence is located}{strength}{[height=8cm,width=12cm]} Figure \ref{strength} summarise his recommendations about the arrangement of evidence. Overall he considered the choice to lie between Stouffer's method, Fisher's method and the logistic method implemented in \func{logitp}. As has already been mentioned Fisher's method cancels whereas the other two do not so if the weak evidence in a small number of $p$--values is not to be over--whelmed by the others then Fisher is the best choice. However where the evidence is more evenly spread Stouffer's method may be preferred. The logistic method represents a compromise between them and is perhaps best suited where the pattern of evidence is not clear in advance. The other methods are not universally ruled out and may be helpful in the specific circumstance outlined in his summaries. \bibliography{metap} \bibliographystyle{plainnat} \end{document} metap/vignettes/metap.Rnw0000644000176200001440000001725114163334232015175 0ustar liggesusers\documentclass[12pt]{article} \usepackage{amsmath,amssymb} %\usepackage{mydef2} \usepackage[round]{natbib} \usepackage{parskip,url} \usepackage{graphicx,subfig} \setlength{\topmargin}{0cm} \addtolength{\textheight}{2cm} %\lhead{} %\input{title} %\VignetteIndexEntry{Introduction to the metap package} \title{Introduction to the \pkg{metap} package} \author{Michael Dewey} \newcommand{\pkg}[1]{\texttt{#1}} \newcommand{\func}[1]{\texttt{#1}} \newcommand{\code}[1]{\texttt{#1}} \newcommand{\codefont}{\footnotesize} \newcommand{\mygraph}[3]{% \begin{figure}[htbp] \includegraphics[height=6cm,width=10cm]{#1} \caption{#2} \label{#3} \end{figure} } \newcommand{\twograph}[8]{% \begin{figure}[htbp] \subfloat[#2\label{#3}]{\includegraphics[height=6cm,width=7cm]{#1}}% \subfloat[#5\label{#6}]{\includegraphics[height=6cm,width=7cm]{#4}} \caption{#7} \label{#8} \end{figure} } \begin{document} \maketitle \section{Introduction} \subsection{What is this document for?} This document describes some methods for the meta--analysis of $p$--values (significance values) and their implementation in the package \pkg{metap}. I welcome feedback about sources of published examples against which I can test the code and any other comments about either the documentation or the code. The problem of meta--analysis of $p$--values is of course not completely unconnected with the more general issue of simultaneous statistical inference. \subsection{Why and when to meta--analyse significance values} The canonical way to meta--analyse a number of primary studies uses estimates of effect sizes from each of them. There are a large number of packages for this purpose available from CRAN and described in the task view \url{http://CRAN.R-project.org/view=MetaAnalysis}. However sometimes the only available information may be $p$--values especially when some of the primary studies were published a long time ago or were published in sources which were less rigorous about insisting on effect sizes. The methods outlined here are designed for this eventuality. The situation may also arise that some of the studies can be combined in a conventional meta--analysis using effect sizes but there are many others which cannot and in that case the conventional meta--analysis of the subset of studies which do have effect sizes may usefully be supplemented by an overall analysis of the $p$--values. Just for the avoidance of doubt, if each study has produced a proportion and the goal is to synthesise them to a common estimate or analyse the differences between them then the standard methods are appropriate not the ones outlined here. The $p$--values in this document are significance levels. The methods are referred to by the name of the function in \func{metap}. Table \ref{funcs} shows other descriptions of each method. \begin{table}[htbp] \begin{tabular}{lll} Function name & \multicolumn{2}{c}{Description(s)} \\[1ex] & \multicolumn{1}{c}{Eponym} \\ \func{invchisq} & Lancaster's method & Inverse chi square \\ \func{invt} & & Inverse t \\ \func{logitp} & & Logistic\\ \func{meanp} \\ \func{meanz} \\ \func{maximump} \\ \func{minimump} & Tippett's method \\ \func{sumlog} & Fisher's method & Chi square (2 df)\\ \func{sump} & Edgington's method & Uniform\\ \func{sumz} & Stouffer's method & Normal\\ \func{truncated} & Truncated Fisher & rank--truncated\\ \func{votep} \\ \func{wilkinsonp} & Wilkinson's method \\ \end{tabular} \caption{Methods considered in this document} \label{funcs} \end{table} \section{Preparation for meta--analysis of $p$--values} \subsection{Preliminaries} I assume you have installed \textsf{R} and \pkg{metap}. You then need to load the package. <<>>= library(metap) @ \subsection{Directionality} It is usual to have a directional hypothesis, for instance that treatment is better than control. For the methods described here a necessary preliminary is to ensure that all the $p$--values refer to the same directional hypothesis. If the value from the primary study is two--sided it needs to be converted. This is not simply a matter of halving the quoted $p$--value as values in the opposite direction need to be reversed. A convenience function \func{two2one} is provided for this. {\codefont <<>>= pvals <- c(0.1, 0.1, 0.9, 0.9, 0.9, 0.9) istwo <- c(TRUE, FALSE, TRUE, FALSE, TRUE, FALSE) toinvert <- c(FALSE, TRUE, FALSE, FALSE, TRUE, TRUE) two2one(pvals, two = istwo, invert = toinvert) @ } Note in particular the way in which $0.9$ is converted under the different scenarios. \subsection{Plotting} It would be a wise precaution to examine the $p$--values graphically or otherwise before subjecting them to further analysis. A separate vignette discusses the range of plots available in the package so here we just show the most simple. As our example we use data from studies of validity of student ratings of their instructors \citep{becker94}. The \func{plotp} provides a Q--Q plot of the $p$--values to detect departure from the uniform distribution. An example is shown in Figure \ref{plotp}. The line is the line of exact fit to the reference distribution, the uniform. The polygon is a simultaneous confidence region such that if points lie outside it we can reject the null hypothesis that the points are drawn iid from a uniform. <>= data(dat.metap) validity <- dat.metap$validity$p plotp(validity) @ \mygraph{metap-plotp}{Q--Q plot from \func{plotp}}{plotp} This plot is more informative than a simple printout. Note that this enhanced plot is only available from version 1.8 of \func{metap}. Previous versions usd a simpler plot. {\codefont <<>>= print(validity) @ } \subsection{Reporting problems in the primary studies} Another issue is what to do with studies which have simply reported on whether a conventional level of significance like 0.05 was achieved or not. If the exact associated $p$ cannot be derived from the statistics quoted in the primary source then the value of the level achieved, in this case 0.05, can be used although this may be conservative. Studies which simply report not significant could be included as having $p=1$ (or $p=0.5$ if it is known that the direction was right) although this is very conservative. The theory of handling $p$--values which have been truncated like this has been developed by \citet{zaykin02} and \func{truncated} provides a convenience wrapper for two methods available in other CRAN packages. \section{Using the methods} All the methods in the package take as their first argument the vector of $p$--values. To use Fisher's method as an example: <<>>= sumlog(validity) @ This confirms what was indeed obvious from the plot that the null hypothesis that these are drawn from a uniform distribution can be rejected. A few require extra information. Those which rely on inverse transformations often need a vector of degrees of freedom. Currently this applies to \func{invchisq} and \func{invt}. Stouffer's method in \func{sumz} optionally uses weights if a vector of weights is provided. Most of the methods (\func{invchisq, invt, logitp, meanz, sumlog, sumz, wilkinsonp}) allow as an option to return the logarithm of the $p$--value which may be useful if it is expected that the return value will be very small. A smaller number (\func{invchisq, invt, sumlog}) allow for input of log $p$--values. \section{Miscellanea} \begin{description} \item[Extractor functions] The standard \code{print} and \code{plot} methods are provided. \item[Omnibus function] A function \func{allmetap} is provided to simultaneously perform a number of the other functions. It may be useful to show how they give different results on the same data. \item[Reading] An annotated bibliography is provided by \citet{cousins08} \end{description} \bibliography{metap} \bibliographystyle{plainnat} \end{document} metap/vignettes/struct.pdf0000644000176200001440000007245313576717575015451 0ustar liggesusers%PDF-1.4 % 3 0 obj << /Length 4 0 R /Filter /FlateDecode >> stream xWˊ\7+-J0! 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consideration in psychological research}, journal = {Psychological Bulletin}, year = {1951}, volume = {48}, pages = {156--158}, keywords = {meta-analysis, significance values} } @article{edgington72a, author = {Edgington, E S}, title = {An additive method for combining probability values from independent experiments}, journal = {Journal of Psychology}, year = {1972}, volume = {80}, pages = {351--363}, keywords = {meta-analysis, significance values} } @article{zaykin11, author = {Zaykin, D V}, title = {Optimally weighted $Z$--test is a powerful method for combining probabilities in meta--analysis}, journal = {Journal of Evolutionary Biology}, volume = {24}, year = {2011}, pages = {1836--1841}, keywords = {meta-analysis, significance values} } @incollection{becker94, author = {Becker, B J}, editor = {Cooper, H and Hedges, L V}, title = {Combining significance levels}, booktitle = {A handbook of research synthesis}, year = {1994}, pages = {215--235}, chapter = {15}, publisher = {Russell Sage}, address = {New York}, keywords = {meta-analysis} } @ARTICLE{schweder82, author = {Schweder, T and Spj{\o}tvoll, E}, year = 1982, title = {Plots of $P$--values to evaluate many tests simultaneously}, journal = {Biometrika}, volume = 69, pages = {493--502}, keywords = {multiple comparison} } @article{benjamini00, author = {Benjamini, Y and Hochberg, Y}, title = {On the adaptive control of the false disovery rate in multiple testing with independent statistics}, journal = {Journal of Educational and Behavioral Statistics}, year = {2000}, volume = {25}, pages = {60--83}, keywords = {multiple comparison} } @article{edgington72b, author = {Edgington, E S}, title = {A normal curve method for combining probability values from independent experiments}, journal = {Journal of Psychology}, year = {1972}, volume = {82}, pages = {85--89}, keywords = {meta-analysis, significance values} } @article{birnbaum54, author = {Birnbaum, A}, title = {Combining independent tests of significance}, journal = {Journal of the American Statistical Association}, year = {1954}, volume = {49}, pages = {559--574}, keywords = {meta-analysis, significance values} } @article{owen09, author = {Owen, A B}, title = {{Karl Pearson's} meta--analysis revisited}, journal = {Annals of Statistics}, year = {2009}, volume = {37}, pages = {3867--3892}, keywords = {meta-analysis, significance values} } @article{liptak58, author = {Lipt\'ak, T}, title = {On the combination of independent tests}, journal = {A Magyar Tudom\'anyos Akad\'emia Matematikai Kutat\'o Int\'ezet\'enek K\"ozlem\'enyi}, year = {1958}, volume = {3}, pages = {171--197}, keywords = {meta-analysis, significance values} } @misc{cousins08, author = {Cousins, R D}, title = {Annotated bibliography of some papers on combining significances or $p$--values}, year = {2008}, note = {arXiv:0705.2209}, keywords = {meta-analysis, significance values} } @article{loughin04, author = {Loughin, T M}, title = {A systematic comparison of methods for combining $p$--values from independent tests}, journal = {Computation Statistics and Data Analysis}, year = {2004}, volume = {47}, pages = {467--485}, keywords = {meta-analysis, significance values} } @article{lancaster61, author = {Lancaster, H}, title = {The combination of probabilities: an application of orthonormal functions}, journal = {Australian Journal of Statistics}, year = {1961}, volume = {3}, pages = {20--33}, keywords = {meta-analysis, significance values} } @article{zaykin02, author = {Zaykin, D V and Zhivotovsky, L A and Westfall, P H and Weir, B S}, title = {Truncated product method for combining $P$--values}, journal = {Genetic Epidemiology}, year = {2002}, volume = {22}, pages = {170--185}, keywords = {meta-analysis, significance values} } @book{fisher25, author = {Fisher, R A}, title = {Statistical methods for research workers}, year = {1925}, publisher = {Oliver and Boyd}, address = {Edinburgh}, } @book{stouffer49, author = {Stouffer, S A and Suchman, E A and DeVinney, L C and Star, S A and Williams, R M Jnr}, title = {The {American} soldier, vol 1: {A}djustment during army life}, year = {1949}, publisher = {Princeton University Press}, address = {Princeton}, } @book{tippett31, author = {Tippett, L H C}, title = {The methods of statistics}, year = {1931}, publisher = {Williams and Norgate}, address = {London}, keywords = {meta-analysis, significance values} } @article{zaykin07, author = {Zaykin, D V and Zhivotovsky, L A and Czika, W and Shao, S and Wolfinger, R D}, title = {Combining p--values in large--scale genomics experiments}, journal = {Pharmaceutical Statistics}, year = {2007}, volume = {6}, pages = {217--236} } @article{dudbridge03, author = {Dudbridge, F and Koeleman, B P C}, title = {Rank truncated product of $P$--values, with application to genomewide association scans}, journal = {Genetic Epidemiology}, year = {2003}, volume = {25}, pages = {360--366} } @article{zhang18, author = {Zhang, H and Tong, T and Landers, J and Wu, Z}, title = {{TF}isher tests: optimal and adaptive thresholding for combining $p$--values}, journal = {arXiv}, year = {2018}, url = {arXiv:1801.04309} } @article{harrison17, author = {Harrison, S and Jones, H E and Martin, R M and Lewis, S J and Higgins, J P T}, title = {The albatros plot: {A} novel graphical tool for presenting the results of diversely reported studies in a systematic review}, journal = {Research Synthesis Methods}, year = {2017}, volume = {8}, pages = {281--289} } @article{zhang16, author = {Zhang, Y--M and Lu, Y and Yang, D and Wu, H--F and Bian, Z--P and Xu, J--D and Gu, C--R and Wang, L--S and Chen, X--J}, title = {The effects of different initiation time of exercise training on left ventricular remodeling and cardiopulmonary rehabilitation in patients with left ventricular dysfunction after myocardial infarction}, journal = {Disability and Rehabilitation}, year = {2016}, volume = {38}, pages = {268--276} } metap/vignettes/plotmetap.Rnw0000644000176200001440000002245014210147175016072 0ustar liggesusers\documentclass[12pt]{article} \usepackage{amsmath,amssymb} %\usepackage{mydef2} \usepackage[round]{natbib} \usepackage{parskip,url} \usepackage{graphicx,subfig} \setlength{\topmargin}{0cm} \addtolength{\textheight}{2cm} \renewcommand{\topfraction}{0.85} \renewcommand{\bottomfraction}{0.5} \renewcommand{\textfraction}{0.15} \renewcommand{\floatpagefraction}{0.8} %\lhead{} %\input{title} %\VignetteIndexEntry{Plotting in the metap package} \title{Plotting in the \pkg{metap} package} \author{Michael Dewey} \newcommand{\pkg}[1]{\texttt{#1}} \newcommand{\func}[1]{\texttt{#1}} \newcommand{\code}[1]{\texttt{#1}} \newcommand{\codefont}{\footnotesize} \newcommand{\mygraph}[3]{% \begin{figure}[htbp] \includegraphics[height=6cm,width=10cm]{#1} \caption{#2} \label{#3} \end{figure} } \newcommand{\twograph}[8]{% \begin{figure}[htbp] \subfloat[#2\label{#3}]{\includegraphics[height=6cm,width=7cm]{#1}}% \subfloat[#5\label{#6}]{\includegraphics[height=6cm,width=7cm]{#4}} \caption{#7} \label{#8} \end{figure} } \begin{document} \maketitle \section{Introduction} \subsection{What is this document for?} This document describes how and why to plot $p$--values in the \pkg{metap} package. Examining the $p$--values graphically or otherwise before subjecting them to further analysis is useful to provide a visual impression of their distribution and to check for excess $p$--values at both extremes.. Three functions are provided for this purpose: \func{albatros}, \func{plotp}, and \func{schweder}. \subsection{Example datasets} As our example we use various data-sets: \begin{description} \item[\func{teachexpect}] Effect of teacher expectations on student IQ \citep{becker94} \item[\code{validity}] The validity of student ratings of their instructors \citep{becker94}. \item[\code{zhang}] The effect of the timing of exercise interventions for patients with cardiovascular disease \citep{zhang16} \end{description} {\codefont <<>>= library(metap) data(dat.metap) teach <- dat.metap$teachexpect validity <- dat.metap$validity$p zhang <- dat.metap$zhang print(validity) @ } \section{Plotting using \func{plotp}} The \func{plotp} provides a Q--Q plot of the $p$--values to detect departure from the uniform distribution. <>= plotp(validity, main = "Validity data") @ \twograph{plotmetap-plotp}{Q--Q plot from \func{plotp}}{plotp}{plotmetap-plotfunc}{Legacy Q--Q plot}{plotfunc}{Plots of validity data}{plotvalid} %\mygraph{plotmetap-plotp}{Q--Q plot from \func{plotp}}{plotp} %\mygraph{plotmetap-plotfunc}{Q--Q plot an object of class \func{metap}}{plotfunc} Figure \ref{plotp} shows the resulting plot. The line represents a fit to the uniform distribution and the polygon is a simultaneous confidence region such that if any point lies outside it we reject the null hypothesis that the points are drawn iid from a uniform. Small $p$--values are to the left of the plot The format of plot shown in Figure \ref{plotp} was first introduced in version 1.8 of \func{metap}. The previous plotting function is still available and it is possible to produce this plot by setting the \func{plotversion} parameter to "old" in the call to \func{plotp}. An example is shown in Figure \ref{plotfunc} which first calls \func{sumlog}. The legacy one will always remain an option. {\codefont <>= plotp(validity, main = "Validity data", plotversion = "old") @ } Note that the \func{plot} method for objects of class \code{"metap"} uses the new version of the plot. This change was introduced in version 1.9 of this package. There are many possible options which can be passed to the plotting function and hence to the \func{qqconf} plotting routine. The documentation for the \func{qqconf} package should be consulted for details. The \func{qqconf} package vignette is also very helpful. We will look at one of those options here though. {\codefont <>= plotp(teach) @ } {\codefont <>= plotp(teach, log10 = TRUE) @ } \twograph{plotmetap-teachlinear}{Linear scaling}{teachlinear}{plotmetap-teachlog}{Log scaling}{teachlog}{Teacher expectancy data}{teach} Figure \ref{teach} shows the teacher expectancy data using the default scaling in sub--figure \subref{teachlinear}. It is hard to see whether some of the points fall outside the boundary. However if we use the log--scaling option shown in sub--figure \subref{teachlog} it becomes much clearer. Note that the scale is reversed between the sub--plots and in \subref{teachlog} the small $p$--values are now on the right. So the cluster of points near the bottom left of the sub--figure \subref{teachlinear} are hard to distinguish as to whether they lie inside the boundary or not. In the log scaling of sub--figure \subref{teachlog} where they appear towards the top right it is much clearer that one does fall outside the boundary and two others are borderline. This reflects the fact that for most of the methods in the \func{metap} package the overall $p$--value is below 0.05. For instance using the logit method we have {\codefont <<>>= logitp(teach) @ } \section{Plotting using \func{schweder}} A function \func{schweder} provides plots with a variety of informative lines superimposed. It plots the ordered $p$--values, $p_{[i]}: p_{[1]} \le \dots{} p_{[2]} \le \dots{} p_{[i]} \dots{} \le p_{[k-1]} \le p_{[k]}$, against $i$. Although the original motivation for the plot is \citet{schweder82} the function uses a different choice of axes due to \citet{benjamini00}. We will use an example dataset on the validity of student ratings quoted in \citet{becker94}. Figure \ref{simple} shows the plot from \func{schweder}. <>= schweder(validity) @ \func{schweder} also offers the possibility of drawing one of a number of straight line summaries. The three possible straight line summaries are shown in Figure \ref{withlines} and are: \begin{itemize} \item the lowest slope line of Benjaimin and Hochberg which is drawn by default as solid, \item a least squares line drawn passing through the point $k+1, 1$ and using a specified fraction of the points which is drawn by default as dotted, \item a line with user specified intercept and slope which is drawn by default as dashed. \end{itemize} <>= schweder(validity, drawline = c("bh", "ls", "ab"), ls.control = list(frac = 0.5), ab.control = list(a = 0, b = 0.01)) @ \twograph{plotmetap-simple}{Simple graph}{simple}{plotmetap-withlines}{With lines}{withlines}{Output from schweder}{schweder} \section{The albatros plot} The albatros plot was introduced in \citet{harrison17} which should be consulted for more details. Basically it consists of plotting a possibly transformed sample size against the transformed $p$--values. The default is to use $\sqrt{N}$ for the $y$--axis and a log transformation for the $x$--axis. The plot also contains contours of constant effect size. A number of possible options are available for effect size type: correlation, standardised mean difference, and odds ratio. <>= validity <- dat.metap$validity fit.v <- albatros(validity$p, validity$n, contours = list(type = "corr", contvals = c(0.25, 0.5, 0.8), ltys = 1:3), axes = list(ylimit = c(1,200), lefttext = "Negative correlation", righttext = "Positive correlation"), main = "Validity") @ \mygraph{plotmetap-albatros}{Albatros plot from of the validity data}{albatros} Figure \ref{albatros} shows the result. Most of the points clearly correspond to positive and substantial correlations although a few are in the opposite direction although not far from the null value (0.5). If the actual effect sizes are available it would be better to use one of the conventional methods for meta--analysing them rather than rely on this method but \citet{harrison17} outline possible use cases. If the studies come from different groups where one might use meta--regression with a moderator for group membership if one had the effect sizes then the albatros plot can display the points using different symbols for groups. This would enable a visual check on whether the groups differed. <>= fit.z <- albatros(zhang$p, zhang$n, contours = list(type = "smd", contvals = c(0.25, 0.5, 1), ltys = 1:3), plotpars = list(pchs = letters[unclass(dat.metap$zhang$phase)]), axes = list(lefttext = "Favours control", righttext = "Favours exercise"), main = "Zhang" ) @ \mygraph{plotmetap-zhang}{Albatros plot of the Zhang et al data}{zhang} Figure \ref{zhang} shows an example using the Zhang et al data-set. The studies involved come from three groups corresponding to three different periods o initiation of exercise. The points are labelled accordingly: "a" initiation during the acute phase, "b" during the healing phase and "c" during the healed phase. The difference between the groups is quite clear here. In fact in \citet{zhang16} the results are handled with stratification into three separate analyses and meta--regression was not used. If some studies had given effect sizes but others did not then an albatros plot with the points marked for group membership and with appropriate contour lines would provide a visual check on whether the unavailable effect sizes were similar to the available ones. \bibliography{metap} \bibliographystyle{plainnat} \end{document} metap/NEWS0000644000176200001440000000520114506264210012055 0ustar liggesusersChanges in version 1.9 - updated documentation - warning if qqconf not installed - removed URL from DESCRIPTION Changes in version 1.8 - updated documentation - added using qqconf for plotting - added new vignette on plotting p-values Changes in version 1.7 - updated data-set cholest - added new data-set: zhang - added log.p parameter to allmetap - added new plotting function: albatros - updated documentation Changes in version 1.6 - updated documentation - added option to allow log inputs to selected functions - updated vignette - added more information to data-sets validity and cholest Changes in version 1.5 - updated vignette - added option to return log p to selected functions - combined all example data-sets into dat.metap Changes in version 1.4 - fixed bug in votep (report by Wolfgang Viechtbauer) - fixed bug in documentation for sump although code was correct (report by Sebastian Canzler) - use mathjaxr for HTML in Rd files - add version dependencies for Rdpack and mathjaxr Changes in version 1.3 - updated documentation - updated vignette - changed to use authors@R Changes in version 1.2 - new function truncated - improved error handling (report by Ana Marija Sokovic) - updated documentation Changes in version 1.1 - new plotting function plotp - split vignette into two Changes in version 1.0 - added new functions: inverse chisq, inverse t, mean z - changed package Rd file to use system macros - changed to using Rdpack for references in Rd files - updated vignette Changes in version 0.9 - added new function allmetap - minor bug in sumz fixed - updated vignette Changes in version 0.8 - updated vignette to include method comparisons Changes in version 0.7-1 - added maximump - updated documentation - this version never uploaded to CRAN Changes in version 0.7 - added vignette - minor bug fixes Changes in version 0.6-3 - test for cancellation error in sump - minor warnings fixes - updated documentation - this version never uploaded to CRAN Changes in version 0.6-2 - importFrom added for CRAN - Description enhanced Changes in version 0.6-1 - new maintainer email address - added CITATION file - this version never uploaded to CRAN Changes in version 0.6 - added weights to sumz - updated documentation Changes in version 0.5-1 - updated DESCRIPTION - First upload to CRAN Changes in version 0.5 - first substantial version metap/R/0000755000176200001440000000000014161100751011555 5ustar liggesusersmetap/R/albatros.R0000644000176200001440000000542514156075077013535 0ustar liggesusersalbatros <- function(p, n, axes = list(xlimit = NULL, ylimit = NULL, lefttext = NULL, righttext = NULL), contours = list(type = NULL, contvals = NULL, ltys = NULL, contlabs = NULL), plotpars = list(yscale = NULL, pchs = NULL, cols = NULL), ...) { xtrans <- function(p) { p2 <- ifelse(p > 0.5, 1 - p, p) res <- log(1 / p2, base = 10) res <- ifelse(p > 0.5, -res, res) res } ytrans <- function(n) { if(is.null(plotpars$yscale)) { yscale <- "sqrt" } else yscale <- plotpars$yscale if(yscale == "classic") { res <- log(n, base = 10) ^ 2 } else if(yscale == "n") { res <- n } else if(yscale == "sqrt") { res <- sqrt(n) } else { warning("Defaulting yscale to sqrt") res <- sqrt(n) } res } # if(length(p) != length(n)) { stop(paste("p", length(p), " and n", length(n), "must be same length")) } keep <- (p < 1) & (p > 0) validp <- p[keep] # remove zeroes and ones for axis calc extreme <- min(min(validp), min(1 - validp)) # set up axes if(is.null(axes$xlimit)) { xlims <- c(-xtrans(extreme), xtrans(extreme)) } else { xlims <- c(-xtrans(axes$xlimit), xtrans(axes$xlimit)) } if(is.null(axes$ylimit)) { ylims <- c(ytrans(min(n)) * 0.9, ytrans(max(n)) * 1.1) } else { ylims <- c(ytrans(axes$ylimit[1]), ytrans(axes$ylimit[2])) } # if(is.null(plotpars$pchs)) { pchs <- rep(1, length(p)) } else { pchs <- plotpars$pchs } if(is.null(plotpars$cols)) { cols <- rep("lightgrey", length(p)) } else { cols <- plotpars$cols } plot(xtrans(p), ytrans(n), xlim = xlims, ylim = ylims, pch = pchs, xaxt = "n", xlab = "p value", yaxt = "n", ylab = "N", ... ) # # set up x-axis values and plot axis sigs <- c(0.05, 0.01) i <- 2 while(sigs[i] > extreme) { sigs[i+1] <- sigs[i] / 10 i <- i + 1 } axis(1, at = c(-xtrans(sigs), 0, xtrans(sigs)), labels = c(sigs, "null", sigs), cex.axis = 0.75, las = 3, ...) # set up y-axis values and plot axis ylabs <- c(1, 2, 5) maxn <- max(n) i <- 3 while(ylabs[i] < maxn) { ylabs[i+1] <- ylabs[i - 2] * 10 i <- i + 1 } axis(2, at = ytrans(ylabs), labels = ylabs, cex.axis = 0.75, las = 2, ...) # plot contours docontours(contours$type, sigs, contours$contvals, xtrans, ytrans, xlims, ylims, contours$ltys, contours$contlabs) if(!is.null(axes$lefttext)) { mtext(axes$lefttext, side = 1, line = 3, adj = 0) } if(!is.null(axes$righttext)) { mtext(axes$righttext, side = 1, line = 3, adj = 1) } res <- list(xlims = xlims, ylims = ylims) res } metap/R/logitp.R0000644000176200001440000000150014110660174013176 0ustar liggesuserslogitp <- function(p, log.p = FALSE) { keep <- (p > 0) & (p < 1) invalid <- sum(1L * keep) < 2 if(invalid) { warning("Must have at least two valid p values") res <- list(t = NA_real_, df = NA_integer_, p = NA_real_, validp = p[keep]) } else { psum <- sum(log(p[keep] / (1 - p[keep]))) k <- length(p[keep]) mult <- -1 / sqrt(k * pi ^ 2 * (5 * k + 2) / (3 * (5 * k + 4))) if(k != length(p)) { warning("Some studies omitted") } t <- mult * psum df <- (5 * k + 4) res <- list(t = t, df = df, p = pt(t, df, lower.tail = FALSE, log.p = log.p), validp = p[keep]) } class(res) <- c("logitp", "metap") res } print.logitp <- function(x, ...) { cat("t = ", x$t, " with df = ", x$df, " p = ", x$p, "\n") invisible(x) } metap/R/two2one.R0000644000176200001440000000065212037557252013314 0ustar liggesuserstwo2one <- function(p, two = NULL, invert = NULL) { np <- length(p) if(is.null(two)) { two <- rep(TRUE, np) } if(is.null(invert)) { invert <- rep(FALSE, np) } # check values of p inrange <- sum(1L * ((p >= 0) & (p <= 1))) if(np != inrange) warning("Some p out of range") onep <- ifelse(two, ifelse(invert, (1 - p) + p / 2, p / 2), ifelse(invert, 1 - p, p) ) onep } metap/R/truncated.R0000644000176200001440000001023313561032314013672 0ustar liggesuserstruncated <- function(p, ptrunc = NULL, rtrunc = NULL, ...) { # dop <- function(validp, ptrunc) { if(requireNamespace("TFisher")) { if((ptrunc <= 0) | (ptrunc > 1)) { warning("The value of ptrunc must be between 0 and 1") warning("Setting p to 0.5") ptrunc <- 0.5 } nincl <- sum(1L * (validp < ptrunc)) nexcl <- sum(1L * (validp >= ptrunc)) if(nincl < 1) warning("No p values left after truncation") if(nexcl < 1) message("No studies removed by truncation") stat <- TFisher::stat.tpm(validp, ptrunc) pval <- 1 - TFisher::p.tpm(stat, length(validp), ptrunc) res <- list(p = pval, stat = stat, validp = validp, ptrunc = ptrunc, n = c(incl = nincl, excl = nexcl), method = "truncated") } else { warning("Need to install TFisher for this option") res <- list(p = NA, stat = NA) } res } # dor <- function(validp, rtrunc, ...) { if(requireNamespace("mutoss")) { if((rtrunc < 1) | (rtrunc > length(validp))) { l <- length(validp) warning(paste("The value of rtrunc must be between 1 and "), l) warning(paste("Setting rtrunc to", l %/% 2)) rtrunc <- l %/% 2 } nincl <- rtrunc nexcl <- length(validp) - nincl if(nincl < 1) warning("No p values left after truncation") if(nexcl < 1) message("No studies removed by truncation") temp <- mutoss::ranktruncated(validp, rtrunc, ...) stat <- temp$RTP$Statistic pval <- temp$RTP$p.Value res <- list(p = pval, stat = stat, validp = validp, rtrunc = rtrunc, n = c(incl = nincl, excl = nexcl), method = "rank") } else { warning("Need to install mutoss for this option") res <- list(p = NA, stat = NA) } res } # keep <- (p > 0) & (p <= 1) if(sum(1L * keep) < 2) { warning("Must have at least two valid p values") res <- list(p = NA, stat = NA) } else { validp <- p[keep] if(length(validp) != length(p)) { warning("Some studies omitted") } usetpm <- !is.null(ptrunc) userank <- !is.null(rtrunc) if(usetpm & userank) { warning("Specifying both ptrunc and rtrunc undefined") res <- list(p = NA, stat = NA) } else if(usetpm) { res <- dop(validp, ptrunc) } else if(userank) { res <- dor(validp, rtrunc) } else { warning("Must specify one of ptrunc or rtrunc") res <- list(p = NA, stat = NA) } } class(res) <- c("truncated", "list") res } print.truncated <- function(x, ...) { cat("stat = ", x$stat, " p = ", x$p, "\n") invisible(x) } summary.truncated <- function(object, ...) { with(object, { cat("stat = ", stat, " p = ", p, "\n") if(!is.na(stat)) { cat(paste("Using", n["incl"], "values of", n["incl"] + n["excl"], "valid p values\n")) if(method == "truncated") { cat("Truncated at p= ", ptrunc, "\n") } if(method == "rank") { cat("Truncated at rank= ", rtrunc, "\n") } } # end valid stat }) # end with invisible(object) } plot.truncated <- function(x, pparams = list(pchs = c(16, 1), pcols = c("black", "black")), ...) { if(is.na(x$stat)) { warning("Nothing to plot") } else { with(x, { p <- sort(validp, decreasing = FALSE) nused <- n["incl"] k <- length(p) plot(1:k, c(rep(0, k-1), 1), type = "n", xlab = "Index", ylab = "p", ...) if(nused == k) { points(1:nused, p[1:nused], pch = pparams$pchs[1], col = pparams$pcols[1]) } else if(nused == 0) { points((nused+1):k, p[(nused+1):k], pch = pparams$pchs[2], col = pparams$pcols[2]) } else { points(1:nused, p[1:nused], pch = pparams$pchs[1], col = pparams$pcols[1]) points((nused+1):k, p[(nused+1):k], pch = pparams$pchs[2], col = pparams$pcols[2]) } }) } invisible(x) } metap/R/sumz.R0000644000176200001440000000274314143225143012707 0ustar liggesuserssumz <- function(p, weights = NULL, data = NULL, subset = NULL, na.action = na.fail, log.p = FALSE, log.input = FALSE) { if(is.null(data)) data <- sys.frame(sys.parent()) mf <- match.call() mf$data <- NULL mf$subset <- NULL mf$na.action <- NULL mf[[1]] <- as.name("data.frame") mf <- eval(mf, data) if(!is.null(subset)) mf <- mf[subset,] mf <- na.action(mf) p <- as.numeric(mf$p) weights <- mf$weights noweights <- is.null(weights) if(noweights) weights <- rep(1, length(p)) if(length(p) != length(weights)) warning("Length of p and weights differ") if(log.input) { keep <- p < 0 } else { keep <- (p > 0) & (p < 1) } invalid <- sum(1L * keep) < 2 if(invalid) { warning("Must have at least two valid p values") res <- list(z = NA_real_, p = NA_real_, validp = p[keep], weights = weights) } else { if(sum(1L * keep) != length(p)) { warning("Some studies omitted") omitw <- weights[!keep] if((sum(1L * omitw) > 0) & !noweights) warning("Weights omitted too") } zp <- (qnorm(p[keep], lower.tail = FALSE, log.p = log.input) %*% weights[keep]) / sqrt(sum(weights[keep]^2)) res <- list(z = zp, p = pnorm(zp, lower.tail = FALSE, log.p = log.p), validp = p[keep], weights = weights) } class(res) <- c("sumz", "metap") res } print.sumz <- function(x, ...) { cat("sumz = ", x$z, "p = ", x$p, "\n") invisible(x) } metap/R/sump.R0000644000176200001440000000206513556530135012701 0ustar liggesuserssump <- function(p) { keep <- (p >= 0) & (p <= 1) invalid <- sum(1L * keep) < 2 if(invalid) { warning("Must have at least two valid p values") res <- list(p = NA_real_, conservativep = NA_real_, validp = p[keep]) } else { sigmap <- sum(p[keep]) k <- length(p[keep]) conservativep <- exp( k * log(sigmap) - lgamma(k + 1)) nterm <- floor(sigmap) + 1 # how many values of sump denom <- lfactorial(k) psum <- 0 terms <- vector("numeric", nterm) for (i in 1:nterm) { terms[i] <- lchoose(k, i - 1) + k * log(sigmap - i + 1) - denom pm <- 2 * (i %% 2) - 1 psum <- psum + pm * exp(terms[i]) } if(k != length(p)) { warning("Some studies omitted") } if(sigmap > 20) { warning("Likely to be unreliable, check with another method") } res <- list(p = psum, conservativep = conservativep, validp = p[keep]) } class(res) <- c("sump", "metap") res } print.sump <- function(x, ...) { cat("psum = ", x$p, "\n") invisible(x) } metap/R/allmetap.R0000644000176200001440000000345714143225126013514 0ustar liggesusersallmetap <- function(p, method = NULL, log.p = FALSE) { if(is.null(method)) stop("Must specify a method") mydata <- '"funcs","eponyms" "logitp", "maximump", "meanp", "meanz", "minimump","Tippett" "sumlog","Fisher" "sump","Edgington" "sumz","Stouffer" ' con <- textConnection(mydata) details <- read.csv(con, stringsAsFactors = FALSE) row.names(details) <- c("logitp", "maximump", "meanp", "meanz", "minimump", "sumlog", "sump", "sumz") close(con) # now which have log.p as parameter logpfuncs <- c("logitp", "meanz", "sumlog", "sumz") # if all specified reset funcnames funcnames <- method if("all" %in% method) funcnames <- row.names(details) # check all funcnames are valid functions keep <- funcnames %in% row.names(details) if(sum(keep * 1L) != length(funcnames)) warning("Some unsupported methods specified") if(log.p) { keep2 <- funcnames %in% logpfuncs } else { keep2 <- keep } funcnames <- funcnames[keep2] if(length(funcnames) < 1) stop("No supported methods specified") helper <- function(x) { thisfunc <- match.fun(row.names(details[x,])) if(log.p) { res <- try(thisfunc(p, log.p = log.p), silent = TRUE) } else { res <- try(thisfunc(p), silent = TRUE) } if(inherits(res, "try-error")) { res <- list(p = NA, valid = NA) } else { res <- list(p = res$p, valid = length(res$validp)) } res } res <- as.data.frame(t(sapply(funcnames, helper))) eponym <- vector("character", nrow(res)) for(i in 1:nrow(res)) { eponym[i] <- details[row.names(res[i,]),"eponyms"] } res$eponym <- eponym class(res) <- c("allmetap", "data.frame") res } print.allmetap <- function(x, digits = 5, ...) { print(format(x, digits = digits, ...), ...) invisible(x) } metap/R/meanp.R0000644000176200001440000000120013556527576013022 0ustar liggesusersmeanp <- function(p) { keep <- (p >= 0) & (p <= 1) invalid <- sum(1L * keep) < 4 if(invalid) { warning("Must have at least four valid p values") res <- list(z = NA_real_, p = NA_real_, validp = p[keep]) } else { pi <- mean(p[keep]) k <- length(p[keep]) z <- (0.5 - pi) * sqrt(12 * k) if(k != length(p)) { warning("Some studies omitted") } res <- list(z = z, p = pnorm(z, lower.tail = FALSE), validp = p[keep]) } class(res) <- c("meanp", "metap") res } print.meanp <- function(x, ...) { cat("z = ", x$z, " p = ", x$p, "\n") invisible(x) } metap/R/sumlog.R0000644000176200001440000000137614110700352013212 0ustar liggesuserssumlog <- function(p, log.p = FALSE) { keep <- (p > 0) & (p <= 1) invalid <- sum(1L * keep) < 2 if(invalid) { warning("Must have at least two valid p values") res <- list(chisq = NA_real_, df = NA_integer_, p = NA_real_, validp = p[keep]) } else { lnp <- log(p[keep]) chisq <- (-2) * sum(lnp) df <- 2 * length(lnp) if(length(lnp) != length(p)) { warning("Some studies omitted") } res <- list(chisq = chisq, df = df, p = pchisq(chisq, df, lower.tail = FALSE, log.p = log.p), validp = p[keep]) } class(res) <- c("sumlog", "metap") res } print.sumlog <- function(x, ...) { cat("chisq = ", x$chisq, " with df = ", x$df, " p = ", x$p, "\n") invisible(x) } metap/R/schweder.R0000644000176200001440000000503313346141432013512 0ustar liggesusersschweder <- function(p, xlab = "Rank of p", ylab = "p", drawline = NULL, # bh.control =list(), bh.lwd = 1, bh.lty = "solid", bh.col = "black", ls.control =list(frac = NULL), ls.lwd = 1, ls.lty = "dotted", ls.col = "black", ab.control =list(a = NULL, b = NULL), ab.lwd = 1, ab.lty = "dashed", ab.col = "black", ...) { bx1y1toa <- function(b, x1, y1) { # find intercept from b, x1, y1 a <- y1 - b * x1 a } bh <- function(p) { # parameters for Benjamini and Hochberg lowet slope line n <- length(p) rankp <- n:1 si <- (1 - p) / (n - rankp + 1) # assumes p in non-ascending order di <- which(diff(si) > 0) ldi <- max(1, di[length(di)]) # in case no slope change b <- si[ldi] res <- list(a = bx1y1toa(b, n + 1, 1), b = b, si = si, di = di, ldi = ldi) res } n <- length(p) stopifnot(n > 1) toplot <- rev(sort(p)) keep <- (toplot >= 0) & (toplot <= 1) toplot <- toplot[keep] if(length(toplot) != n) warning('Some p values omitted') n <- length(toplot) if(n < 1) stop("Not even one to plot") x <- n:1 plot(x, toplot, ylab = ylab, xlab = xlab, ylim = c(0, 1), xlim = c(0, n+1), ...) res <- list(p = toplot) if("bh" %in% drawline) { params <- bh(toplot) abline(a = params$a, b = params$b, lty = bh.lty, lwd = bh.lwd, col = bh.col) res <- c(res, bh.params = list(a = params$a, b = params$b, si = params$si, di = params$di, ldi = params$ldi)) } if("ls" %in% drawline) { if(is.null(ls.control$frac)) { warning("Must specify fraction for ls") } else { frac <- ls.control$frac newy <- toplot - 1 # transform so that line is forced newx <- x - (n + 1) # through (n+1),1 rather than 0,0 plim <- newy[n * frac] fit <- lm(newy ~ newx - 1, subset = newy > plim) b <- coef(fit)[1] # correct slope a <- bx1y1toa(b, (n + 1), 1) # passing through (n+1,1 abline(a = a, b = b, lty = ls.lty, lwd = ls.lwd, col = ls.col) res <- c(res, ls.params = list(a = a, b = b)) } } if ("ab" %in% drawline) { if( is.null(ab.control$a) | is.null(ab.control$b) ) { warning("No parameters for a and b line") } else { abline(a = ab.control$a, b = ab.control$b,lty = ab.lty, lwd = ab.lwd, col = ab.col) res <- c(res, ab.params = list(a = ab.control$a, b = ab.control$b)) } } invisible(res) } metap/R/docontours.R0000644000176200001440000000351614155647367014132 0ustar liggesusersdocontours <- function(conttype, xvals, contvals, xtrans, ytrans, xlims, ylims, ltys, contlabs) { # corr2n <- function(p, r) { res <- qnorm(p) ^ 2 / atanh(r) ^ 2 + 3 res } # smd2n <- function(p, smd) { res <- qnorm(p) ^ 2 * (8 + smd ^2) / (2 * smd ^ 2) res } # or2n <- function(p, or) { lnor2 <- log(or) ^ 2 res <- qnorm(p) ^ 2 * (8 * pi ^ 2 + 3 * lnor2) / (6 * lnor2) res } # valid <- TRUE if(is.null(conttype)) { valid <- FALSE } else if(is.null(contvals)) { valid <- FALSE } else if(!conttype %in% c("smd", "or", "corr")) { valid <- FALSE warning(paste("Unrecognised effect type", conttype)) } else if(conttype == "smd") { contfunc <- smd2n } else if(conttype == "corr") { contfunc <- corr2n } else if(conttype == "or") { contfunc <- or2n } if(valid) { pvals <- c(0.4, xvals) l <- length(contvals) if(is.null(ltys) | length(ltys != l)) { ltys <- 1:l } else if(length(ltys) == 1) { ltys <- rep(ltys[1], l) } locallabs <- TRUE if(!is.null(contlabs)) locallabs <- contlabs for(i in 1:l) { nvals <- contfunc(pvals, contvals[i]) temp <- spline(xtrans(pvals), ytrans(nvals), n = 101) # now find where it leaves plotting area len <- length(temp$x) if(locallabs) { j <- 1 while(temp$x[j] < xlims[2] & temp$y[j] < ylims[2] & j < len) { j <- j + 1 } textx <- temp$x[j] texty <- temp$y[j] text(textx, texty, as.character(contvals[i]), pos = 2) } lines(temp, lty = ltys[i]) lines(spline(-xtrans(pvals), ytrans(nvals), n = 101), lty = ltys[i]) } } } metap/R/votep.R0000644000176200001440000000222213664454562013056 0ustar liggesusersvotep <- function(p, alpha = 0.5) { alpha <- ifelse(alpha > 1, alpha / 100, alpha) # if percent stopifnot(alpha > 0, alpha < 1) keep <- (p >= 0) & (p <= 1) alp <- vector("numeric", 2) if(alpha <= 0.5) { alp[1] <- alpha alp[2] <- 1 - alpha } else { alp[2] <- alpha alp[1] <- 1 - alpha } invalid <- sum(1L * keep) < 2 if(invalid) { warning("Must have at least two valid p values") res = list(p = NA_real_, pos = NA_integer_, neg = NA_integer_, alpha = alpha, validp = p[keep]) } else { pi <- p[keep] k <- length(pi) pos <- sum(1L * (pi < alp[1])) neg <- sum(1L * (pi > alp[2])) if(k != length(p)) { warning("Some studies omitted") } if((pos + neg) <= 0) { warning("All p values are within specified limits of alpha") p <- 1 } else { p = binom.test(pos, pos + neg, 0.5, alternative = "greater")$p.value } res = list(p = p, pos = pos, neg = neg, alpha = alpha, validp = pi) } class(res) <- c("votep", "metap") res } print.votep <- function(x, ...) { cat("p = ", x$p, "\n") invisible(x) } metap/R/invchisq.R0000644000176200001440000000236414110663750013540 0ustar liggesusersinvchisq <- function(p, k, data = NULL, subset = NULL, na.action = na.fail, log.p = FALSE) { if(is.null(data)) data <- sys.frame(sys.parent()) mf <- match.call() mf$data <- NULL mf$subset <- NULL mf$na.action <- NULL mf[[1]] <- as.name("data.frame") mf <- eval(mf, data) if(!is.null(subset)) mf <- mf[subset,] mf <- na.action(mf) p <- as.numeric(mf$p) k <- as.numeric(mf$k) if(length(k) == 1) { k <- rep(k, length(p)) } else { } keep <- (p > 0) & (p <= 1) & (k > 0) invalid <- sum(1L * keep) < 2 if(invalid) { warning("Must have at least two valid p values") res <- list(chisq = NA_real_, df = NA_integer_, p = NA_real_, validp = p[keep]) } else { pvals <- p[keep] k <- k[keep] if(length(pvals) != length(p)) { warning("Some studies omitted") } chisq <- qchisq(pvals, k, lower.tail = FALSE) chi <- sum(chisq) df <- sum(k) res <- list(chisq = chi, df = df, p = pchisq(chi, df, lower.tail = FALSE, log.p = log.p), validp = pvals) } class(res) <- c("invchisq", "metap") res } print.invchisq <- function(x, ...) { cat("chisq = ", x$chisq, " with df = ", x$df, " p = ", x$p, "\n") invisible(x) } metap/R/wilkinsonp.R0000644000176200001440000000372114117650525014112 0ustar liggesuserswilkinsonp <- function(p, r = 1, alpha = 0.05, log.p = FALSE) { alpha <- ifelse(alpha > 1, alpha / 100, alpha) # if percent stopifnot(alpha > 0, alpha < 1) alpha <- ifelse(alpha > 0.5, 1 - alpha, alpha) # map to 0 to 0.5 keep <- (p >= 0) & (p <= 1) invalid <- sum(1L * keep) < 2 if (invalid) { warning("Must have at least two valid p values") res <- list(p = NA_real_, pr = NA_real_, r = r, critp = NA_real_, alpha = alpha, validp = p[keep]) } else { pi <- p[keep] k <- length(pi) if(k != length(p)) { warning("Some studies omitted") } if((r < 1) | (r > k)) { r <- 1 warning("Illegal r set to 1") } pi <- sort(pi) pr <- pi[r] res <- list(p = pbeta(pr, r, k + 1 - r, log.p = log.p), pr = pr, r = r, critp = qbeta(alpha, r, k + 1 - r), alpha = alpha, validp = pi) } class(res) <- c("wilkinsonp", "metap") res } maximump <- function(p, alpha = 0.05, log.p = FALSE) { keep <- (p >= 0) & (p <= 1) validp <- p[keep] k <- length(validp) res <- wilkinsonp(p, r = k, alpha, log.p) class(res) <- c("maximump", "metap") res } minimump <- function(p, alpha = 0.05, log.p = FALSE) { res <- wilkinsonp(p, r = 1, alpha, log.p) class(res) <- c("minimump", "metap") res } print.wilkinsonp <- function(x, ...) { r <- x$r p <- x$p if(r == 1) { cat("p = ", p, " using ", paste("minimum p", sep = ""), "\n") } else if(r == 2) { cat("p = ", p, " using ", paste(r, "nd minimum p", sep = ""), "\n") } else if(r == 3) { cat("p = ", p, " using ", paste(r, "rd minimum p", sep = ""), "\n") } else { cat("p = ", p, " using ", paste(r, "th minimum p", sep = ""), "\n") } invisible(x) } print.maximump <- function(x, ...) { p <- x$p cat("p = ", p, " using maximum p", "\n") invisible(x) } print.minimump <- function(x, ...) { p <- x$p cat("p = ", p, " using minimum p", "\n") invisible(x) } metap/R/invt.R0000644000176200001440000000217614110663240012667 0ustar liggesusersinvt <- function(p, k, data = NULL, subset = NULL, na.action = na.fail, log.p = FALSE) { if(is.null(data)) data <- sys.frame(sys.parent()) mf <- match.call() mf$data <- NULL mf$subset <- NULL mf$na.action <- NULL mf[[1]] <- as.name("data.frame") mf <- eval(mf, data) if(!is.null(subset)) mf <- mf[subset,] mf <- na.action(mf) p <- as.numeric(mf$p) k <- as.numeric(mf$k) if(length(k) == 1) { k <- rep(k, length(p)) } else { } keep <- (p > 0) & (p <= 1) & (k > 2) invalid <- sum(1L * keep) < 2 if(invalid) { warning("Must have at least two valid p values") res <- list(z = NA_real_, p = NA_real_, validp = p[keep]) } else { pvals <- p[keep] k <- k[keep] if(length(pvals) != length(p)) { warning("Some studies omitted") } z <- sum(qt(pvals, k, lower.tail = FALSE)) / sqrt(sum(k / (k - 2))) res <- list(z = z, p = pnorm(z, lower.tail = FALSE, log.p = log.p), validp = pvals) } class(res) <- c("invt", "metap") res } print.invt <- function(x, ...) { cat("z = ", x$z, " p = ", x$p, "\n") invisible(x) } metap/R/meanz.R0000644000176200001440000000130614110664165013022 0ustar liggesusersmeanz <- function(p, log.p = FALSE) { keep <- (p > 0) & (p < 1) invalid <- sum(1L * keep) < 2 if(invalid) { warning("Must have at least two valid p values") res <- list(z = NA_real_, p = NA_real_, validp = p[keep]) } else { if(sum(1L * keep) != length(p)) { warning("Some studies omitted") } zvals <- (qnorm(p[keep], lower.tail = FALSE)) zp <- mean(zvals) / (sd(zvals) / sqrt(length(p[keep]))) res <- list(z = zp, p = pnorm(zp, lower.tail = FALSE, log.p = log.p), validp = p[keep]) } class(res) <- c("meanz", "metap") res } print.meanz <- function(x, ...) { cat("meanz = ", x$z, "p = ", x$p, "\n") invisible(x) } metap/R/plotp.R0000644000176200001440000000162714210124205013037 0ustar liggesusersplotp <- function(pvals, plotversion = "qqconf", ...) { keep <- !is.na(pvals) validp <- pvals[keep] # remove NA keep <- validp >= 0 & validp <= 1 if(sum(1L * keep) < 1) stop("No points to plot") n <- length(validp) if(sum(1L * keep) != n) warning("Out of range points omitted") y <- validp[keep] n <= length(y) if(plotversion == "qqconf") { if(requireNamespace("qqconf")) { qqconf::qq_conf_plot(y, distribution = qunif, ...) } else { warning("qqconf not installed, consider setting plotversion to old") } } else { qqplot(qunif(ppoints(n)), y, xlab = "Theoretical", ylab = "Empirical", ...) qqline(y, distribution = qunif, ...) } res <- list(validp = y) invisible(res) } plot.metap <- function(x, plotversion = "qqconf", ...) { plotp(x$validp, plotversion = plotversion, ...) invisible(x) 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################################################### ### code chunk number 1: plotmetap.Rnw:70-76 ################################################### library(metap) data(dat.metap) teach <- dat.metap$teachexpect validity <- dat.metap$validity$p zhang <- dat.metap$zhang print(validity) ################################################### ### code chunk number 2: plotp ################################################### plotp(validity, main = "Validity data") ################################################### ### code chunk number 3: plotfunc ################################################### plotp(validity, main = "Validity data", plotversion = "old") ################################################### ### code chunk number 4: teachlinear ################################################### plotp(teach) ################################################### ### code chunk number 5: teachlog ################################################### plotp(teach, log10 = TRUE) ################################################### ### code chunk number 6: plotmetap.Rnw:167-168 ################################################### logitp(teach) ################################################### ### code chunk number 7: simple ################################################### schweder(validity) ################################################### ### code chunk number 8: withlines ################################################### schweder(validity, drawline = c("bh", "ls", "ab"), ls.control = list(frac = 0.5), ab.control = list(a = 0, b = 0.01)) ################################################### ### code chunk number 9: albatros ################################################### validity <- dat.metap$validity fit.v <- albatros(validity$p, validity$n, contours = list(type = "corr", contvals = c(0.25, 0.5, 0.8), ltys = 1:3), axes = list(ylimit = c(1,200), lefttext = "Negative correlation", righttext = "Positive correlation"), main = "Validity") ################################################### ### code chunk number 10: zhang ################################################### fit.z <- albatros(zhang$p, zhang$n, contours = list(type = "smd", contvals = c(0.25, 0.5, 1), ltys = 1:3), plotpars = list(pchs = letters[unclass(dat.metap$zhang$phase)]), axes = list(lefttext = "Favours control", righttext = "Favours exercise"), main = "Zhang" ) metap/inst/doc/compare.Rnw0000644000176200001440000005756614136254755015257 0ustar liggesusers\documentclass[12pt]{article} \usepackage{amsmath,amssymb} %\usepackage{mydef2} \usepackage[round]{natbib} \usepackage{parskip,url} \usepackage{graphicx,subfig} \setlength{\topmargin}{0cm} \addtolength{\textheight}{2cm} %\lhead{} %\input{title} %\VignetteIndexEntry{Comparison of methods in the metap package} \title{Comparison of methods in the \pkg{metap} package} \author{Michael Dewey} \newcommand{\pkg}[1]{\texttt{#1}} \newcommand{\func}[1]{\texttt{#1}} \newcommand{\code}[1]{\texttt{#1}} \newcommand{\codefont}{\footnotesize} \newcommand{\mygraph}[3]{% \begin{figure}[htbp] \includegraphics[height=6cm,width=10cm]{compare-#1} \caption{#2} \label{#3} \end{figure} } % in mypdf fourth parameter needs [] \newcommand{\mypdf}[4]{% \begin{figure}[htbp] \includegraphics#4{#1.pdf} \caption{#2} \label{#3} \end{figure} } \newcommand{\twograph}[8]{% \begin{figure}[htbp] \subfloat[#2\label{#3}]{\includegraphics[height=6cm,width=7cm]{compare-#1}}% \subfloat[#5\label{#6}]{\includegraphics[height=6cm,width=7cm]{compare-#4}} \caption{#7} \label{#8} \end{figure} } \begin{document} \maketitle \section{Introduction} \subsection{What is this document for?} This document describes some methods for the meta--analysis of $p$--values (significance values) contained in the package \pkg{metap} and contains comments on the performance of the various algorithms under a small number of different scenarios with hints on the choice of method. \subsection{Notation} The $k$ studies give rise to $p$--values, $p_i,\;i = 1, \dots, k$. These are assumed to be independent. We shall also need the ordered $p$--values: $p_{[1]} \le p_{[2]}, \dots, \le p_{[k]}$ and weights $w_i,\;i = 1, \dots, k$. Logarithms are natural. A function for combining $p$--values is denoted $g$. The size of the test is $\alpha$. We may also need $k$ degrees of freedom, $\nu_i$. The methods are referred to by the name of the function in \func{metap}. Table \ref{funcs} shows other descriptions of each method. \begin{table}[htbp] \begin{tabular}{lll} Function name & \multicolumn{2}{c}{Description(s)} \\[1ex] & \multicolumn{1}{c}{Eponym} \\ \func{invchisq} & Lancaster's method & Inverse chi square \\ \func{invt} & & Inverse t \\ \func{logitp} & & Logistic\\ \func{meanp} \\ \func{meanz} \\ \func{maximump} \\ \func{minimump} & Tippett's method \\ \func{sumlog} & Fisher's method & Chi square (2 df)\\ \func{sump} & Edgington's method & Uniform\\ \func{sumz} & Stouffer's method & Normal\\ \func{truncated} & Truncated Fisher\\ \func{truncated} & & rank--truncated\\ \func{votep} \\ \func{wilkinsonp} & Wilkinson's method \\ \end{tabular} \caption{Methods considered in this document} \label{funcs} \end{table} \section{Theoretical results} There have been various attempts to clarify the problem and to discuss optimality of the methods. A detailed account was provided by \citet{liptak58}. \citet{birnbaum54} considered the property of admissibility. A method is admissible if when it rejects $H_0$ for a set of $p_i$ it will also reject $H_0$ for $P^*_i$ where $p^*_i \le p_i$ for all $i$. He considered that Fisher's and Tippett's method were admissible. See also \citet{owen09}. He also points out the problem is poorly specified. This may account for the number of methods available and their differing behaviour. The null hypothesis $H_0$ is well defined, that all $p_i$ have a uniform distribution on the unit interval. There are two classes of alternative hypothesis \begin{itemize} \item $H_A$: all $p_i$ have the same (unknown) non--uniform, non--increasing density, \item $H_B$: at least one $p_i$ has an (unknown) non--uniform, non--increasing density. \end{itemize} If all the tests being combined come from what are basically replicates then $H_A$ is appropriate whereas if they are of different kinds of test or different conditions then $H_B$ is appropriate. Note that Birnbaum specifically considers the possibility that the tests being combined may be very different for instance some tests of means, some of variances, and so on. \section{The methods} \subsection{Comparison scenarios} To provide a standard of comparison we shall use the following two situations. Some authors have also used the case of exactly two $p_i$. \begin{description} %\subsubsection{What if all $p_i = p$?\label{twopisection}} \item[What if all $p_i = p$?]\label{twopisection} Perhaps surprisingly there are substantial differences here as we shall see when we look at each method. We shall describe how the returned value varies with $p$ and $k$. %\subsubsection{Cancellation} \item[Cancellation] When the collection of primary studies contains a number of values significant in both directions the methods can give very different results. If the intention of the synthesis is to examine a directional hypothesis one would want a method where these cancelled out. The decision between methods should be made on theoretical grounds of course. We shall use the following four values as our example. \end{description} {\codefont <<>>= cancel <- c(0.001, 0.001, 0.999, 0.999) @ } <>= library(metap) data(dat.metap) validity <- dat.metap$validity$p genvec <- function(pvals, kvals, fun, name) { ps <- length(pvals) ks <- length(kvals) temp <- matrix(-1, nrow = ps, ncol = ks) for(i in 1:ps) for(j in 1:ks) { temp[i, j] <- fun(rep(pvals[i], kvals[j]))$p } temp2 <- as.vector(temp) res <- data.frame(method = rep(name, length(temp2)), p = rep(pvals, ks), k = rep(kvals, each = ps), g = temp2 ) res } @ \subsection{Methods using transformation of the $p$--values} One class of methods relies on transforming the $p$--values first. \begin{table}[htbp] \begin{tabular}{lll} Function name & Definition & Critical value \\[1ex] \func{invchisq} & $\sum_{i=1}^k \chi^2_{\nu_i}(p_i)$ & $\chi^2_{\sum{\nu_i}}(\alpha)$ \\[1ex] \func{invt} & $\frac{\sum_{i=1}^k t_{\nu_i}(p_i)}% {\sqrt{\sum_{i=1}^k \frac{\nu_i}{\nu_i - 2}}}$ & $z(\alpha)$ \\[1ex] \func{logitp} & $\frac{\sum_{i=1}^k \log\frac{p}{1 - p}}{C}$ & $t_{5k+4}$ \\ & where $C = \sqrt\frac{k \pi^2 (5 k + 2)}{3(5 k + 4)}$ & \\[1ex] \func{meanz} & $\frac{\bar{z}}{s_{\bar{z}}}$ & $t_{k-1}(\alpha)$ \\ & where $\bar{z} = \sum_{i=1}^k \frac{z(p_i)}{k}$ \\ & and $s_{\bar{z}} = \frac{s_z}{\sqrt{k}}$ & \\[1ex] \func{sumlog} & $\sum_{i=1}^{k} - 2 \log p_i$ & $\chi_{2k}(\alpha)$ \\[1ex] \func{sumz} & $\frac{\sum_{i=1}^k z(p_i)}{\sqrt{k}}$ & $z(\alpha)$\\ \end{tabular} \caption{Definitions of methods using transformation of the $p$ values} \label{transdefs} \end{table} <>= kvals <- c(4, 5, 6, 8, 10, 15, 20) pvals <- c(0.2, 0.3, 0.3679, 0.4, 0.5, 0.6) dat <- rbind( genvec(pvals, kvals, logitp, "logitp"), genvec(pvals, kvals, meanz, "meanz"), genvec(pvals, kvals, sumlog, "sumlog"), genvec(pvals, kvals, sumz, "sumz") ) @ <>= lattice::xyplot(g ~ k | method, groups = p, type = "l", data = dat, auto.key = list(space = "left", lines = TRUE, title = "p"), ylab = "g(p)" ) @ \subsubsection{The method of summation of logs, Fisher's method} See Table \ref{transdefs} for the definition. This works because $- 2 \log p_i$ is a $\chi^2_2$ and the sum of $\chi^2$ is itself a $\chi^2$ with degrees of freedom equal to the sum of the degrees of freedom of the individual $\chi^2$. Of course the sum of the log of the $p_i$ is also the log of the product of the $p_i$. Fisher's method \citep{fisher25} is provided in \func{sumlog}. <>= set.seed(18122019) temp <- matrix(runif(10000), nrow = 100) fisher <- apply(temp, 1, function(x) sumlog(x)$p) lanc4 <- apply(temp, 1, function(x) invchisq(x, 4)$p) lanc16 <- apply(temp, 1, function(x) invchisq(x, 16)$p) lanc256 <- apply(temp, 1, function(x) invchisq(x, 256)$p) banda <- function(x, y) { res <- data.frame(sum = x + y, diff = (x - y)) res } dat <- data.frame(rbind(banda(fisher, lanc4), banda(fisher, lanc16), banda(fisher, lanc256), banda(lanc4, lanc16), banda(lanc4, lanc256), banda(lanc16, lanc256) ), name = factor(c(rep("FL4", 100), rep("FL16", 100), rep("FL256", 100), rep("L4L16", 100), rep("L4L256", 100), rep("L16L256", 100)), levels = c("FL4", "FL16", "FL256", "L4L16", "L4L256", "L16L256") ) ) @ <>= lattice::xyplot(diff ~ sum | name, data = dat, panel = function(x, y, ...) { lattice::panel.xyplot(x, y, ...) lattice::panel.abline(h = mean(y), lty = 2) lattice::panel.abline(h = mean(y) + 1.96 * sd(y), lty = 3) lattice::panel.abline(h = mean(y) - 1.96 * sd(y), lty = 3) } ) @ <>= stouff <- apply(temp, 1, function(x) sumz(x)$p) invt4 <- apply(temp, 1, function(x) invt(x, 4)$p) invt16 <- apply(temp, 1, function(x) invt(x, 16)$p) invt256 <- apply(temp, 1, function(x) invt(x, 256)$p) banda <- function(x, y) { res <- data.frame(sum = x + y, diff = (x - y)) res } dat <- data.frame(rbind(banda(stouff, invt4), banda(stouff, invt16), banda(stouff, invt256), banda(invt4, invt16), banda(invt4, invt256), banda(invt16, invt256) ), name = factor(c(rep("St4", 100), rep("St16", 100), rep("St256", 100), rep("t4t16", 100), rep("t4t256", 100), rep("t16t256", 100)), levels = c("St4", "St16", "St256", "t4t16", "t4t256", "t16t256") ) ) @ <>= lattice::xyplot(diff ~ sum | name, data = dat, panel = function(x, y, ...) { lattice::panel.xyplot(x, y, ...) lattice::panel.abline(h = mean(y), lty = 2) lattice::panel.abline(h = mean(y) + 1.96 * sd(y), lty = 3) lattice::panel.abline(h = mean(y) - 1.96 * sd(y), lty = 3) } ) @ As can be seen in Figure \ref{equalp} when all the $p_i=p$ \func{sumlog} returns a value which decreases with $k$ when $p<0.32$, increases with $k$ when $p>0.37$, and in between increases with $k$ and then decreases. Some detailed algebra provided in a post to https://stats.stackexchange.com/questions/243003 by Christoph