DESeq/DESCRIPTION0000644000175500017550000000207313556150211014252 0ustar00biocbuildbiocbuildPackage: DESeq Version: 1.39.0 Title: Differential gene expression analysis based on the negative binomial distribution Author: Simon Anders, EMBL Heidelberg Maintainer: Simon Anders Imports: genefilter, geneplotter, methods, MASS, RColorBrewer Depends: BiocGenerics (>= 0.7.5), Biobase (>= 2.21.7), locfit, lattice Suggests: pasilla (>= 0.2.10), vsn, gplots Description: Estimate variance-mean dependence in count data from high-throughput sequencing assays and test for differential expression based on a model using the negative binomial distribution License: GPL (>= 3) URL: http://www-huber.embl.de/users/anders/DESeq Collate: class_and_slots.R core.R methods.R plotDispEsts.R welcome.R biocViews: ImmunoOncology, Sequencing, ChIPSeq, RNASeq, SAGE, DifferentialExpression git_url: https://git.bioconductor.org/packages/DESeq git_branch: master git_last_commit: e51de49 git_last_commit_date: 2019-10-29 Date/Publication: 2019-10-29 NeedsCompilation: yes Packaged: 2019-10-29 23:51:37 UTC; biocbuild DESeq/NAMESPACE0000644000175500017550000000175313554551773014007 0ustar00biocbuildbiocbuildimport( BiocGenerics ) import( Biobase ) import( lattice ) importFrom( genefilter, rowVars ) importFrom( geneplotter, multiecdf ) importFrom( RColorBrewer, brewer.pal ) useDynLib( DESeq, calc_pvals ) exportClasses( "CountDataSet" ) exportMethods( counts, "counts<-", sizeFactors, "sizeFactors<-", conditions, "conditions<-", dispTable, "dispTable", estimateSizeFactors, estimateDispersions ) export( newCountDataSet, estimateVarianceFunctions, # defunct varianceFitDiagnostics, # defunct residualsEcdfPlot, # defunct nbinomTest, getBaseMeansAndVariances, nbinomTestForMatrices, estimateSizeFactorsForMatrix, scvPlot, # defunct getVarianceStabilizedData, varianceStabilizingTransformation, makeExampleCountDataSet, adjustScvForBias, fitNbinomGLMsForMatrix, fitNbinomGLMs, nbkd.sf, nbinomGLMTest, dispTable, fitInfo, plotDispEsts, plotMA, plotPCA, newCountDataSetFromHTSeqCount ) DESeq/NEWS0000644000175500017550000001462213554551773013266 0ustar00biocbuildbiocbuildversion 1.9.12: (2012-09-05) - added function newCountDataSetFromHTSeqCount version 1.9.7: (2012-05-25) - fixed handling of rank-deficient observations now also in estimateDispersions version 1.9.6: - fixed that varianceStabilizingTransformation was missing in exports version 1.9.5: - added function plotDispEsts version 1.9.4: (2012-04-24) - fixed handling of rank-deficient observations version 1.9.2: (2012-04-05) - fixed bug in pooled-CR dispersion estimation version 1.9.1: (2012-04-01) - Added a new function 'varianceStabilizingTransformation' version 1.7.10: (2011-03-26) - Added pooled-CR method. - Fixed error message for insufficient replication. version 1.7.9: (2011-03-16) - Fixed error in vignette. - Silenced warnings from nbinomFitGLM about convergence; this information is given in the result anyway. version 1.7.8: (2011-03-15) - The VST is now roughly equal to log2 for local dispersion fits, too. version 1.7.7: (2011-03-15) - changed the variance stabilizing transformation once more; this time it is hopefully correct. The derivation of the formula is now documented in the new file vst.pdf. version 1.7.6: - fixed regression bug in getVarianceStabilizedData: the formula for parametric dispersion fit was wrong since I "fixed" the factor to get log2 asymptotic behaviour. version 1.7.1 - 1.7.5: - various changes to vignette by whuber version 1.6.0 / 1.7.0: (Summary of important changes between Bioc release 2.8 to 2.9) - changes to dispersion estimation scheme to improve handling of outliers (see vignette for details) - refactorized the workflow and overhauled and expanded the vignette (see there for changes to user interface) - various changes and bug fixes (see appendix in vignette and NEWS file) version 1.5.29: (2011-10-10) - fixed a bug in parametricDispersionFit. (Thanks to Alejandro Reyes for spotting and fixing this one.) version 1.5.27: (2011-10-18) - method="pooled" is now default in estimateDispersions - added 'fitInfo' accessor function version 1.5.24: (2011-08-10) - fitNbinomGLM no longer stops when glm.fit throws an error version 1.5.23: (2011-07-14) - fixed bug in 'nbinomTest' again; now using a symmetric two-tailed test (i.e., the one-tailed p value is doubled) - added warning in case of method='blind' if not used together with sharingMode='fit-only' version 1.5.22: (2011-07-14) - fixed bug in 'nbinomTest' that led to wrong p values for dispersions larger than 1 version 1.5.21: (2011-07-14) - minor changes to vignette version 1.5.20: (2011-07-07) - fixed bug in 'getVarianceStabilizedData' - more informative error message if parametric fit fails versions 1.5.1 to 1.5.19: (2011-06 / 2011-07) refactorized the way how dispersion estimation is handled, overhauled the vignette - vignette now uses data from 'pasilla' package as example - GLMs explained in vignette - 'estimateVarianceFunctions' renamed to 'estimateDispersions' - estimateDispersions now stores intermediate results in 'fitInfo' slot - new functionality for 'estimateDispersion': 'sharingMode' option with new sharing modes 'maximum' and 'gene-est-only'; 'fitType' with new fitting type 'parametric'; changed defaults for these; new method 'pooled-CR' to do edgeR-style CR estimation etc. - several diagnostic functions removed - lots of further small changes version 1.3.3: (2011-03-08) - added 'locfunc' argument to 'estimateSizeFactor' and 'estimateSizeFactorForMatrix' version 1.3.2: (2011-03-08) - added 'glmControl' argument to 'nbinomFitGLM' and 'nbinomGLMsForMatrix' version 1.3.2: (2011-02-11) - updated CITATION version 1.1.13: (2010-09-06) - corrected the sometimes missing names attribute in rawVarFuncTable version 1.1.12: (2010-09-06) - fixed a bug in the 'resVarB' column of the result of 'nbinomTest'. version 1.1.11: (2010-08-17) - fixed a bug in getVarianceStabilizedData; it failed to preserve normalization. This is because the transformation function for each sample were different if the size factors differed. The function now uses an average size factor. However, the veriance stabilizing transformation is still not perfect: the variance still increases slightly with the mean. This needs a bit more work As an alternative to judge similarity of samples, I have added two new functions, getRawScvForSamplePair and getRawScvDistanceMatrix. See their help pages. version 1.1.10: (2010-08-17) - fixed bug in makeExampleCountDataSet: colnames were wrong version 1.1.9: (2010-07-21) - removed the variance adjustment factors introduced earlier; they caused more trouble than they were worth. version 1.1.8: (2010-07-09) - GLM functionality added but not yet documented version 1.1.7: (2010-06-05) - no change, just bumped version number as the build server seemed to have gotten confused version 1.1.6: (2010-06-02) - changed arguments for estimateVarianceFunctionsin preparation for a planned new feature; instead of pool=FALSE or pool=TRUE, use method="normal" or method="blind". version 1.1.5: (2010-06-01) - fixed a small bug that caused p values to sometimes slighly exceed 1.0 due to rounding errors version 1.1.4: (2010-05-15) - corrected a serious documentation bug: the effect of the variance adjustment factors was described the wrong way round - changed scvPlot: now does a bias correction by default version 1.1.3: (2010-05-06) - added a CITATION file version 1.1.2: (2010-05-03) - replaced the C function to calculate the p values. The new version is now a bit more conservative with its approximation, trying to ensure that p values are always rather approximated as too high. Furthermore, it considers the values 0 and kS as critical points, too, which makes a difference at very high overdispersion. - changed the default value for the accuracy guidance 'eps' from 3e-3 to 1e-4, as the former seemed to have been a bit too high. (The approximation broke down in rare cases.) - The 'eps' parameter is now exposed in 'nbinomTest' as well. version 1.1.1: (2010-04-29) - added "variance adjustment factors" in order to allow for manual scaling of the raw variance estimate in case that the residual ECDF plots indicate a bad fit - fixed a bug which caused the resVarB column of the data frame returned by nbinomTest to be wrong - changed the scvPlot function to now show conditions rather than raw variance functions - changed the way how 'rawVarFunc' interprets its second argument - updated the vignette DESeq/R/0000755000175500017550000000000013554551773012763 5ustar00biocbuildbiocbuildDESeq/R/class_and_slots.R0000644000175500017550000001341513554551773016265 0ustar00biocbuildbiocbuildsetClass( "CountDataSet", contains = "eSet", representation = representation( fitInfo = "environment", dispTable = "character", multivariateConditions = "logical" ), prototype = prototype( new( "VersionedBiobase", versions = c( classVersion("eSet"), CountDataSet = "1.1.0" ) ) ) ) newCountDataSet <- function( countData, conditions, sizeFactors=NULL, phenoData = NULL, featureData = NULL ) { countData <- as.matrix( countData ) if( any( round( countData ) != countData ) ) stop( "The countData is not integer." ) mode( countData ) <- "integer" if( is.null( sizeFactors ) ) { sizeFactors <- rep( NA_real_, ncol(countData) ) } else warning( "The 'sizeFactor' argument is deprecated. Use 'estimateSizeFactors'." ) if( is.null( phenoData ) ) phenoData <- annotatedDataFrameFrom( countData, byrow=FALSE ) if( is.null( featureData ) ) featureData <- annotatedDataFrameFrom( countData, byrow=TRUE ) phenoData$`sizeFactor` <- sizeFactors varMetadata( phenoData )[ "sizeFactor", "labelDescription" ] <- "size factor (relative estimate of sequencing depth)" if( is( conditions, "matrix" ) ) conditions <- as.data.frame( conditions ) if( is( conditions, "data.frame" ) || is( conditions, "AnnotatedDataFrame" ) ) { stopifnot( nrow( conditions ) == ncol( countData ) ) conditions <- as( conditions, "AnnotatedDataFrame" ) dimLabels( conditions ) <- dimLabels( phenoData ) rownames( pData(conditions) ) <- rownames( pData(phenoData) ) # TODO: What if the rownames were set? phenoData <- combine( phenoData, conditions ) multivariateConditions <- TRUE rvft <- c( `_all` = NA_character_ ) } else { conditions <- factor( conditions ) stopifnot( length( conditions ) == ncol( countData ) ) phenoData$`condition` <- factor( conditions ) varMetadata( phenoData )[ "condition", "labelDescription" ] <- "experimental condition, treatment or phenotype" multivariateConditions <- FALSE rvft <- rep( NA_character_, length(levels(conditions)) ) } cds <- new( "CountDataSet", assayData = assayDataNew( "environment", counts=countData ), phenoData = phenoData, featureData = featureData, multivariateConditions = multivariateConditions, fitInfo = new.env( hash=TRUE ), dispTable = rvft ) cds } setValidity( "CountDataSet", function( object ) { if( length( object@multivariateConditions ) != 1 ) return( "multivariateConditions is not scalar." ) if( ! "sizeFactor" %in% names(pData(object)) ) return( "phenoData does not contain a 'sizeFactor' columns.") if( ! is( pData(object)$`sizeFactor`, "numeric" ) ) return( "The 'sizeFactor' column in phenoData is not numeric." ) if( ! object@multivariateConditions ) { if( ! "condition" %in% names(pData(object)) ) return( "phenoData does not contain a 'condition' columns." ) if( ! is( pData(object)$`condition`, "factor" ) ) return( "The 'condition' column in phenoData is not a factor." ) } if( !is.integer( counts(object) ) ) return( "the count data is not in integer mode" ) if( any( counts(object) < 0 ) ) return( "the count data contains negative values" ) TRUE } ) setMethod("counts", signature(object="CountDataSet"), function(object, normalized=FALSE ) { if(!normalized) { assayData(object)[["counts"]] } else { if(any(is.na( sizeFactors(object)))) { stop( "Please first calculate size factors or set normalized=FALSE") } else { t(t( assayData(object)[["counts"]] ) / sizeFactors(object) ) } } }) setReplaceMethod("counts", signature(object="CountDataSet", value="matrix"), function( object, value ) { assayData(object)[[ "counts" ]] <- value validObject(object) object }) setMethod("sizeFactors", signature(object="CountDataSet"), function(object) { sf <- pData(object)$sizeFactor names( sf ) <- colnames( counts(object) ) sf }) setReplaceMethod("sizeFactors", signature(object="CountDataSet", value="numeric"), function( object, value ) { pData(object)$sizeFactor <- value validObject( object ) object }) setMethod("conditions", signature(object="CountDataSet"), function( object, ... ) { if(length(list(...))!=0) warning("in conditions: Ignoring second and/or further arguments.") if( object@multivariateConditions && !("condition" %in% colnames(pData(object)))) stop( "Could not find 'condition' column in pData." ) conds <- pData(object)$`condition` names( conds ) <- colnames( counts(object) ) conds }) setReplaceMethod("conditions", signature(object="CountDataSet"), function( object, value ) { if( object@multivariateConditions ) stop( "The 'conditions<-' accessor is only for simple single-factor conditions, but you have specified multivariate conditions. Access them via 'pData<-'." ) pData(object)$`condition` <- factor( value ) validObject( object ) object }) setMethod("dispTable", signature(object="CountDataSet"), function( object ) { object@dispTable }) setReplaceMethod("dispTable", signature(object="CountDataSet"), function( object, value ) { object@dispTable <- value validObject( object ) object }) fitInfo <- function( cds, name=NULL ) { stopifnot( is( cds, "CountDataSet" ) ) if( length( ls( cds@fitInfo ) ) == 0 ) stop( "No fits available. Call 'estimateDispersions' first." ) if( length( ls( cds@fitInfo ) ) > 1 && is.null(name) ) stop( "More than one fitInfo object available. Specify by name. (See 'ls(cds@fitInfo)' for a list.)" ) if( length( ls( cds@fitInfo ) ) == 1 && is.null(name) ) name = ls( cds@fitInfo )[ 1 ] cds@fitInfo[[ name]] } DESeq/R/core.R0000644000175500017550000003221013554551773014034 0ustar00biocbuildbiocbuildestimateSizeFactorsForMatrix <- function( counts, locfunc = median ) { loggeomeans <- rowMeans( log(counts) ) apply( counts, 2, function(cnts) exp( locfunc( ( log(cnts) - loggeomeans )[ is.finite(loggeomeans) ] ) ) ) } getBaseMeansAndVariances <- function( counts, sizeFactors ) { # Divides the counts by sizeFactors and calculates the estimates for # base means and variances for each gene. data.frame( baseMean = rowMeans( t( t(counts) / sizeFactors ) ), baseVar = rowVars( t( t(counts) / sizeFactors ) ) ) } modelMatrixToConditionFactor <- function( modelMatrix ) { nr = nrow(modelMatrix) if(nr<2) stop("nrow(modelMatrix) must be >=2.") mmconds <- 1:nr for( i in 2:nr ) for( j in 1:(i-1) ) if( all( modelMatrix[i,] == modelMatrix[j,] ) ) { mmconds[i] = mmconds[j] break } factor( as.integer( factor( mmconds ) ) ) } getBaseMeansAndPooledVariances <- function( counts, sizeFactors, conditions ) { basecounts <- t( t(counts) / sizeFactors ) replicated_sample <- conditions %in% names(which(table(conditions)>1)) df <- sum(replicated_sample) - length( unique( conditions[ replicated_sample ] ) ) data.frame( baseMean = rowMeans( basecounts ), baseVar = rowSums( sapply( tapply( ( seq_len(ncol(counts)) )[ replicated_sample ], factor( conditions[ replicated_sample ] ), function(cols) rowSums( ( basecounts[,cols] - rowMeans(basecounts[,cols]) )^2 ) ), identity ) ) / df ) } parametricDispersionFit <- function( means, disps ) { coefs <- c( .1, 1 ) iter <- 0 while(TRUE) { residuals <- disps / ( coefs[1] + coefs[2] / means ) good <- which( (residuals > 1e-4) & (residuals < 15) ) fit <- glm( disps[good] ~ I(1/means[good]), family=Gamma(link="identity"), start=coefs ) oldcoefs <- coefs coefs <- coefficients(fit) if( !all( coefs > 0 ) ) stop( "Parametric dispersion fit failed. Try a local fit and/or a pooled estimation. (See '?estimateDispersions')" ) if( sum( log( coefs / oldcoefs )^2 ) < 1e-6 ) break iter <- iter + 1 if( iter > 10 ) { warning( "Dispersion fit did not converge." ) break } } names( coefs ) <- c( "asymptDisp", "extraPois" ) ans <- function( q ) coefs[1] + coefs[2] / q attr( ans, "coefficients" ) <- coefs ans } estimateAndFitDispersionsFromBaseMeansAndVariances <- function( means, variances, sizeFactors, fitType = c( "parametric", "local" ), locfit_extra_args=list(), lp_extra_args=list(), adjustForBias=TRUE ) { fitType <- match.arg( fitType ) xim <- mean( 1/sizeFactors ) dispsAll <- ( variances - xim * means ) / means^2 variances <- variances[ means > 0 ] disps <- dispsAll[ means > 0 ] means <- means[ means > 0 ] if( adjustForBias ) disps <- adjustScvForBias( disps, length( sizeFactors ) ) if( fitType == "local" ) { fit <- do.call( "locfit", c( list( variances ~ do.call( "lp", c( list( log(means) ), lp_extra_args ) ), family = "gamma" ), locfit_extra_args ) ) rm( means ) rm( variances ) if( adjustForBias ) ans <- function( q ) adjustScvForBias( pmax( ( safepredict( fit, log(q) ) - xim * q ) / q^2, 1e-8 ), length(sizeFactors) ) else ans <- function( q ) pmax( ( safepredict( fit, log(q) ) - xim * q ) / q^2, 1e-8 ) # Note: The 'pmax' construct above serves to limit the overdispersion to a minimum # of 10^-8, which should be indistinguishable from 0 but ensures numerical stability. } else if( fitType == "parametric" ) { ans <- parametricDispersionFit( means, disps ) } else stop( "Unknown fitType." ) attr( ans, "fitType" ) <- fitType list( disps=dispsAll, dispFunc=ans ) } profileLogLikelihood <- function( disp, mm, y, muhat ) { # calculate the log likelihood: if(length(disp) != length(y)){ disp <- rep(disp, length(y)) } ll <- sum( sapply( seq(along=y), function(i) dnbinom( y[i], mu=muhat[i], size=1/disp[i], log=TRUE ) ) ) # transform the residuals, i.e., y - muhat, to the linear # predictor scale by multiplying them with the derivative # of the link function, i.e., by 1/muhat, and add this to the # linear predictors, log(muhat), to get the predictors that # are used in the IWLS regression z <- log(muhat) + ( y - muhat ) / muhat # the variance function of the NB is as follows v0 <- muhat + disp * muhat^2 # transform the variance vector to linear predictor scale by # multiplying with the squared derivative of the link to # get the (reciprocal) weights for the IWLS w <- 1 / ( ( 1 / muhat )^2 * v0 ) # All we need from the IRLS run is the QR decomposition of # its matrix qrres <- qr( mm*sqrt(w) ) # from it, we extract we leverages and calculate the Cox-Reid # term: cr <- sum( log( abs( diag( qrres$qr )[ seq_len(qrres$rank) ] ) ) ) # return the profile log likelihood: ll - cr } estimateAndFitDispersionsWithCoxReid <- function( counts, modelFormula, modelFrame, sizeFactors, fitType = c( "parametric", "local" ), locfit_extra_args=list(), lp_extra_args=list(), initialGuess=.1 ) { if( as.character(modelFormula[2]) == "count" ) modelFormula <- modelFormula[-2] # the '[-2]' removes the lhs, i.e., the response mm <- model.matrix( modelFormula, modelFrame ) disps <- apply( counts, 1, function( y ) { fit <- try( glm.fit( mm, y, family=MASS::negative.binomial( initialGuess ), offset=log(sizeFactors) ), silent=TRUE ) if( inherits( fit, "try-error" ) ) NA else { if( df.residual(fit) == 0 ) stop( "No residual degrees of freedom. Most likely the design is lacking sufficient replication." ) exp( optimize( function(logalpha) profileLogLikelihood( exp(logalpha), mm, y, fitted.values(fit) ), log( c( 1e-11, 1e5 ) ), maximum=TRUE )$maximum ) } } ) means <- colMeans( t(counts) / sizeFactors ) xim <- mean( 1/sizeFactors ) if( fitType == "local" ) { fit <- do.call( "locfit", c( list( disps[means>0] ~ do.call( "lp", c( list( log(means[means>0]) ), lp_extra_args ) ), family = "gamma" ), locfit_extra_args ) ) rm( means ) ans <- function( q ) pmax( ( safepredict( fit, log(q) ) - xim * q ) / q^2, 1e-8 ) # Note: The 'pmax' construct above serves to limit the overdispersion to a minimum # of 10^-8, which should be indistinguishable from 0 but ensures numerical stability. } else if( fitType == "parametric" ) ans <- parametricDispersionFit( means, disps ) else stop( "Unkknown fitType." ) attr( ans, "fitType" ) <- fitType list( disps=disps, dispFunc=ans ) } safepredict <- function( fit, x ) { # A wrapper around predict to avoid the issue that predict.locfit cannot # propagate NAs and NaNs properly. res <- rep.int( NA_real_, length(x) ) res[ is.finite(x) ] <- predict( fit, x[is.finite(x)] ) res } nbinomTestForMatrices <- function( countsA, countsB, sizeFactorsA, sizeFactorsB, dispsA, dispsB ) { kAs <- rowSums( cbind(countsA) ) kBs <- rowSums( cbind(countsB) ) mus <- rowMeans( cbind( t( t( countsA ) / sizeFactorsA ), t( t( countsB ) / sizeFactorsB ) ) ) fullVarsA <- pmax( mus * sum( sizeFactorsA ) + dispsA * mus^2 * sum(sizeFactorsA^2), mus * sum( sizeFactorsA ) * (1+1e-8) ) fullVarsB <- pmax( mus * sum( sizeFactorsB ) + dispsB * mus^2 * sum(sizeFactorsB^2), mus * sum( sizeFactorsB ) * (1+1e-8) ) sumDispsA <- ( fullVarsA - mus * sum( sizeFactorsA ) ) / ( mus * sum( sizeFactorsA ) )^2 sumDispsB <- ( fullVarsB - mus * sum( sizeFactorsB ) ) / ( mus * sum( sizeFactorsB ) )^2 sapply( seq(along=kAs), function(i) { if( kAs[i] == 0 & kBs[i] == 0 ) return( NA ) # probability of all possible counts sums with the same total count: ks <- 0 : ( kAs[i] + kBs[i] ) ps <- dnbinom( ks, mu = mus[i] * sum( sizeFactorsA ), size = 1/sumDispsA[i] ) * dnbinom( kAs[i] + kBs[i] - ks, mu = mus[i] * sum( sizeFactorsB ), size = 1/sumDispsB[i] ) # probability