Hanck suggests that the breakpoint is $e^{-1} = 0.3679$. Where the $p_i$ are less than this then for a sufficiently large $k$ (several hundred) the result will be significant and not if above that. Over the range of $k$ we are plotting this bound is not yet closely approached. \mygraph{transeqp}{Behaviour of the methods using transformed $p$ values for $k$ values of $p=p_i$}{equalp} \subsubsection{Inverse $\chi^2$ Lancaster's method} It would of course be possible to generalise Fisher's method to use transformation to $\chi^2$ with any other number of degrees of freedom rather than 2. \citet{lancaster61} suggests that this is highly correlated with \func{sumlog}. Lancaster's method is provided in \func{invchisq}. In fact the resemblance to \func{sumlog} becomes less as the number of degrees of freedom increases. Figure \ref{fishlanc} shows for a small number of selected degrees of freedom how it compares to Fisher's method. \twograph{fishlanc}{Fisher's method and Lancaster's method}{fishlanc}{stouffinvt}{Stouffer's method and inverse $t$}{stouffinvt}{Sum and difference plots of Fisher v Lancaster and Stouffer v inverse $t$}{compfishstouff} \subsubsection{The method of summation of $z$ values, Stouffer's method} The method of summation of $z$ values is provided in \func{sumz} \citep{stouffer49}. See Table \ref{transdefs} for the definition. As can be seen in Figure \ref{equalp} it returns a value for our $p_i=p$ example which decreases with $k$ when $p$ below 0.5 and increases above. A weighted version of Stouffer's method is available %\begin{equation} $\frac{\sum_{i=1}^k w_i z(p_i)}{\sqrt {\sum_{i=1}^k w_i ^ 2}}$ %\end{equation} where $w_i$ are the weights. In the absence of effect sizes (in which case a method using effect sizes would be more appropriate anyway) best results are believed to be obtained with weights proportional to the square root of the sample sizes \citep{zaykin11} following \citet{liptak58}. \subsubsection{Mean of normals method} There is also a method closely related to Stouffer's using the mean of normals provided in \func{meanz} also defined in Table \ref{transdefs} which has very similar properties except that when all the $p_i$ are equal it either gives 0 or 1 as can be seen in Figure \ref{equalp}. <<>>= meanz(c(0.3, 0.31))$p meanz(c(0.1, 0.2))$p @ The method of \func{meanz} also has the unusual property that a set of $p$--values which are all less than those in another set can still give rise to a larger overall $p$. See example above. This is the only method considered here which has this property so if it is a desirable one then that is the only method to consider. \subsubsection{The inverse $t$ method} A closely related method is the inverse $t$ method. See Table \ref{transdefs} for the definition. This method is provided in \func{invt}. As is clear from the definition this method tends to Stouffer's method as $\nu_i \to \infty$. Figure \ref{stouffinvt} shows this for selected degrees of freedom. \subsubsection{The method of summation of logits} See Table \ref{transdefs} for the definition. This method is provided in \func{logitp}. The constant $C$ was arrived at by equating skewness and kurtosis with that of the $t$--distribution \citep{loughin04}. As can be seen in Figure \ref{equalp} this method returns a value for our $p_i=p$ example which decreases with $k$ when $p$ below 0.5 and increases above. \subsubsection{Examples for methods using transformations of the $p$ values} <>= log10p <- function(x) { res <- round(-log(x, base = 10), 2) res } @ \begin{table}[htbp] \begin{tabular}{lll} Function name & \multicolumn{1}{c}{validity} & \multicolumn{1}{c}{cancel} \\ & \multicolumn{1}{c}{value expressed} \\ & \multicolumn{1}{c}{as $-\log_{10}p$} \\[1ex] \func{logitp} & \Sexpr{log10p(logitp(validity)$p)} & \Sexpr{logitp(cancel)$p} \\ \func{meanz} & \Sexpr{log10p(meanz(validity)$p)} & \Sexpr{meanz(cancel)$p} \\ \func{sumlog} & \Sexpr{log10p(sumlog(validity)$p)} & \Sexpr{round(sumlog(cancel)$p, 5)} \\ \func{sumz} & \Sexpr{log10p(sumz(validity)$p)} & \Sexpr{sumz(cancel)$p}\\ \end{tabular} \caption{Examples of methods using transformation of the $p$ values} \label{transexamples} \end{table} Using the same example dataset which we have already plotted and our cancellation dataset we have the values in Table \ref{transexamples}. As can be seen all the methods cancel except for \func{sumlog}. The agreement for the validity dataset is close except for \func{meanz} whoch gives a value several orders of magnitude greater than the other three. Lancaster's method and inverse $t$ are not shown as they are both infinite families of possible methods and in any event are similar to Fisher's method and Stouffer's method respectively. \subsection{Methods using untransformed $p$--values} \begin{table}[htbp] \begin{tabular}{lll} Function name & Definition & Critical value \\[1ex] \func{meanp} & $\bar p = \frac{\sum_{i=1}^k p_i}{k}$ \\ & $z = (0.5 - \bar{p}) \sqrt{12k}$ & $z(\alpha)$ \\ \func{minimump} & $p_{[1]}$ & $1 - (1 - \alpha)^{\frac{1}{k}}$ \\ \func{maximump} & $p_{[k]}$ & $\alpha^k$ \\ \func{wilkinsonp} & $p_{[r]}$ & $\sum_{s=r}^k {k \choose s}\alpha^s (1 - \alpha)^{k-s}$\\[1ex] \func{sump} & $\frac{(S)^k}{k!}% - {k \choose 1}\frac{(S - 1)^k}{k!}% + {k \choose 2}\frac{(S - 2)^k}{k!} - \dots$ & $\alpha$ \\ & where $S = \sum_{i=1}^k p_i$ \\ \end{tabular} \caption{Definitions of methods not using transformation of the $p$ values, % the series for \func{sump} continues until the term in in the numerator $(S-i)$ becomes negative} \label{untransdefs} \end{table} <>= kvals <- c(4, 5, 6, 8, 10, 15, 20) pvals <- c(0.2, 0.3, 0.3679, 0.4, 0.5, 0.6) dat <- rbind( genvec(pvals, kvals, meanp, "meanp"), genvec(pvals, kvals, maximump, "maximump"), genvec(pvals, kvals, minimump, "minimump"), genvec(pvals, kvals, sump, "sump"), genvec(pvals, kvals, votep, "votep") ) @ <>= lattice::xyplot(g ~ k | method, groups = p, type = "l", data = dat, auto.key = list(space = "left", lines = TRUE, title = "p"), ylab = "g(p)" ) @ \mygraph{untranseqp}{Behaviour of the methods using untransformed $p$ values for $k$ values of $p=p_i$}{unequalp} \subsubsection{The method of minimum $p$, maximum $p$, and Wilkinson's method} The methods of minimum $p$ \citep{tippett31}, maximum $p$ and Wilkinson \citep{wilkinson51} are defined in Table \ref{untransdefs}. Wilkinson's method depends on which value (the $r$th) of $p_{[i]}$ is selected. % p is pbeta(p[r], r, k+1-r) % critical p is qbeta(alpha, r, k+1-r) Wilkinson's method is provided in \func{wilkinsonp} and a convenience function \func{minimump} with its own \code{print} method is provided for the minimum $p$ method ($r=1$). It is also possible to use the method for the maximum $p$ (that is $r=k$) and a convenience function \func{maximump} is provided for that purpose. As can be seen in Figure \ref{unequalp} these methods return a value for our $p_i=p$ example which always increases with $k$ which is true for \func{minimump} and which always decreases with $k$ which is true for \func{maximump} \subsubsection{The method of summation of $p$--values, Edgington's method\label{sump}} Defined in Table \ref{untransdefs} \citep{edgington72a}. This method is provided in \func{sump}. As can be seen in Figure \ref{unequalp} this method returns a value for our $p_i=p$ example which decreases with $k$ when $p$ below 0.5 and increases above. Some authors use a simpler version, $\frac{(\sum p)^k}{k!}$, for instance \citet{rosenthal78} in the text although compare his Table 4. This can be very conservative when $\sum p > 1$ There seems no particular need to use this method but it is returned by \func{sump} as the value of \code{conservativep} for use in checking published values. Note also that there can be numerical problems for extreme values of $S$ and in that case recourse might be made to \func{meanp} which has similar properties. \subsubsection{The mean $p$ method} Defined in Table \ref{untransdefs}. Although this method is attributed to Edgington \citep{edgington72b} when the phrase Edgington's method is used it refers to the method of summation of $p$--values described above in Section \ref{sump}. As can be seen in Figure \ref{unequalp} this method returns a value for our $p_i=p$ example which decreases with $k$ when $p$ below 0.5 and increases above. Not surprisingly this method gives very similar results to Edington's other method implemented in \func{sump} and since it does not have the numerical problems of that method it might perhaps be preferred. \subsubsection{Examples for methods using untransformed $p$--values} Using the same example dataset which we have already plotted and our cancellation dataset we have the values in Table \ref{untransexamples}. As can be seen \func{meanp} and \func{sump} cancel but the other two do not. Agreement here is not so good especially for the maximum p method. Wilkinson's method not shown as it depends on the value of $r$. \begin{table}[htbp] \begin{tabular}{lrl} Function name & \multicolumn{1}{c}{validity} & \multicolumn{1}{c}{cancel} \\ & \multicolumn{1}{c}{value expressed} \\ & \multicolumn{1}{c}{as $-\log_{10}p$} \\[1ex] \\[1ex] \func{minimump} & \Sexpr{log10p(minimump(validity)$p)} & \Sexpr{round(minimump(cancel)$p, 5)} \\ \func{maximump} & \Sexpr{log10p(maximump(validity)$p)} & \Sexpr{round(maximump(cancel)$p, 5)} \\ \func{meanp} & \Sexpr{log10p(meanp(validity)$p)} & \Sexpr{meanp(cancel)$p}\\ \func{sump} & \Sexpr{log10p(sump(validity)$p)} & \Sexpr{sump(cancel)$p} \\ \end{tabular} \caption{Examples for methods using the untransformed $p$ values} \label{untransexamples} \end{table} \subsection{Other methods} \subsubsection{The method of vote--counting} A simple way of looking at the problem is vote counting. Strictly speaking this is not a method which combines $p$--values in the same sense as the other methods. If most of the studies have produced results in favour of the alternative hypothesis irrespective of whether any of them is individually significant then that might be regarded as evidence for that alternative. The numbers for and against may be compared with what would be expected under the null using the binomial distribution. A variation on this would allow for a neutral zone of studies which are considered neither for nor against. For instance one might only count studies which have reached some conventional level of statistical significance in the two different directions. This method returns a value for our $p_i=p$ example which is 1 for $p$ values above 0.5 and otherwise invariant with $p$ but decreases with $k$. This method does cancel significant values in both directions. \begin{table}[htbp] \begin{tabular}{lll} Function name & validity & cancel \\[1ex] \func{votep} & \Sexpr{round(votep(validity)$p, 6)} & \Sexpr{round(votep(cancel)$p, 5)} \\ \end{tabular} \caption{Examples for vote counting} \label{votepexamples} \end{table} \subsubsection{Methods not using all $p$--values} If there is a hypothesis that the signal will be concentrated in only a few $p$--values then alternative methods are available in \func{truncated}. This is a wrapper to two packages available on CRAN: \pkg{TFisher} which provides the truncated Fisher method \citep{zaykin07,zhang18} and \pkg{mutoss} which provides the rank--truncated Fisher method \citep{dudbridge03}. Note that Table \ref{truncatedexamples} only shows results for the validity data--set as, since the methods explicitly only consider results in one direction the cancellation issue does not arise. \begin{table}[htbp] \begin{tabular}{lll} Function name & truncated at $p$ = 0.5 & truncated at rank = 5 \\[1ex] \func{truncated} & \Sexpr{log10p(truncated(validity, ptrunc = 0.5)$p)} & \Sexpr{log10p(truncated(validity, rtrunc = 5)$p)} \\ \end{tabular} \caption{Examples for truncated using the validity data--set expressed as $-\log_{10}p$} \label{truncatedexamples} \end{table} These methods are appropriate for the situation where it is known that many of the $p$--values are noise and there will only be a few signals. \section{Loughin's recommendations} In his simulation study \citet{loughin04} carried out extensive comparisons. Note that he did not consider all the methods implemented here. These omissions are not too important for our purposes. The methods implemented here as \func{invchisq}, \func{invt}, \func{meanp} and \func{meanz} are all very similar to ones which he did study. The truncation methods appeared about the same time as his work but in any case are fundamentally different. Vote counting is arguably not a method of the same sort. As Loghin points out the first thing to consider is whether large $p$--values should cancel small ones. If this is not desired then the only methods to consider are those in \func{sumlog} (Fisher), \func{minimump} (Tippett) and \func{maximump}. \mypdf{struct}{Loughin's recommendations based on structure}{struct}{[height=6cm,width=8cm]} He bases his recommendations on criteria of structure and the arrangement of evidence against $H_0$. Figure \ref{struct} shows a summary of his recommendations about the structure of the evidence. \mypdf{strength}{Loughin's recommendations based on where the strength of the evidence is located}{strength}{[height=8cm,width=12cm]} Figure \ref{strength} summarise his recommendations about the arrangement of evidence. Overall he considered the choice to lie between Stouffer's method, Fisher's method and the logistic method implemented in \func{logitp}. As has already been mentioned Fisher's method cancels whereas the other two do not so if the weak evidence in a small number of $p$--values is not to be over--whelmed by the others then Fisher is the best choice. However where the evidence is more evenly spread Stouffer's method may be preferred. The logistic method represents a compromise between them and is perhaps best suited where the pattern of evidence is not clear in advance. The other methods are not universally ruled out and may be helpful in the specific circumstance outlined in his summaries. \bibliography{metap} \bibliographystyle{plainnat} \end{document} metap/inst/doc/struct.gv0000644000176200001440000000175513576717030015005 0ustar liggesusersdigraph test { rankdir = "LR" fontname = "Helvetica" node[fontname = "Helvetica"] edge[fontname = "Helvetica"] structure [label = "What\nis\nstructure?", shape=diamond] small [label = <
sumlog (Fisher)
minimump (Tippett)
>] large [label = <
sump (Edgington)
maximump
>] equal [label = <
sumz (Stouffer)
logitp
>] structure -> small [label = "Emphasise small p-values"] structure -> large [label = "Emphasise large p-values"] structure -> equal [label = "Emphasise p-values equally"] } metap/inst/doc/metap.Rnw0000644000176200001440000001725114163334232014707 0ustar liggesusers\documentclass[12pt]{article} \usepackage{amsmath,amssymb} %\usepackage{mydef2} \usepackage[round]{natbib} \usepackage{parskip,url} \usepackage{graphicx,subfig} \setlength{\topmargin}{0cm} \addtolength{\textheight}{2cm} %\lhead{} %\input{title} %\VignetteIndexEntry{Introduction to the metap package} \title{Introduction to the \pkg{metap} package} \author{Michael Dewey} \newcommand{\pkg}[1]{\texttt{#1}} \newcommand{\func}[1]{\texttt{#1}} \newcommand{\code}[1]{\texttt{#1}} \newcommand{\codefont}{\footnotesize} \newcommand{\mygraph}[3]{% \begin{figure}[htbp] \includegraphics[height=6cm,width=10cm]{#1} \caption{#2} \label{#3} \end{figure} } \newcommand{\twograph}[8]{% \begin{figure}[htbp] \subfloat[#2\label{#3}]{\includegraphics[height=6cm,width=7cm]{#1}}% \subfloat[#5\label{#6}]{\includegraphics[height=6cm,width=7cm]{#4}} \caption{#7} \label{#8} \end{figure} } \begin{document} \maketitle \section{Introduction} \subsection{What is this document for?} This document describes some methods for the meta--analysis of $p$--values (significance values) and their implementation in the package \pkg{metap}. I welcome feedback about sources of published examples against which I can test the code and any other comments about either the documentation or the code. The problem of meta--analysis of $p$--values is of course not completely unconnected with the more general issue of simultaneous statistical inference. \subsection{Why and when to meta--analyse significance values} The canonical way to meta--analyse a number of primary studies uses estimates of effect sizes from each of them. There are a large number of packages for this purpose available from CRAN and described in the task view \url{http://CRAN.R-project.org/view=MetaAnalysis}. However sometimes the only available information may be $p$--values especially when some of the primary studies were published a long time ago or were published in sources which were less rigorous about insisting on effect sizes. The methods outlined here are designed for this eventuality. The situation may also arise that some of the studies can be combined in a conventional meta--analysis using effect sizes but there are many others which cannot and in that case the conventional meta--analysis of the subset of studies which do have effect sizes may usefully be supplemented by an overall analysis of the $p$--values. Just for the avoidance of doubt, if each study has produced a proportion and the goal is to synthesise them to a common estimate or analyse the differences between them then the standard methods are appropriate not the ones outlined here. The $p$--values in this document are significance levels. The methods are referred to by the name of the function in \func{metap}. Table \ref{funcs} shows other descriptions of each method. \begin{table}[htbp] \begin{tabular}{lll} Function name & \multicolumn{2}{c}{Description(s)} \\[1ex] & \multicolumn{1}{c}{Eponym} \\ \func{invchisq} & Lancaster's method & Inverse chi square \\ \func{invt} & & Inverse t \\ \func{logitp} & & Logistic\\ \func{meanp} \\ \func{meanz} \\ \func{maximump} \\ \func{minimump} & Tippett's method \\ \func{sumlog} & Fisher's method & Chi square (2 df)\\ \func{sump} & Edgington's method & Uniform\\ \func{sumz} & Stouffer's method & Normal\\ \func{truncated} & Truncated Fisher & rank--truncated\\ \func{votep} \\ \func{wilkinsonp} & Wilkinson's method \\ \end{tabular} \caption{Methods considered in this document} \label{funcs} \end{table} \section{Preparation for meta--analysis of $p$--values} \subsection{Preliminaries} I assume you have installed \textsf{R} and \pkg{metap}. You then need to load the package. <<>>= library(metap) @ \subsection{Directionality} It is usual to have a directional hypothesis, for instance that treatment is better than control. For the methods described here a necessary preliminary is to ensure that all the $p$--values refer to the same directional hypothesis. If the value from the primary study is two--sided it needs to be converted. This is not simply a matter of halving the quoted $p$--value as values in the opposite direction need to be reversed. A convenience function \func{two2one} is provided for this. {\codefont <<>>= pvals <- c(0.1, 0.1, 0.9, 0.9, 0.9, 0.9) istwo <- c(TRUE, FALSE, TRUE, FALSE, TRUE, FALSE) toinvert <- c(FALSE, TRUE, FALSE, FALSE, TRUE, TRUE) two2one(pvals, two = istwo, invert = toinvert) @ } Note in particular the way in which $0.9$ is converted under the different scenarios. \subsection{Plotting} It would be a wise precaution to examine the $p$--values graphically or otherwise before subjecting them to further analysis. A separate vignette discusses the range of plots available in the package so here we just show the most simple. As our example we use data from studies of validity of student ratings of their instructors \citep{becker94}. The \func{plotp} provides a Q--Q plot of the $p$--values to detect departure from the uniform distribution. An example is shown in Figure \ref{plotp}. The line is the line of exact fit to the reference distribution, the uniform. The polygon is a simultaneous confidence region such that if points lie outside it we can reject the null hypothesis that the points are drawn iid from a uniform. <>= data(dat.metap) validity <- dat.metap$validity$p plotp(validity) @ \mygraph{metap-plotp}{Q--Q plot from \func{plotp}}{plotp} This plot is more informative than a simple printout. Note that this enhanced plot is only available from version 1.8 of \func{metap}. Previous versions usd a simpler plot. {\codefont <<>>= print(validity) @ } \subsection{Reporting problems in the primary studies} Another issue is what to do with studies which have simply reported on whether a conventional level of significance like 0.05 was achieved or not. If the exact associated $p$ cannot be derived from the statistics quoted in the primary source then the value of the level achieved, in this case 0.05, can be used although this may be conservative. Studies which simply report not significant could be included as having $p=1$ (or $p=0.5$ if it is known that the direction was right) although this is very conservative. The theory of handling $p$--values which have been truncated like this has been developed by \citet{zaykin02} and \func{truncated} provides a convenience wrapper for two methods available in other CRAN packages. \section{Using the methods} All the methods in the package take as their first argument the vector of $p$--values. To use Fisher's method as an example: <<>>= sumlog(validity) @ This confirms what was indeed obvious from the plot that the null hypothesis that these are drawn from a uniform distribution can be rejected. A few require extra information. Those which rely on inverse transformations often need a vector of degrees of freedom. Currently this applies to \func{invchisq} and \func{invt}. Stouffer's method in \func{sumz} optionally uses weights if a vector of weights is provided. Most of the methods (\func{invchisq, invt, logitp, meanz, sumlog, sumz, wilkinsonp}) allow as an option to return the logarithm of the $p$--value which may be useful if it is expected that the return value will be very small. A smaller number (\func{invchisq, invt, sumlog}) allow for input of log $p$--values. \section{Miscellanea} \begin{description} \item[Extractor functions] The standard \code{print} and \code{plot} methods are provided. \item[Omnibus function] A function \func{allmetap} is provided to simultaneously perform a number of the other functions. It may be useful to show how they give different results on the same data. \item[Reading] An annotated bibliography is provided by \citet{cousins08} \end{description} \bibliography{metap} \bibliographystyle{plainnat} \end{document} metap/inst/doc/compare.pdf0000644000176200001440000074556214510765337015261 0ustar liggesusers%PDF-1.5 % 1 0 obj << /Type /ObjStm /Length 3563 /Filter /FlateDecode /N 64 /First 522 >> stream x[[s6}_iIɝNf|N\IAi[Yr%:q|!Љaqw,X$Ӝ)3$fYa972xƭь &R Kd2a2G=iI2R~Ɣx3R36 ؐPT ưQ3ƍDCQ3F )fiPJ4j¤pS)ԬR H&d'W̐h jV 2Yi̺!^ԬlJD& Kj|1%blOKv?]'O\y1tw\THa΅΄1ߥw? 