of observed count sums: pobs <- dnbinom( kAs[i], mu = mus[i] * sum( sizeFactorsA ), size = 1/sumDispsA[i] ) * dnbinom( kBs[i], mu = mus[i] * sum( sizeFactorsB ), size = 1/sumDispsB[i] ) stopifnot( pobs == ps[ kAs[i]+1 ] ) if( kAs[i] * sum( sizeFactorsB ) < kBs[i] * sum( sizeFactorsA ) ) numer <- ps[ 1 : (kAs[i]+1) ] else numer <- ps[ (kAs[i]+1) : length(ps) ] min( 1, 2 * sum(numer) / sum(ps) ) } ) } # Note: The following function is never called; it is here only for # documentation purposes, as it has been used to produce the data object # scvBiasCorrectionFits, which is stored in the file # inst/scvBiasCorrectionFits.rda, gets loadewd by the line after this # function and is used by the function adjustScvForBias # # To do: the correct place for this type of documentation is a vignette # prepareScvBiasCorrectionFits <- function( maxnrepl=15, mu=100000, ngenes=10000, true_raw_scv = c( seq( 0, 2, length.out=100 )[-1], seq( 2, 10, length.out=20 )[-1] ) ) lapply( 2:maxnrepl, function( m ) { est_raw_scv <- sapply( true_raw_scv, function( alpha ) { k <- matrix( rnbinom( ngenes*m, mu=mu, size=1/alpha ), ncol=m ) k <- k[ rowSums(k)>0, ] mean( rowVars(k) / rowMeans(k)^2 ) } ) locfit( true_raw_scv ~ lp( est_raw_scv, nn=.2 ) ) } ) load( system.file ( "extra/scvBiasCorrectionFits.rda", package="DESeq" ) ) adjustScvForBias <- function( scv, nsamples ) { stopifnot( nsamples > 1 ) if( nsamples - 1 > length( scvBiasCorrectionFits ) ) scv else ifelse( scv > .02, pmax( safepredict( scvBiasCorrectionFits[[ nsamples-1 ]], scv ), 1e-8 * scv ), scv ) # For scv < .02, our fit is too coarse, but no correction seems necessary anyway } nbkd.sf <- function( r, sf ) { fam <- list( family = sprintf( "nbkd,r=%g", r ), link = "log_sf", linkfun = function( mu ) log( mu/sf ), linkinv = function (eta) pmax(sf*exp(eta), .Machine$double.eps), mu.eta = function (eta) pmax(sf*exp(eta), .Machine$double.eps), variance = function(mu) mu + mu^2 / r, dev.resids = function( y, mu, wt ) 2 * wt * ( ifelse( y > 0, y * log( y / mu ), 0 ) + (r + y) * log( (r+mu)/(r+y) ) ), aic = function (y, n, mu, wt, dev) NA, # what for? initialize = expression( { n <- rep.int(1, nobs) # What is n? mustart <- y + 0.1 } ), valid.mu <- function(mu) all( mu > 0 ), valid.eta <- function(eta) TRUE, simulate <- NA ) class(fam) <- "family" fam } fitNbinomGLMsForMatrix <- function( counts, sizeFactors, rawScv, modelFormula, modelFrame, quiet=FALSE, reportLog2=TRUE, glmControl=list() ) { stopifnot( length(sizeFactors) == ncol(counts) ) stopifnot( length(rawScv) == nrow(counts) ) stopifnot( nrow(modelFrame) == ncol(counts) ) stopifnot( is( modelFormula, "formula" ) ) if( as.character( modelFormula[[1]] ) != "~" ) stop( "Formula does not have a '~' as top-level operator." ) if( as.character( modelFormula[[2]] ) != "count" ) stop( "Left-hand side of model formula must be 'count'." ) goodRows <- is.finite( rawScv ) & rowSums(counts) > 0 modelMatrix <- model.matrix( modelFormula[c(1,3)], modelFrame ) res <- t( sapply( which(goodRows), function(i) { if( !quiet & i %% 1000 == 0 ) cat( '.' ) nbfam <- nbkd.sf( 1 / rawScv[i], sizeFactors ) fit <- try( glm.fit( modelMatrix, counts[i,], family=nbfam, control = glmControl ), silent=TRUE ) if( !inherits( fit, "try-error" ) ) c( coefficients(fit), deviance = deviance(fit), df.residual = fit$df.residual, converged = fit$converged ) else { coefs <- rep( NA, ncol(modelMatrix ) ) names(coefs) <- colnames(modelMatrix) #warning( as.character( fit ) ) c( coefs, deviance = NA, df.residual = NA, converged = FALSE ) } } ) ) if( !quiet ) cat( "\n" ) df.residual <- max( na.omit( res[ , "df.residual" ] ) ) if( !all( na.omit( res[ , "df.residual" ] == df.residual ) ) ) { res[ res[ , "df.residual" ] != df.residual, "deviance" ] <- NA warning( "Some deviances set to NA due to reduction in degrees of freedom." ) } # Put in the NAs res2 <- data.frame( row.names = row.names( counts ), apply( res, 2, function( col ) { a <- rep( NA_real_, nrow(counts) ) a[goodRows] <- col a } ) ) colnames(res2) <- colnames(res) if( reportLog2 ) res2[ , seq_len(ncol(res2)-3) ] <- res2[ , seq_len(ncol(res2)-3) ] / log(2) res2$converged <- as.logical( res2$converged ) res2 <- res2[ , colnames(res) != "df.residual" ] attr( res2, "df.residual" ) <- df.residual res2 } DESeq/R/methods.R0000644000175500017550000003277313554551773014565 0ustar00biocbuildbiocbuildsetMethod("estimateSizeFactors", signature(object="CountDataSet"), function( object, locfunc=median, ... ) { if( length(list(...)) != 0 ) warning( "in estimateSizeFactors: Ignoring extra argument(s)." ) sizeFactors(object) <- estimateSizeFactorsForMatrix( counts(object), locfunc ) object }) setMethod("estimateDispersions", signature(object="CountDataSet"), function( object, method = c( "pooled", "pooled-CR", "per-condition", "blind" ), sharingMode = c( "maximum", "fit-only", "gene-est-only" ), fitType = c( "parametric", "local" ), locfit_extra_args=list(), lp_extra_args=list(), modelFrame = NULL, modelFormula = count ~ condition, ... ) { stopifnot( is( object, "CountDataSet" ) ) if( any( is.na( sizeFactors(object) ) ) ) stop( "NAs found in size factors. Have you called already 'estimateSizeFactors'?" ) method <- match.arg( method ) sharingMode <- match.arg( sharingMode ) fitType <- match.arg( fitType ) if( length(list(...)) != 0 ) warning( "in estimateDispersions: Ignoring extra argument(s)." ) if( object@multivariateConditions && ! method %in% c( "blind", "pooled", "pooled-CR" ) ) stop( "You have specified multivariate conditions (i.e., passed a data frame with conditions). In this case, you cannot use method 'per-condition'." ) if( sharingMode == "gene-est-only" ) warning( "in estimateDispersions: sharingMode=='gene-est-only' will cause inflated numbers of false positives unless you have many replicates." ) ## FIXME this warning should only be emitted when the number of replicates is indeed small. # Remove results from previous fits fData(object) <- fData(object)[ , ! colnames(fData(object)) %in% paste( "disp", object@dispTable, sep="_" ), drop=FALSE ] object@dispTable <- character() object@fitInfo = new.env( hash=TRUE ) if( method == "blind" ) { bmv <- getBaseMeansAndVariances( counts(object), sizeFactors(object) ) dispsAndFunc <- estimateAndFitDispersionsFromBaseMeansAndVariances( bmv$baseMean, bmv$baseVar, sizeFactors(object), fitType, locfit_extra_args, lp_extra_args ) object@fitInfo[[ "blind" ]] <- list( perGeneDispEsts = dispsAndFunc$disps, dispFunc = dispsAndFunc$dispFunc, fittedDispEsts = dispsAndFunc$dispFunc( bmv$baseMean ), df = ncol(counts(object)) - 1, sharingMode = sharingMode ) if( object@multivariateConditions ) dispTable(object) <- c( "_all" = "blind" ) else { a <- rep( "blind", length( levels( conditions(object) ) ) ) names(a) <- levels( conditions(object) ) object@dispTable <- a } } else if( method == "per-condition" ) { replicated <- names( which( tapply( conditions(object), conditions(object), length ) > 1 ) ) if( length( replicated ) < 1 ) stop( "None of your conditions is replicated. Use method='blind' to estimate across conditions, or 'pooled-CR', if you have crossed factors." ) nonreplicated <- names( which( tapply( conditions(object), conditions(object), length ) == 1 ) ) overall_basemeans <- rowMeans( counts( object, normalized=TRUE ) ) for( cond in replicated ) { cols <- conditions(object)==cond bmv <- getBaseMeansAndVariances( counts(object)[ , cols ], sizeFactors(object)[ cols ] ) dispsAndFunc <- estimateAndFitDispersionsFromBaseMeansAndVariances( bmv$baseMean, bmv$baseVar, sizeFactors(object)[cols], fitType, locfit_extra_args, lp_extra_args ) object@fitInfo[[ cond ]] <- list( perGeneDispEsts = dispsAndFunc$disps, dispFunc = dispsAndFunc$dispFunc, fittedDispEsts = dispsAndFunc$dispFunc( overall_basemeans ), # Note that we do not use bmv$baseMean here df = sum(cols) - 1, sharingMode = sharingMode ) } object@dispTable <- sapply( levels(conditions(object)), function( cond ) ifelse( cond %in% replicated, cond, "max" ) ) } else if( method == "pooled" || method == "pooled-CR" ) { if( method == "pooled" ) { if( object@multivariateConditions ) { if( is.null( modelFrame ) ) modelFrame <- pData(object)[ , colnames(pData(object)) != "sizeFactor" ] conds <- modelMatrixToConditionFactor( modelFrame ) } else conds <- conditions(object) if( !any( duplicated( conds ) ) ) stop( "None of your conditions is replicated. Use method='blind' to estimate across conditions, or 'pooled-CR', if you have crossed factors." ) bmv <- getBaseMeansAndPooledVariances( counts(object), sizeFactors(object), conds ) baseMeans <- bmv$baseMean dispsAndFunc <- estimateAndFitDispersionsFromBaseMeansAndVariances( bmv$baseMean, bmv$baseVar, sizeFactors(object), fitType, locfit_extra_args, lp_extra_args ) df <- ncol(counts(object)) - length(unique(conds)) } else { # method == "pooled-CR" if( is.null( modelFrame ) ) modelFrame <- pData(object)[ , colnames(pData(object)) != "sizeFactor", drop=FALSE ] baseMeans <- rowMeans( counts( object, normalized=TRUE ) ) dispsAndFunc <- estimateAndFitDispersionsWithCoxReid( counts(object), modelFormula, modelFrame, sizeFactors(object), fitType, locfit_extra_args, lp_extra_args ) df <- NA } object@fitInfo[[ "pooled" ]] <- list( perGeneDispEsts = dispsAndFunc$disps, dispFunc = dispsAndFunc$dispFunc, fittedDispEsts = dispsAndFunc$dispFunc( baseMeans ), df = df, sharingMode = sharingMode ) dt = if( object@multivariateConditions ) c( "_all" = "pooled" ) else character(0) if("condition" %in% colnames(pData(object))) { a <- rep( "pooled", length( levels( conditions(object) ) ) ) names(a) <- levels( conditions(object) ) dt = c(dt, a) } dispTable(object) = dt } else stop(sprintf("Invalid method '%s'.", method)) for( n in ls(object@fitInfo) ) fData(object)[[ paste( "disp", n, sep="_" ) ]] <- switch( sharingMode, `fit-only` = object@fitInfo[[ n ]]$fittedDispEsts, `gene-est-only` = { a <- object@fitInfo[[ n ]]$perGeneDispEsts a[ is.nan(a) ] <- 0 pmax( a, 1e-8 ) }, `maximum` = pmax( object@fitInfo[[ n ]]$fittedDispEsts, object@fitInfo[[ n ]]$perGeneDispEsts, na.rm=TRUE ), stop(sprintf("Invalid sharingMode '%s'.", sharingMode)) ) ## switch if( "max" %in% object@dispTable ) fData(object)[["disp_max"]] <- do.call( pmax, c( fData(object)[ , colnames(fData(object)) %in% paste( "disp", object@dispTable, sep="_" ), drop=FALSE ], na.rm=TRUE ) ) validObject( object ) object }) estimateVarianceFunctions <- function( ... ) .Defunct("estimateDispersions" ) varianceFitDiagnostics <- residualsEcdfPlot <- scvPlot <- function( ... ) .Defunct(msg=sprintf("The function '%s' is defunct. See the vignette of the package 'DESeq' for better suggestions on how to check fit quality.", as.character(sys.call(sys.parent())[[1L]]))) nbinomTest <- function( cds, condA, condB, pvals_only=FALSE, eps=NULL ) { stopifnot( is( cds, "CountDataSet" ) ) #if( cds@multivariateConditions ) # stop( "For CountDataSets with multivariate conditions, only the GLM-based test can be used." ) if( all( is.na( dispTable(cds) ) ) ) stop( "Call 'estimateDispersions' first." ) if( dispTable(cds)[condA] == "blind" || dispTable(cds)[condB] == "blind" ) { if( fitInfo( cds, "blind" )$sharingMode != "fit-only" ) warning( 'You have used \'method="blind"\' in estimateDispersion without also setting \'sharingMode="fit-only"\'. This will not yield useful results.' ) } stopifnot( condA %in% levels(conditions(cds)) ) stopifnot( condB %in% levels(conditions(cds)) ) if( !is.null(eps) ) warning( "The 'eps' argument is defunct and hence ignored." ) colA <- conditions(cds)==condA colB <- conditions(cds)==condB bmv <- getBaseMeansAndVariances( counts(cds)[,colA|colB], sizeFactors(cds)[colA|colB] ) rawScvA <- fData(cds)[ , paste( "disp", dispTable(cds)[condA], sep="_" ) ] rawScvB <- fData(cds)[ , paste( "disp", dispTable(cds)[condB], sep="_" ) ] pval <- nbinomTestForMatrices( counts(cds)[,colA], counts(cds)[,colB], sizeFactors(cds)[colA], sizeFactors(cds)[colB], rawScvA, rawScvB ) if( pvals_only ) pval else { bmvA <- getBaseMeansAndVariances( counts(cds)[,colA], sizeFactors(cds)[colA] ) bmvB <- getBaseMeansAndVariances( counts(cds)[,colB], sizeFactors(cds)[colB] ) data.frame( id = rownames( counts(cds) ), baseMean = bmv$baseMean, baseMeanA = bmvA$baseMean, baseMeanB = bmvB$baseMean, foldChange = bmvB$baseMean / bmvA$baseMean, log2FoldChange = log2( bmvB$baseMean / bmvA$baseMean ), pval = pval, padj = p.adjust( pval, method="BH" ), # resVarA = cds@fitInfo[[ dispTable(cds)[condA] ]]$perGeneDispEsts / rawScvA, # resVarB = cds@fitInfo[[ dispTable(cds)[condB] ]]$perGeneDispEsts / rawScvB, stringsAsFactors = FALSE ) } } getVarianceStabilizedData <- function( cds ) { stopifnot( is( cds, "CountDataSet" ) ) if( "blind" %in% ls(cds@fitInfo) ) fitInfo <- cds@fitInfo[["blind"]] else if( "pooled" %in% ls(cds@fitInfo) ) fitInfo <- cds@fitInfo[["pooled"]] else stop( "Use 'estimateDispersions' with 'method=\"blind\"' (or \"pooled\") before calling 'getVarianceStabilizedData'" ) ncounts <- t( t(counts(cds)) / sizeFactors(cds) ) if( attr( fitInfo$dispFunc, "fitType" ) == "parametric" ) { coefs <- attr( fitInfo$dispFunc, "coefficients" ) vst <- function( q ) log( (1 + coefs["extraPois"] + 2 * coefs["asymptDisp"] * q + 2 * sqrt( coefs["asymptDisp"] * q * ( 1 + coefs["extraPois"] + coefs["asymptDisp"] * q ) ) ) / ( 4 * coefs["asymptDisp"] ) ) / log(2) vst( ncounts ) } else { # non-parametric fit -> numerical integration xg <- sinh( seq( asinh(0), asinh(max(ncounts)), length.out=1000 ) )[-1] xim <- mean( 1/sizeFactors(cds) ) baseVarsAtGrid <- fitInfo$dispFunc( xg ) * xg^2 + xim * xg integrand <- 1 / sqrt( baseVarsAtGrid ) splf <- splinefun( asinh( ( xg[-1] + xg[-length(xg)] )/2 ), cumsum( ( xg[-1] - xg[-length(xg)] ) * ( integrand[-1] + integrand[-length(integrand)] )/2 ) ) h1 <- quantile( rowMeans(ncounts), .95 ) h2 <- quantile( rowMeans(ncounts), .999 ) eta <- ( log2(h2) - log2(h1) ) / ( splf(asinh(h2)) - splf(asinh(h1)) ) xi <- log2(h1) - eta * splf(asinh(h1)) tc <- sapply( colnames(counts(cds)), function(clm) eta * splf( asinh( ncounts[,clm] ) ) + xi ) rownames( tc ) <- rownames( counts(cds) ) tc } } varianceStabilizingTransformation <- function (cds) { new("ExpressionSet", exprs = getVarianceStabilizedData(cds), phenoData = phenoData(cds), featureData = featureData(cds), experimentData = experimentData(cds), annotation = annotation(cds), protocolData = protocolData(cds)) } makeExampleCountDataSet <- function( ) { ngenes <- 10000 q0 <- rexp( ngenes, rate=1/250 ) is_DE <- runif( ngenes ) < .3 lfc <- rnorm( ngenes, sd=2 ) q0A <- ifelse( is_DE, q0 * 2^( lfc/2 ), q0 ) q0B <- ifelse( is_DE, q0 * 2^( -lfc/2 ), q0 ) true_sf <- c( 1., 1.3, .7, .9, 1.6 ) conds <- c( "A", "A", "B", "B", "B" ) m <- t( sapply( seq_len(ngenes), function(i) sapply( 1:5, function( j ) rnbinom( 1, mu = true_sf[j] * ifelse( conds[j]=="A", q0A[i], q0B[i] ), size = 1/.2 ) ) ) ) colnames(m) <- c( "A1", "A2", "B1", "B2", "B3" ) rownames(m) <- paste( "gene", seq_len(ngenes), ifelse( is_DE, "T", "F" ), sep="_" ) newCountDataSet( m, conds ) } fitNbinomGLMs <- function( cds, modelFormula, glmControl=list() ) { stopifnot( is( cds, "CountDataSet" ) ) if( "disp_pooled" %in% colnames( fData(cds) ) ) disps <- fData(cds)$disp_pooled else if( "disp_blind" %in% colnames( fData(cds) ) ) { if( fitInfo( cds, "blind" )$sharingMode != "fit-only" ) warning( 'You have used \'method="blind"\' in estimateDispersion without also setting \'sharingMode="fit-only"\'. This will not yield useful results.' ) disps <- fData(cds)$disp_blind } else stop( "Call 'estimateDispersions' with 'method=\"pooled\"' (or 'blind') first." ) fitNbinomGLMsForMatrix( counts(cds), sizeFactors(cds), disps, modelFormula, pData(cds), glmControl=glmControl ) } nbinomGLMTest <- function( resFull, resReduced ) 1 - pchisq( resReduced$deviance - resFull$deviance, attr( resReduced, "df.residual" ) - attr( resFull, "df.residual" ) ) newCountDataSetFromHTSeqCount <- function( sampleTable, directory="." ) { l <- lapply( as.character( sampleTable[,2] ), function(fn) read.table( file.path( directory, fn ) ) ) if( ! all( sapply( l, function(a) all( a$V1 == l[[1]]$V1 ) ) ) ) stop( "Gene IDs (first column) differ between files." ) tbl <- sapply( l, function(a) a$V2 ) rownames(tbl) <- l[[1]]$V1 colnames(tbl) <- sampleTable[,1] specialRows <- rownames(tbl) %in% c( "no_feature", "ambiguous", "too_low_aQual", "not_aligned", "alignment_not_unique" ) tbl <- tbl[ !specialRows, ] if( ncol(sampleTable) == 3 ) newCountDataSet( tbl, sampleTable[,3] ) else newCountDataSet( tbl, sampleTable[,-(1:2)] ) } DESeq/R/plotDispEsts.R0000644000175500017550000000367513554551773015556 0ustar00biocbuildbiocbuildplotMA = function(x, ylim, col = ifelse(x$padj>=0.1, "gray32", "red3"), linecol = "#ff000080", xlab = "mean of normalized counts", ylab = expression(log[2]~fold~change), log = "x", cex=0.45, ...) { if (!(is.data.frame(x) && all(c("baseMean", "log2FoldChange") %in% colnames(x)))) stop("'x' must be a data frame with columns named 'baseMean', 'log2FoldChange'.") force( col ) col = col[ x$baseMean != 1 ] x = subset(x, baseMean!=0) py = x$log2FoldChange if(missing(ylim)) ylim = c(-1,1) * quantile(abs(py[is.finite(py)]), probs=0.99) * 1.1 plot(x$baseMean, pmax(ylim[1], pmin(ylim[2], py)), log=log, pch=ifelse(pyylim[2], 2, 16)), cex=cex, col=col, xlab=xlab, ylab=ylab, ylim=ylim, ...) abline(h=0, lwd=4, col=linecol) } plotDispEsts = function( cds, name=NULL, ymin, linecol="#ff000080", xlab = "mean of normalized counts", ylab = "dispersion", log = "xy", cex = 0.45, ... ) { px = rowMeans( counts( cds, normalized=TRUE ) ) sel = (px>0) px = px[sel] py = fitInfo(cds, name=name)$perGeneDispEsts[sel] if(missing(ymin)) ymin = 10^floor(log10(min(py[py>0], na.rm=TRUE))-0.1) plot(px, pmax(py, ymin), xlab=xlab, ylab=ylab, log=log, pch=ifelse(py= 3 ) brewer.pal(nlevels(fac), "Paired") else c( "green", "blue" ) xyplot(PC2 ~ PC1, groups=fac, data=as.data.frame(pca$x), pch=16, cex=2, aspect = "iso", col=colours, main = draw.key(key = list( rect = list(col = colours), text = list(levels(fac)), rep = FALSE))) } DESeq/R/welcome.R0000644000175500017550000000071413554551773014543 0ustar00biocbuildbiocbuild# ========================================================================== # package initialization # ========================================================================== .onAttach = function(libname, pkgname) { msg = "Welcome to 'DESeq'. For improved performance, usability and functionality, please consider migrating to 'DESeq2'." msg = strwrap(msg, exdent=4, indent=4) packageStartupMessage(paste(msg, collapse="\n"), appendLF=TRUE) } DESeq/build/0000755000175500017550000000000013556150211013641 5ustar00biocbuildbiocbuildDESeq/build/vignette.rds0000644000175500017550000000034013556150211016175 0ustar00biocbuildbiocbuildb```b`@YH394kpj^P^9c^bNeqf^B.PBJbIByfIBIFXBAbrvbz*vs R$ء% H 2ּb y) 3GZY_Ӄ -3'foHf e2|s  =XQ.PP ;DESeq/inst/0000755000175500017550000000000013556150211013517 5ustar00biocbuildbiocbuildDESeq/inst/CITATION0000644000175500017550000000121113554551773014667 0ustar00biocbuildbiocbuildcitEntry(entry="article", title = "Differential expression analysis for sequence count data", author = personList( as.person("Simon Anders"), as.person("Wolfgang Huber")), year = 2010, journal = "Genome Biology", volume = "11", pages = "R106", doi = "10.1186/gb-2010-11-10-r106", url = "http://genomebiology.com/2010/11/10/R106/", textVersion = paste("Simon Anders and Wolfgang Huber (2010):", "Differential expression analysis for sequence count data.", "Genome Biology 11:R106" ) ) DESeq/inst/doc/0000755000175500017550000000000013556150211014264 5ustar00biocbuildbiocbuildDESeq/inst/doc/DESeq.R0000644000175500017550000004460013556150210015353 0ustar00biocbuildbiocbuild### R code from vignette source 'DESeq.Rnw' ################################################### ### code chunk number 1: options ################################################### options(digits=3, width=100) ################################################### ### code chunk number 2: systemFile ################################################### datafile = system.file( "extdata/pasilla_gene_counts.tsv", package="pasilla" ) datafile ################################################### ### code chunk number 3: readTable ################################################### pasillaCountTable = read.table( datafile, header=TRUE, row.names=1 ) head( pasillaCountTable ) ################################################### ### code chunk number 4: pasillaDesign ################################################### pasillaDesign = data.frame( row.names = colnames( pasillaCountTable ), condition = c( "untreated", "untreated", "untreated", "untreated", "treated", "treated", "treated" ), libType = c( "single-end", "single-end", "paired-end", "paired-end", "single-end", "paired-end", "paired-end" ) ) pasillaDesign ################################################### ### code chunk number 5: pairedSamples ################################################### pairedSamples = pasillaDesign$libType == "paired-end" countTable = pasillaCountTable[ , pairedSamples ] condition = pasillaDesign$condition[ pairedSamples ] ################################################### ### code chunk number 6: DESeq.Rnw:163-165 ################################################### head(countTable) condition ################################################### ### code chunk number 7: condition (eval = FALSE) ################################################### ## #not run ## condition = factor( c( "untreated", "untreated", "treated", "treated" ) ) ################################################### ### code chunk number 8: conditionCheck ################################################### stopifnot( identical( condition, factor( c( "untreated", "untreated", "treated", "treated" ) ) ) ) ################################################### ### code chunk number 9: instantiate ################################################### library( "DESeq" ) cds = newCountDataSet( countTable, condition ) ################################################### ### code chunk number 10: estimateSizeFactors ################################################### cds = estimateSizeFactors( cds ) sizeFactors( cds ) ################################################### ### code chunk number 11: headcounts2 ################################################### head( counts( cds, normalized=TRUE ) ) ################################################### ### code chunk number 12: estimateDispersions ################################################### cds = estimateDispersions( cds ) ################################################### ### code chunk number 13: str ################################################### str( fitInfo(cds) ) ################################################### ### code chunk number 14: figFit ################################################### plotDispEsts( cds ) ################################################### ### code chunk number 15: DESeq.Rnw:309-310 ################################################### all(table(conditions(cds))==2) ################################################### ### code chunk number 16: head ################################################### head( fData(cds) ) ################################################### ### code chunk number 17: nbt1 ################################################### res = nbinomTest( cds, "untreated", "treated" ) ################################################### ### code chunk number 18: nbt2 ################################################### head(res) ################################################### ### code chunk number 19: checkClaims ################################################### stopifnot(identical(colnames(res), c("id", "baseMean", "baseMeanA", "baseMeanB", "foldChange", "log2FoldChange", "pval", "padj"))) ################################################### ### code chunk number 20: figDE ################################################### plotMA(res) ################################################### ### code chunk number 21: histp ################################################### hist(res$pval, breaks=100, col="skyblue", border="slateblue", main="") ################################################### ### code chunk number 22: ressig1 ################################################### resSig = res[ res$padj < 0.1, ] ################################################### ### code chunk number 23: ressig2 ################################################### head( resSig[ order(resSig$pval), ] ) ################################################### ### code chunk number 24: ressig3 ################################################### head( resSig[ order( resSig$foldChange, -resSig$baseMean ), ] ) ################################################### ### code chunk number 25: ressig4 ################################################### head( resSig[ order( -resSig$foldChange, -resSig$baseMean ), ] ) ################################################### ### code chunk number 26: writetable ################################################### write.csv( res, file="My Pasilla Analysis Result Table.csv" ) ################################################### ### code chunk number 27: ncu ################################################### ncu = counts( cds, normalized=TRUE )[ , conditions(cds)=="untreated" ] ################################################### ### code chunk number 28: MArepl ################################################### plotMA(data.frame(baseMean = rowMeans(ncu), log2FoldChange = log2( ncu[,2] / ncu[,1] )), col = "black") ################################################### ### code chunk number 29: subset ################################################### cdsUUT = cds[ , 1:3] pData( cdsUUT ) ################################################### ### code chunk number 30: est123 ################################################### cdsUUT = estimateSizeFactors( cdsUUT ) cdsUUT = estimateDispersions( cdsUUT ) resUUT = nbinomTest( cdsUUT, "untreated", "treated" ) ################################################### ### code chunk number 31: figDE_Tb ################################################### plotMA(resUUT) ################################################### ### code chunk number 32: subset2 ################################################### cds2 = cds[ ,c( "untreated3", "treated3" ) ] ################################################### ### code chunk number 33: cds2 ################################################### cds2 = estimateDispersions( cds2, method="blind", sharingMode="fit-only" ) ################################################### ### code chunk number 34: res2 ################################################### res2 = nbinomTest( cds2, "untreated", "treated" ) ################################################### ### code chunk number 35: figDE2 ################################################### plotMA(res2) ################################################### ### code chunk number 36: addmarg ################################################### addmargins( table( res_sig = res$padj < .1, res2_sig = res2$padj < .1 ) ) ################################################### ### code chunk number 37: reminderFullData ################################################### head( pasillaCountTable ) pasillaDesign ################################################### ### code chunk number 38: fct ################################################### cdsFull = newCountDataSet( pasillaCountTable, pasillaDesign ) ################################################### ### code chunk number 39: estsfdisp ################################################### cdsFull = estimateSizeFactors( cdsFull ) cdsFull = estimateDispersions( cdsFull ) ################################################### ### code chunk number 40: figFitPooled ################################################### plotDispEsts( cdsFull ) ################################################### ### code chunk number 41: fit1 ################################################### fit1 = fitNbinomGLMs( cdsFull, count ~ libType + condition ) fit0 = fitNbinomGLMs( cdsFull, count ~ libType ) ################################################### ### code chunk number 42: fitstr ################################################### str(fit1) ################################################### ### code chunk number 43: pvalsGLM ################################################### pvalsGLM = nbinomGLMTest( fit1, fit0 ) padjGLM = p.adjust( pvalsGLM, method="BH" ) ################################################### ### code chunk number 44: addmarg2 ################################################### tab1 = table( "paired-end only" = res$padj < .1, "all samples" = padjGLM < .1 ) addmargins( tab1 ) ################################################### ### code chunk number 45: tablesignfitInfocdsperGeneDispEsts ################################################### table(sign(fitInfo(cds)$perGeneDispEsts - fitInfo(cdsFull)$perGeneDispEsts)) ################################################### ### code chunk number 46: figDispScatter ################################################### trsf = function(x) log( (x + sqrt(x*x+1))/2 ) plot( trsf(fitInfo(cds)$perGeneDispEsts), trsf(fitInfo(cdsFull)$perGeneDispEsts), pch=16, cex=0.45, asp=1) abline(a=0, b=1, col="red3") ################################################### ### code chunk number 47: lookatfit1 ################################################### head(fit1) ################################################### ### code chunk number 48: fullAnalysisSimple ################################################### cdsFullB = newCountDataSet( pasillaCountTable, pasillaDesign$condition ) cdsFullB = estimateSizeFactors( cdsFullB ) cdsFullB = estimateDispersions( cdsFullB ) resFullB = nbinomTest( cdsFullB, "untreated", "treated" ) ################################################### ### code chunk number 49: table ################################################### tab2 = table( `all samples simple` = resFullB$padj < 0.1, `all samples GLM` = padjGLM < 0.1 ) addmargins(tab2) ################################################### ### code chunk number 50: rs ################################################### rs = rowSums ( counts ( cdsFull )) theta = 0.4 use = (rs > quantile(rs, probs=theta)) table(use) cdsFilt = cdsFull[ use, ] ################################################### ### code chunk number 51: check ################################################### stopifnot(!any(is.na(use))) ################################################### ### code chunk number 52: fitFilt ################################################### fitFilt1 = fitNbinomGLMs( cdsFilt, count ~ libType + condition ) fitFilt0 = fitNbinomGLMs( cdsFilt, count ~ libType ) pvalsFilt = nbinomGLMTest( fitFilt1, fitFilt0 ) padjFilt = p.adjust(pvalsFilt, method="BH" ) ################################################### ### code chunk number 53: doublecheck ################################################### stopifnot(all.equal(pvalsFilt, pvalsGLM[use])) ################################################### ### code chunk number 54: tab ################################################### padjFiltForComparison = rep(+Inf, length(padjGLM)) padjFiltForComparison[use] = padjFilt tab3 = table( `no filtering` = padjGLM < .1, `with filtering` = padjFiltForComparison < .1 ) addmargins(tab3) ################################################### ### code chunk number 55: figscatterindepfilt ################################################### plot(rank(rs)/length(rs), -log10(pvalsGLM), pch=16, cex=0.45) ################################################### ### code chunk number 56: histindepfilt ################################################### h1 = hist(pvalsGLM[!use], breaks=50, plot=FALSE) h2 = hist(pvalsGLM[use], breaks=50, plot=FALSE) colori = c(`do not pass`="khaki", `pass`="powderblue") ################################################### ### code chunk number 57: fighistindepfilt ################################################### barplot(height = rbind(h1$counts, h2$counts), beside = FALSE, col = colori, space = 0, main = "", ylab="frequency") text(x = c(0, length(h1$counts)), y = 0, label = paste(c(0,1)), adj = c(0.5,1.7), xpd=NA) legend("topright", fill=rev(colori), legend=rev(names(colori))) ################################################### ### code chunk number 58: sortP ################################################### orderInPlot = order(pvalsFilt) showInPlot = (pvalsFilt[orderInPlot] <= 0.08) alpha = 0.1 ################################################### ### code chunk number 59: sortedP ################################################### plot(seq(along=which(showInPlot)), pvalsFilt[orderInPlot][showInPlot], pch=".", xlab = expression(rank(p[i])), ylab=expression(p[i])) abline(a=0, b=alpha/length(pvalsFilt), col="red3", lwd=2) ################################################### ### code chunk number 60: doBH ################################################### whichBH = which(pvalsFilt[orderInPlot] <= alpha*seq(0, 1, length=length(pvalsFilt))) ## Test some assertions: ## - whichBH is a contiguous set of integers from 1 to length(whichBH) ## - the genes selected by this graphical method coincide with those ## from p.adjust (i.e. padjFilt) stopifnot(length(whichBH)>0, identical(whichBH, seq(along=whichBH)), padjFilt[orderInPlot][ whichBH] <= alpha, padjFilt[orderInPlot][-whichBH] > alpha) ################################################### ### code chunk number 61: SchwSpjot ################################################### j = round(length(pvalsFilt)*c(1, .66)) px = (1-pvalsFilt[orderInPlot[j]]) py = ((length(pvalsFilt)-1):0)[j] slope = diff(py)/diff(px) ################################################### ### code chunk number 62: SchwederSpjotvoll ################################################### plot(1-pvalsFilt[orderInPlot], (length(pvalsFilt)-1):0, pch=".", xlab=expression(1-p[i]), ylab=expression(N(p[i]))) abline(a=0, b=slope, col="red3", lwd=2) ################################################### ### code chunk number 63: defvsd ################################################### cdsBlind = estimateDispersions( cds, method="blind" ) vsd = varianceStabilizingTransformation( cdsBlind ) ################################################### ### code chunk number 64: vsd1 ################################################### ##par(mai=ifelse(1:4 <= 2, par("mai"), 0)) px = counts(cds)[,1] / sizeFactors(cds)[1] ord = order(px) ord = ord[px[ord] < 150] ord = ord[seq(1, length(ord), length=50)] last = ord[length(ord)] vstcol = c("blue", "black") matplot(px[ord], cbind(exprs(vsd)[, 1], log2(px))[ord, ], type="l", lty=1, col=vstcol, xlab="n", ylab="f(n)") legend("bottomright", legend = c( expression("variance stabilizing transformation"), expression(log[2](n/s[1]))), fill=vstcol) ################################################### ### code chunk number 65: vsd2 ################################################### library("vsn") par(mfrow=c(1,2)) notAllZero = (rowSums(counts(cds))>0) meanSdPlot(log2(counts(cds)[notAllZero, ] + 1)) meanSdPlot(vsd[notAllZero, ]) ################################################### ### code chunk number 66: modlr ################################################### mod_lfc = (rowMeans( exprs(vsd)[, conditions(cds)=="treated", drop=FALSE] ) - rowMeans( exprs(vsd)[, conditions(cds)=="untreated", drop=FALSE] )) ################################################### ### code chunk number 67: dah ################################################### lfc = res$log2FoldChange table(lfc[!is.finite(lfc)], useNA="always") ################################################### ### code chunk number 68: colourramp ################################################### logdecade = 1 + round( log10( 1+rowMeans(counts(cdsBlind, normalized=TRUE)) ) ) lfccol = colorRampPalette( c( "gray", "blue" ) )(6)[logdecade] ################################################### ### code chunk number 69: figmodlr ################################################### ymax = 4.5 plot( pmax(-ymax, pmin(ymax, lfc)), mod_lfc, xlab = "ordinary log-ratio", ylab = "moderated log-ratio", cex=0.45, asp=1, col = lfccol, pch = ifelse(lfc<(-ymax), 60, ifelse(lfc>ymax, 62, 16))) abline( a=0, b=1, col="red3") ################################################### ### code chunk number 70: cdsFullBlind ################################################### cdsFullBlind = estimateDispersions( cdsFull, method = "blind" ) vsdFull = varianceStabilizingTransformation( cdsFullBlind ) ################################################### ### code chunk number 71: heatmap ################################################### library("RColorBrewer") library("gplots") select = order(rowMeans(counts(cdsFull)), decreasing=TRUE)[1:30] hmcol = colorRampPalette(brewer.pal(9, "GnBu"))(100) ################################################### ### code chunk number 72: figHeatmap2a ################################################### heatmap.2(exprs(vsdFull)[select,], col = hmcol, trace="none", margin=c(10, 6)) ################################################### ### code chunk number 73: figHeatmap2b ################################################### heatmap.2(counts(cdsFull)[select,], col = hmcol, trace="none", margin=c(10,6)) ################################################### ### code chunk number 74: sampleClust ################################################### dists = dist( t( exprs(vsdFull) ) ) ################################################### ### code chunk number 75: figHeatmapSamples ################################################### mat = as.matrix( dists ) rownames(mat) = colnames(mat) = with(pData(cdsFullBlind), paste(condition, libType, sep=" : ")) heatmap.2(mat, trace="none", col = rev(hmcol), margin=c(13, 13)) ################################################### ### code chunk number 76: figPCA ################################################### print(plotPCA(vsdFull, intgroup=c("condition", "libType"))) ################################################### ### code chunk number 77: sessi ################################################### sessionInfo() DESeq/inst/doc/DESeq.Rnw0000644000175500017550000016674113554551773015754 0ustar00biocbuildbiocbuild%\VignetteIndexEntry{Analysing RNA-Seq data with the "DESeq" package} %\VignettePackage{DESeq} % To compile this document % library('cacheSweave');rm(list=ls());Sweave('DESeq.Rnw',driver=cacheSweaveDriver());system("pdflatex DESeq") \documentclass[10pt,oneside]{article} \newcommand{\thetitle}{Differential expression of RNA-Seq data at the gene level -- the DESeq package} %\usepackage[pdftitle={\thetitle},pdfauthor={Wolfgang Huber}]{whbiocvignette} \usepackage{whbiocvignette} \title{\textsf{\textbf{\thetitle}}} \author{Simon Anders$^1$, Wolfgang Huber\\[1em]European Molecular Biology Laboratory (EMBL),\\ Heidelberg, Germany\\ \texttt{$^1$sanders@fs.tum.de}} % The following command makes use of SVN's 'Date' keyword substitution % To activate this, I used: svn propset svn:keywords Date DESeq.Rnw \date{\Rpackage{DESeq} version \Sexpr{packageDescription("DESeq")$Version} (Last revision \StrMid{$Date$}{8}{18})} \SweaveOpts{keep.source=TRUE,eps=FALSE,pdf=FALSE,png=TRUE,include=FALSE,width=5.4,height=3.7,resolution=180} \begin{document} <>= options(digits=3, width=100) @ \maketitle \begin{abstract} A basic task in the analysis of count data from RNA-Seq is the detection of differentially expressed genes. The count data are presented as a table which reports, for each sample, the number of reads that have been assigned to a gene. Analogous analyses also arise for other assay types, such as comparative ChIP-Seq. The package \Rpackage{DESeq} provides methods to test for differential expression by use of the negative binonial distribution and a shrinkage estimator for the distribution's variance\footnote{Other Bioconductor packages with similar aims are \Rpackage{edgeR} and \Rpackage{baySeq}.}. This vignette explains the use of the package. For an exposition of the statistical method, please see our paper~\cite{Anders:2010:GB} and the additional information in Section~\ref{sec:changes}. \end{abstract} \tableofcontents %-------------------------------------------------- \section{Input data and preparations} \label{sec:prep} %-------------------------------------------------- \subsection{The count table} %-------------------------------------------------- As input, the \Rpackage{DESeq} package expects count data as obtained, e.\,g., from RNA-Seq or another high-throughput sequencing experiment, in the form of a rectangular table of integer values. The table cell in the $i$-th row and the $j$-th column of the table tells how many reads have been mapped to gene $i$ in sample $j$. Analogously, for other types of assays, the rows of the table might correspond e.\,g.\ to binding regions (with ChIP-Seq) or peptide sequences (with quantitative mass spectrometry). The count values must be raw counts of sequencing reads. This is important for \Rpackage{DESeq}'s statistical model to hold, as only the actual counts allow assessing the measurement precision correctly. Hence, please do do not supply other quantities, such as (rounded) normalized counts, or counts of covered base pairs -- this will only lead to nonsensical results. Furthermore, it is important that each column stems from an independent biological replicate. For technical replicates (e.\,g.\ when the same library preparation was distributed over multiple lanes of the sequencer), please sum up their counts to get a single column, corresponding to a unique biological replicate. This is needed in order to allow \Rpackage{DESeq} to estimate variability in the experiment correctly. To obtain such a count table for your own data, you will need to create it from your sequence alignments and suitable annotation. In Bioconductor, you can use the function \Rfunction{summarizeOverlaps} in the \Rpackage{GenomicRanges} package. See the vignette, reference~\cite{summarizeOverlaps}, for a worked example. Another possibility is provided by the Bioconductor package \Rpackage{easyRNASeq}. Another easy way to produce such a table from the output of the aligner is to use the \texttt{htseq-count} script distributed with the \emph{HTSeq} Python package. Even though \emph{HTSeq} is written in Python, you do not need to know any Python to use \texttt{htseq-count}. See \url{http://www-huber.embl.de/users/anders/HTSeq/doc/count.html}. HTSeq-count produces one count file for each sample. \Rpackage{DESeq} offers the function \Rfunction{newCountDataSetFromHTSeqCount}, described below, to get an analysis started from these files. In this vignette, we will work with the gene level read counts from the \Rpackage{pasilla} data package. This data set is from an experiment on \emph{Drosophila melanogaster} cell cultures and investigated the effect of RNAi knock-down of the splicing factor \emph{pasilla}~\cite{Brooks2010}. The detailed transcript of how we produced the \Rpackage{pasilla} count table from second