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y)) res } dat <- data.frame(rbind(banda(fisher, lanc4), banda(fisher, lanc16), banda(fisher, lanc256), banda(lanc4, lanc16), banda(lanc4, lanc256), banda(lanc16, lanc256) ), name = factor(c(rep("FL4", 100), rep("FL16", 100), rep("FL256", 100), rep("L4L16", 100), rep("L4L256", 100), rep("L16L256", 100)), levels = c("FL4", "FL16", "FL256", "L4L16", "L4L256", "L16L256") ) ) ################################################### ### code chunk number 6: fishlanc ################################################### lattice::xyplot(diff ~ sum | name, data = dat, panel = function(x, y, ...) { lattice::panel.xyplot(x, y, ...) lattice::panel.abline(h = mean(y), lty = 2) lattice::panel.abline(h = mean(y) + 1.96 * sd(y), lty = 3) lattice::panel.abline(h = mean(y) - 1.96 * sd(y), lty = 3) } ) ################################################### ### code chunk number 7: compare.Rnw:296-317 ################################################### stouff <- apply(temp, 1, function(x) sumz(x)$p) invt4 <- apply(temp, 1, function(x) invt(x, 4)$p) invt16 <- apply(temp, 1, function(x) invt(x, 16)$p) invt256 <- apply(temp, 1, function(x) invt(x, 256)$p) banda <- function(x, y) { res <- data.frame(sum = x + y, diff = (x - y)) res } dat <- data.frame(rbind(banda(stouff, invt4), banda(stouff, invt16), banda(stouff, invt256), banda(invt4, invt16), banda(invt4, invt256), banda(invt16, invt256) ), name = factor(c(rep("St4", 100), rep("St16", 100), rep("St256", 100), rep("t4t16", 100), rep("t4t256", 100), rep("t16t256", 100)), levels = c("St4", "St16", "St256", "t4t16", "t4t256", "t16t256") ) ) ################################################### ### code chunk number 8: stouffinvt ################################################### lattice::xyplot(diff ~ sum | name, data = dat, panel = function(x, y, ...) { lattice::panel.xyplot(x, y, ...) lattice::panel.abline(h = mean(y), lty = 2) lattice::panel.abline(h = mean(y) + 1.96 * sd(y), lty = 3) lattice::panel.abline(h = mean(y) - 1.96 * sd(y), lty = 3) } ) ################################################### ### code chunk number 9: compare.Rnw:400-402 ################################################### meanz(c(0.3, 0.31))$p meanz(c(0.1, 0.2))$p ################################################### ### code chunk number 10: compare.Rnw:438-442 ################################################### log10p <- function(x) { res <- round(-log(x, base = 10), 2) res } ################################################### ### code chunk number 11: compare.Rnw:492-501 ################################################### kvals <- c(4, 5, 6, 8, 10, 15, 20) pvals <- c(0.2, 0.3, 0.3679, 0.4, 0.5, 0.6) dat <- rbind( genvec(pvals, kvals, meanp, "meanp"), genvec(pvals, kvals, maximump, "maximump"), genvec(pvals, kvals, minimump, "minimump"), genvec(pvals, kvals, sump, "sump"), genvec(pvals, kvals, votep, "votep") ) ################################################### ### code chunk number 12: untranseqp ################################################### lattice::xyplot(g ~ k | method, groups = p, type = "l", data = dat, auto.key = list(space = "left", lines = TRUE, title = "p"), ylab = "g(p)" ) metap/inst/doc/plotmetap.Rnw0000644000176200001440000002245014210147175015604 0ustar liggesusers\documentclass[12pt]{article} \usepackage{amsmath,amssymb} %\usepackage{mydef2} \usepackage[round]{natbib} \usepackage{parskip,url} \usepackage{graphicx,subfig} \setlength{\topmargin}{0cm} \addtolength{\textheight}{2cm} \renewcommand{\topfraction}{0.85} \renewcommand{\bottomfraction}{0.5} \renewcommand{\textfraction}{0.15} \renewcommand{\floatpagefraction}{0.8} %\lhead{} %\input{title} %\VignetteIndexEntry{Plotting in the metap package} \title{Plotting in the \pkg{metap} package} \author{Michael Dewey} \newcommand{\pkg}[1]{\texttt{#1}} \newcommand{\func}[1]{\texttt{#1}} \newcommand{\code}[1]{\texttt{#1}} \newcommand{\codefont}{\footnotesize} \newcommand{\mygraph}[3]{% \begin{figure}[htbp] \includegraphics[height=6cm,width=10cm]{#1} \caption{#2} \label{#3} \end{figure} } \newcommand{\twograph}[8]{% \begin{figure}[htbp] \subfloat[#2\label{#3}]{\includegraphics[height=6cm,width=7cm]{#1}}% \subfloat[#5\label{#6}]{\includegraphics[height=6cm,width=7cm]{#4}} \caption{#7} \label{#8} \end{figure} } \begin{document} \maketitle \section{Introduction} \subsection{What is this document for?} This document describes how and why to plot $p$--values in the \pkg{metap} package. Examining the $p$--values graphically or otherwise before subjecting them to further analysis is useful to provide a visual impression of their distribution and to check for excess $p$--values at both extremes.. Three functions are provided for this purpose: \func{albatros}, \func{plotp}, and \func{schweder}. \subsection{Example datasets} As our example we use various data-sets: \begin{description} \item[\func{teachexpect}] Effect of teacher expectations on student IQ \citep{becker94} \item[\code{validity}] The validity of student ratings of their instructors \citep{becker94}. \item[\code{zhang}] The effect of the timing of exercise interventions for patients with cardiovascular disease \citep{zhang16} \end{description} {\codefont <<>>= library(metap) data(dat.metap) teach <- dat.metap$teachexpect validity <- dat.metap$validity$p zhang <- dat.metap$zhang print(validity) @ } \section{Plotting using \func{plotp}} The \func{plotp} provides a Q--Q plot of the $p$--values to detect departure from the uniform distribution. <>= plotp(validity, main = "Validity data") @ \twograph{plotmetap-plotp}{Q--Q plot from \func{plotp}}{plotp}{plotmetap-plotfunc}{Legacy Q--Q plot}{plotfunc}{Plots of validity data}{plotvalid} %\mygraph{plotmetap-plotp}{Q--Q plot from \func{plotp}}{plotp} %\mygraph{plotmetap-plotfunc}{Q--Q plot an object of class \func{metap}}{plotfunc} Figure \ref{plotp} shows the resulting plot. The line represents a fit to the uniform distribution and the polygon is a simultaneous confidence region such that if any point lies outside it we reject the null hypothesis that the points are drawn iid from a uniform. Small $p$--values are to the left of the plot The format of plot shown in Figure \ref{plotp} was first introduced in version 1.8 of \func{metap}. The previous plotting function is still available and it is possible to produce this plot by setting the \func{plotversion} parameter to "old" in the call to \func{plotp}. An example is shown in Figure \ref{plotfunc} which first calls \func{sumlog}. The legacy one will always remain an option. {\codefont <>= plotp(validity, main = "Validity data", plotversion = "old") @ } Note that the \func{plot} method for objects of class \code{"metap"} uses the new version of the plot. This change was introduced in version 1.9 of this package. There are many possible options which can be passed to the plotting function and hence to the \func{qqconf} plotting routine. The documentation for the \func{qqconf} package should be consulted for details. The \func{qqconf} package vignette is also very helpful. We will look at one of those options here though. {\codefont <>= plotp(teach) @ } {\codefont <>= plotp(teach, log10 = TRUE) @ } \twograph{plotmetap-teachlinear}{Linear scaling}{teachlinear}{plotmetap-teachlog}{Log scaling}{teachlog}{Teacher expectancy data}{teach} Figure \ref{teach} shows the teacher expectancy data using the default scaling in sub--figure \subref{teachlinear}. It is hard to see whether some of the points fall outside the boundary. However if we use the log--scaling option shown in sub--figure \subref{teachlog} it becomes much clearer. Note that the scale is reversed between the sub--plots and in \subref{teachlog} the small $p$--values are now on the right. So the cluster of points near the bottom left of the sub--figure \subref{teachlinear} are hard to distinguish as to whether they lie inside the boundary or not. In the log scaling of sub--figure \subref{teachlog} where they appear towards the top right it is much clearer that one does fall outside the boundary and two others are borderline. This reflects the fact that for most of the methods in the \func{metap} package the overall $p$--value is below 0.05. For instance using the logit method we have {\codefont <<>>= logitp(teach) @ } \section{Plotting using \func{schweder}} A function \func{schweder} provides plots with a variety of informative lines superimposed. It plots the ordered $p$--values, $p_{[i]}: p_{[1]} \le \dots{} p_{[2]} \le \dots{} p_{[i]} \dots{} \le p_{[k-1]} \le p_{[k]}$, against $i$. Although the original motivation for the plot is \citet{schweder82} the function uses a different choice of axes due to \citet{benjamini00}. We will use an example dataset on the validity of student ratings quoted in \citet{becker94}. Figure \ref{simple} shows the plot from \func{schweder}. <>= schweder(validity) @ \func{schweder} also offers the possibility of drawing one of a number of straight line summaries. The three possible straight line summaries are shown in Figure \ref{withlines} and are: \begin{itemize} \item the lowest slope line of Benjaimin and Hochberg which is drawn by default as solid, \item a least squares line drawn passing through the point $k+1, 1$ and using a specified fraction of the points which is drawn by default as dotted, \item a line with user specified intercept and slope which is drawn by default as dashed. \end{itemize} <>= schweder(validity, drawline = c("bh", "ls", "ab"), ls.control = list(frac = 0.5), ab.control = list(a = 0, b = 0.01)) @ \twograph{plotmetap-simple}{Simple graph}{simple}{plotmetap-withlines}{With lines}{withlines}{Output from schweder}{schweder} \section{The albatros plot} The albatros plot was introduced in \citet{harrison17} which should be consulted for more details. Basically it consists of plotting a possibly transformed sample size against the transformed $p$--values. The default is to use $\sqrt{N}$ for the $y$--axis and a log transformation for the $x$--axis. The plot also contains contours of constant effect size. A number of possible options are available for effect size type: correlation, standardised mean difference, and odds ratio. <>= validity <- dat.metap$validity fit.v <- albatros(validity$p, validity$n, contours = list(type = "corr", contvals = c(0.25, 0.5, 0.8), ltys = 1:3), axes = list(ylimit = c(1,200), lefttext = "Negative correlation", righttext = "Positive correlation"), main = "Validity") @ \mygraph{plotmetap-albatros}{Albatros plot from of the validity data}{albatros} Figure \ref{albatros} shows the result. Most of the points clearly correspond to positive and substantial correlations although a few are in the opposite direction although not far from the null value (0.5). If the actual effect sizes are available it would be better to use one of the conventional methods for meta--analysing them rather than rely on this method but \citet{harrison17} outline possible use cases. If the studies come from different groups where one might use meta--regression with a moderator for group membership if one had the effect sizes then the albatros plot can display the points using different symbols for groups. This would enable a visual check on whether the groups differed. <>= fit.z <- albatros(zhang$p, zhang$n, contours = list(type = "smd", contvals = c(0.25, 0.5, 1), ltys = 1:3), plotpars = list(pchs = letters[unclass(dat.metap$zhang$phase)]), axes = list(lefttext = "Favours control", righttext = "Favours exercise"), main = "Zhang" ) @ \mygraph{plotmetap-zhang}{Albatros plot of the Zhang et al data}{zhang} Figure \ref{zhang} shows an example using the Zhang et al data-set. The studies involved come from three groups corresponding to three different periods o initiation of exercise. The points are labelled accordingly: "a" initiation during the acute phase, "b" during the healing phase and "c" during the healed phase. The difference between the groups is quite clear here. In fact in \citet{zhang16} the results are handled with stratification into three separate analyses and meta--regression was not used. If some studies had given effect sizes but others did not then an albatros plot with the points marked for group membership and with appropriate contour lines would provide a visual check on whether the unavailable effect sizes were similar to the available ones. \bibliography{metap} \bibliographystyle{plainnat} \end{document} metap/inst/doc/strength.gv0000644000176200001440000000622213576717176015324 0ustar liggesusersdigraph test { rankdir = "LR" fontname = "Helvetica" node[fontname = "Helvetica"] edge[fontname = "Helvetica"] {rank = same; eqklt10; eqany; someklt10; someany; majority; modst; anypower; strongtot; modtot; weaktot;} evidence [label = "Location\nof\nevidence", shape = diamond] eqinall [label = "N\nof\nstudies", shape = diamond] evidence -> eqinall [label = "Equally in all"] eqklt10 [label = <
sump (Edgington)
maximump
>] eqany [label = <
sumz (Stouffer)
logitp
>] eqinall -> eqklt10 [label = "< 10"] eqinall -> eqany [label = "any"] someinall [label = "N\nof\nstudies", shape = diamond] evidence -> someinall [label = "Some in all"] someklt10 [label = <
sump (Edgington)
maximump
>] someany [label = <
sumz (Stouffer)
logitp
>] someinall -> someklt10 [label = "< 10"] someinall -> someany [label = "any"] majority [label = <
sumz (Stouffer)
logitp
>] evidence -> majority [label = "In the majority"] minority [label = "Strength\nof\nevidence", shape = diamond] evidence -> minority [label = "In the minority"] modst [label = <
sumlog (Fisher)
>] anypower [label = <
sumz (Stouffer)
logitp
>] minority -> modst [label = "Moderate or strong"] minority -> anypower [label = "Any power"] onetest [label = "Strength\nof\ntotal evidence", shape = diamond] evidence -> onetest [label = "In one test only"] strongtot [label = <
minimump (Tippett)
>] modtot [label = <
sumlog (Fisher)
>] weaktot [label = <
sumz (Stouffer)
logitp
>] onetest -> strongtot [label = "Strong total evidence"] onetest -> modtot [label = "Moderate total evidence"] onetest -> weaktot [label = "Weak total evidence"] } metap/inst/CITATION0000644000176200001440000000002714506265665013510 0ustar liggesuserscitation(auto = meta)