generation sequencing (Illumina) FASTQ files is provided in the vignette of the data package \Rpackage{pasilla}. The table is supplied by the \Rpackage{pasilla} package as a text file of tab-separated values. The function \Rfunction{system.file} tells us where this file is stored on your computer. % <>= datafile = system.file( "extdata/pasilla_gene_counts.tsv", package="pasilla" ) datafile @ % Have a look at the file with a text editor to see how it is formatted. To read this file with R, we use the function \Rfunction{read.table}. % <>= pasillaCountTable = read.table( datafile, header=TRUE, row.names=1 ) head( pasillaCountTable ) @ % Here, \texttt{header=TRUE} indicates that the first line contains column names and \texttt{row.names=1} means that the first column should be used as row names. This leaves us with a \Rclass{data.frame} containing integer count values. %-------------------------------------------------- \subsection{The metadata} %-------------------------------------------------- The best data are useless without metadata. \Rpackage{DESeq} uses familiar idioms in Bioconductor to manage the metadata that go with the count table. The metadata can be divided into three groups: information about the samples (table colums), about the features (table rows), and about the overall experiment. First, we need a description of the samples, which we keep in a \Rclass{data.frame} whose columns correspond to different types of information, and whose rows correspond to the \Sexpr{ncol(pasillaCountTable)} samples: <>= pasillaDesign = data.frame( row.names = colnames( pasillaCountTable ), condition = c( "untreated", "untreated", "untreated", "untreated", "treated", "treated", "treated" ), libType = c( "single-end", "single-end", "paired-end", "paired-end", "single-end", "paired-end", "paired-end" ) ) pasillaDesign @ % Here, simply use a chunk of R code to set up this define. More often, you will read this into R from a spreadsheet table, using the R functions \Rfunction{read.table} or \Rfunction{read.csv}; or perhaps even from a relational database table using R's database access facilities. To analyse these samples, we will have to account for the fact that we have both single-end and paired-end method. To keep things simple at the start, we defer the discussion of this to Section~\ref{sec:GLM} and first demonstrate a simple analysis by using only the paired-end samples. % <>= pairedSamples = pasillaDesign$libType == "paired-end" countTable = pasillaCountTable[ , pairedSamples ] condition = pasillaDesign$condition[ pairedSamples ] @ % Now, we have data input as follows. % <<>>= head(countTable) condition @ % For your own data, create such a factor simply with <>= #not run condition = factor( c( "untreated", "untreated", "treated", "treated" ) ) @ <>= stopifnot( identical( condition, factor( c( "untreated", "untreated", "treated", "treated" ) ) ) ) @ % We can now instantiate a \Rclass{CountDataSet}, which is the central data structure in the \Rpackage{DESeq} package: % <>= library( "DESeq" ) cds = newCountDataSet( countTable, condition ) @ If you have used \emph{htseq-count} (see above) to obtain your read counts, you can use the funtion \Rfunction{newCountDataSetFromHTSeqCount} to obtain a CountDataSe directly from the count files produced by \emph{htseq-count}. To this end, produce a data frame, similar to \emph{pasillaDesign} constructed above, with the sample names in the first column, the file names in the scond column, and the condition in the third column (or, if you have more than one factor in your design matrix, all these factors in the third and folling columns), and pass this data frame to the function. See the help page (``\texttt{?newCountDataSetFromHTSeqCount}'') for further details. The \Rclass{CountDataSet} class is derived from \Rpackage{Biobase}'s \Rclass{eSet} class and so shares all features of this standard Bioconductor class. Furthermore, accessors are provided for its data slots\footnote{In fact, the object \Robject{pasillaGenes} from the \Rpackage{pasilla} package is of class \Rclass{CountDataSet}, and we could do the subsequent analysis on the basis of this object. Here we re-create \Robject{cds} from elementary data types, a \Rclass{data.frame} and a \Rclass{factor}, for pedagogic effect.}. For example, the counts can be accessed with the \Rfunction{counts} function, as we will see in the next section. %------------------------------------------------------------ \subsection{Normalisation} %------------------------------------------------------------ As a first processing step, we need to estimate the effective library size. This step is sometimes also called \emph{normalisation}, even though there is no relation to normality or a normal distribution. The effective library size information is called the \emph{size factors} vector, since the package only needs to know the relative library sizes. If the counts of non-differentially expressed genes in one sample are, on average, twice as high as in another (because the library was sequenced twice as deeply), the size factor for the first sample should be twice that of the other sample~\cite{Anders:2010:GB,Anders:2012:GR}. The function \Rfunction{estimateSizeFactors} estimates the size factors from the count data. (See the man page of \Rfunction{estimateSizeFactorsForMatrix} for technical details on the calculation.) % <>= cds = estimateSizeFactors( cds ) sizeFactors( cds ) @ If we divide each column of the count table by the size factor for this column, the count values are brought to a common scale, making them comparable. When called with \texttt{normalized=TRUE}, the \texttt{counts} accessor function performs this calculation. This is useful, e.g., for visualization. % <>= head( counts( cds, normalized=TRUE ) ) @ %------------------------------------------------------------ \section{Variance estimation} %------------------------------------------------------------ The inference in \Rpackage{DESeq} relies on an estimation of the typical relationship between the data's variance and their mean, or, equivalently, between the data's dispersion and their mean. The \emph{dispersion} can be understood as the square of the coefficient of biological variation. So, if a gene's expression typically differs from replicate to replicate sample by 20\%, this gene's dispersion is $0.2^2=.04$. Note that the variance seen between counts is the sum of two components: the sample-to-sample variation just mentioned, and the uncertainty in measuring a concentration by counting reads. The latter, known as shot noise or Poisson noise, is the dominating noise source for lowly expressed genes. The former dominates for highly expressed genes. The sum of both, shot noise and dispersion, is considered in the differential expression inference. Hence, the variance $v$ of count values is modelled as \[ v = s \mu + \alpha s^2\mu^2, \] where $\mu$ is the expected normalized count value (estimated by the average normalized count value), $s$ is the size factor for the sample under consideration, and $\alpha$ is the dispersion value for the gene under consideration. To estimate the dispersions, use this command. <>= cds = estimateDispersions( cds ) @ We could now proceed straight to the testing for differetial expression in Section~\ref{sec:DE}. However, let us first spend a little more time with looking at the results of \Rfunction{estimateDispersions}, in order to better understand the subsequent inference. Also, verification of the dispersion plot Figure~\ref{figFit}, explained below, is an aspect of data quality control: how well do the data accord to the expectations of our analytic approach? Quality assessment is a crucial step of the data analysis, and we will see further quality diagnostics in Section~\ref{sec:quality}. The function \Rfunction{estimateDispersions} performs three steps. First, it estimates a dispersion value for each gene, then it fits a curve through the estimates. Finally, it assigns to each gene a dispersion value, using a choice between the per-gene estimate and the fitted value. To allow the user to inspect the intermediate steps, a \Robject{fitInfo} object is stored, which contains the per-gene estimate, the fitted curve and the values that will subsequently be used for inference. % <>= str( fitInfo(cds) ) @ % \label{fitInfo} It is useful to inspect the results of these steps visually. We can plot the per-gene estimates against the mean normalized counts per gene and overlay the fitted curve by using the function \Rfunction{plotDispEsts} (Fig.~\ref{figFit}). % \begin{figure} \centering \includegraphics[width=.6\textwidth]{DESeq-figFit} \caption{Empirical (black dots) and fitted (red lines) dispersion values plotted against the mean of the normalised counts.} \label{figFit} \end{figure} % <>= plotDispEsts( cds ) @ % check a claim made in the paragraph below. <>= all(table(conditions(cds))==2) @ As we estimated the dispersions from a small number of replicates, the estimates scatter with quite some sampling variance around their true values. An initial assumption that one could make is that the regression line shown in Figure~\ref{figFit} models the true underlying dispersions, and that the variation of the point estimates around simply reflects sampling variance. This is the assumption that we put forward in the first paper on \Rpackage{DESeq}~\cite{Anders:2010:GB}. However, subsequent experience with larger data sets indicates that not all of the variability of the points around the regression line seen in Figure~\ref{figFit} is sampling variance: some of it reflects differences of the true, underlying variance between different genes. Hence, the default behaviour of \Rpackage{DESeq} now uses a more prudent or conservative approach: if a per-gene estimates lies below the regression line, we assume that this might indeed be sampling variance, and shift the estimate upwards to the value predicted by the regression line. If, however, the per-gene estimate lies above the line, we do not shift it downwards to the line, but rather keep it as is. The option \texttt{sharingMode} of the function \Rfunction{estimateDispersions} can be used to control this behaviour. The value \texttt{sharingMode="maximum"} corresponds to the default. If you have many replicates (where \emph{many} starts at around 7), the choice \texttt{sharingMode="gene-est-only"} will typically be more adequate. If you would like to use the behaviour described in~\cite{Anders:2010:GB}, this is achieved by specifying \texttt{sharingMode="fit-only"}. Another difference of the current \Rpackage{DESeq} version to the original method described in the paper is the way how the mean-dispersion relation is fitted. By default, \Rfunction{estimateDispersions} now performs a parametric fit: Using a gamma-family GLM, two coefficients $\alpha_0, \alpha_1$ are found to parametrize the fit as $\alpha = \alpha_0 + \alpha_1/\mu$. (The values of the two coefficients can be found in the \texttt{fitInfo} object, as attribute \texttt{coefficients} to \texttt{dispFunc}.) For some data sets, the parametric fit may give bad results, in which case one should try a local fit (the method described in the paper), which is available via the option \texttt{fitType="local"} to \Rfunction{estimateDispersions}. In any case, the dispersion values which will be used by the subsequent testing are stored in the feature data slot of \texttt{cds}: % <>= head( fData(cds) ) @ % \fixme{Why is the value for FBgn00000014 Inf and not 0 (given that all counts are 0)?} You can verify that these values are indeed the maxima from the two value vectors in \Robject{fitInfo(cds)}, which we saw on page~\pageref{fitInfo}. Advanced users who want to fiddle with the dispersion estimation can change the values in \texttt{fData(cds)} prior to calling the testing function. %------------------------------------------------------------ \section{Inference: Calling differential expression} \label{sec:DE} %------------------------------------------------------------ \subsection{Standard comparison between two experimental conditions} Having estimated the dispersion for each gene, it is straight-forward to look for differentially expressed genes. To contrast two conditions, e.g., to see whether there is differential expression between conditions ``untreated'' and ``treated'', we simply call the function \Rfunction{nbinomTest}. It performs the tests as described in~\cite{Anders:2010:GB} and returns a data frame with the $p$ values and other useful information. % <>= res = nbinomTest( cds, "untreated", "treated" ) <>= head(res) @ % <>= stopifnot(identical(colnames(res), c("id", "baseMean", "baseMeanA", "baseMeanB", "foldChange", "log2FoldChange", "pval", "padj"))) @ The interpretation of the columns of \Rclass{\Sexpr{class(res)}} is as follows. \noindent \begin{tabular}{lp{0.8\textwidth}} \texttt{id}&feature identifier\\ \texttt{baseMean}&mean normalised counts, averaged over all samples from both conditions\\ \texttt{baseMeanA}&mean normalised counts from condition A\\ \texttt{baseMeanB}&mean normalised counts from condition B\\ \texttt{foldChange}&fold change from condition A to B\\ \texttt{log2FoldChange}&the logarithm (to basis 2) of the fold change\\ \texttt{pval}&$p$ value for the statistical significance of this change\\ \texttt{padj}&$p$ value adjusted for multiple testing with the Benjamini-Hochberg procedure (see the R function \Rfunction{p.adjust}), which controls false discovery rate (FDR)\\ \end{tabular} \begin{figure}[ht] \centering \includegraphics[width=.6\textwidth]{DESeq-figDE} \caption{Plot of normalised mean versus $log_2$ fold change for the contrast \emph{untreated} versus \emph{treated}.} \label{figDE} \end{figure} \vspace{1.5ex} Let us first plot the $\log_2$ fold changes against the mean normalised counts, colouring in red those genes that are significant at 10\% FDR (Figure~\ref{figDE}). % <>= plotMA(res) @ %$ % \begin{figure}[ht] \centering \includegraphics[width=.6\textwidth]{DESeq-histp} \caption{Histogram of $p$-values from the call to nbinomTest.} \label{fighistp} \end{figure} It is also instructive to look at the histogram of $p$ values (Figure~\ref{fighistp}). The enrichment of low $p$ values stems from the differentially expressed genes, while those not differentially expressed are spread uniformly over the range from zero to one (except for the $p$ values from genes with very low counts, which take discrete values and so give rise to high counts for some bins at the right.) % <>= hist(res$pval, breaks=100, col="skyblue", border="slateblue", main="") @ We can filter for significant genes, according to some chosen threshold for the false dicovery rate (FDR), <>= resSig = res[ res$padj < 0.1, ] @ and list, e.\,g., the most significantly differentially expressed genes: <>= head( resSig[ order(resSig$pval), ] ) @ We may also want to look at the most strongly down-regulated of the significant genes, <>= head( resSig[ order( resSig$foldChange, -resSig$baseMean ), ] ) @ or at the most strongly up-regulated ones: <>= head( resSig[ order( -resSig$foldChange, -resSig$baseMean ), ] ) @ To save the output to a file, use the R functions \Rfunction{write.table} and \Rfunction{write.csv}. (The latter is useful if you want to load the table in a spreadsheet program such as Excel.) <>= write.csv( res, file="My Pasilla Analysis Result Table.csv" ) @ \begin{figure}[ht] \centering \includegraphics[width=.6\textwidth]{DESeq-MArepl} \caption{Plot of the log2 fold change between the untreated replicates versus average expression strength.} \label{figMArepl} \end{figure} Note in Fig.~\ref{figDE} how the power to detect significant differential expression depends on the expression strength. For weakly expressed genes, stronger changes are required for the gene to be called significantly expressed. To understand the reason for this let, us compare the normalized counts between two replicate samples, here taking the two untreated samples as an example: % <>= ncu = counts( cds, normalized=TRUE )[ , conditions(cds)=="untreated" ] @ \Robject{ncu} is now a matrix with two columns. % <>= plotMA(data.frame(baseMean = rowMeans(ncu), log2FoldChange = log2( ncu[,2] / ncu[,1] )), col = "black") @ % As one can see in Figure~\ref{figMArepl}, the log fold changes between replicates are stronger for lowly expressed genes than for highly expressed ones. We ought to conclude that a gene's expression is influenced by the treatment only if the change between treated and untreated samples is stronger than what we see between replicates, and hence, the dividing line between red and black in Figure~\ref{figDE} mimics the shape seen in Figure~\ref{figMArepl}. %------------------------------------------------------------ \subsection{Working partially without replicates} %------------------------------------------------------------ If you have replicates for one condition but not for the other, you can still proceed as before. In such cases only the conditions with replicates will be used to estimate the dispersion. Of course, this is only valid if you have good reason to believe that the unreplicated condition does not have larger variation than the replicated one. To demonstrate, we subset our data object to only three samples: <>= cdsUUT = cds[ , 1:3] pData( cdsUUT ) @ \begin{figure}[ht] \centering \includegraphics[width=.6\textwidth]{DESeq-figDE_Tb} \caption{MvA plot for the contrast ``treated'' vs.\ ``untreated'', using two treated and only one untreated sample.} \label{figDE_Tb} \end{figure} Now, we do the analysis as before. <>= cdsUUT = estimateSizeFactors( cdsUUT ) cdsUUT = estimateDispersions( cdsUUT ) resUUT = nbinomTest( cdsUUT, "untreated", "treated" ) @ We produce the analogous plot as before, again with <>= plotMA(resUUT) @ %$ Figure~\ref{figDE_Tb} shows the same symmetry in up- and down-regulation as in Fig.~\ref{figDE}, but a certain asymmetry in the boundary line for significance. This has an easy explanation: low counts suffer from proportionally stronger shot noise than high counts, and since there is only one ``untreated'' sample versus two ``treated'' ones, a stronger downward fold-change is required to be called significant than for the upward direction. %-------------------------------------------------- \subsection{Working without any replicates} %-------------------------------------------------- Proper replicates are essential to interpret a biological experiment. After all, if one compares two conditions and finds a difference, how else can one know that this difference is due to the different conditions and would not have arisen between replicates, as well, just due to experimental or biological noise? Hence, any attempt to work without replicates will lead to conclusions of very limited reliability. Nevertheless, such experiments are sometimes undertaken, and the \Rpackage{DESeq} package can deal with them, even though the soundness of the results may depend much on the circumstances. Our primary assumption is now that the mean is a good predictor for the dispersion. Once we accept this assumption, we may argue as follows: Given two samples from different conditions and a number of genes with comparable expression levels, of which we expect only a minority to be influenced by the condition, we may take the dispersion estimated from comparing their counts \emph{across} conditions as ersatz for a proper estimate of the variance across replicates. After all, we assume most genes to behave the same within replicates as across conditions, and hence, the estimated variance should not be affected too much by the influence of the hopefully few differentially expressed genes. Furthermore, the differentially expressed genes will only cause the dispersion estimate to be too high, so that the test will err to the side of being too conservative. We shall now see how well this works for our example data. We reduce our count data set to just two columns, one ``untreated'' and one ``treated'' sample: <>= cds2 = cds[ ,c( "untreated3", "treated3" ) ] @ Now, without any replicates at all, the \Rfunction{estimateDispersions} function will refuse to proceed unless we instruct it to ignore the condition labels and estimate the variance by treating all samples as if they were replicates of the same condition: <>= cds2 = estimateDispersions( cds2, method="blind", sharingMode="fit-only" ) @ Note the option \texttt{sharingMode="fit-only"}. Remember that the default, \texttt{sharingMode="maximum"}, takes care of outliers, i.e., genes with dispersion much larger than the fitted values. Without replicates, we cannot catch such outliers and so have to disable this functionality. Now, we can attempt to find differential expression: <>= res2 = nbinomTest( cds2, "untreated", "treated" ) @ \begin{figure}[ht] \centering \includegraphics[width=.6\textwidth]{DESeq-figDE2} \caption{MvA plot, from a test using no replicates.} \label{figDE2} \end{figure} Unsurprisingly, we find much fewer hits, as can be seen from the plot (Fig.\ \ref{figDE2}) <>= plotMA(res2) @ and from this table, tallying the number of significant hits in our previous and our new, restricted analysis: <>= addmargins( table( res_sig = res$padj < .1, res2_sig = res2$padj < .1 ) ) @ %------------------------------------------------------------------------------------------------- \section{Multi-factor designs} \label{sec:GLM} %------------------------------------------------------------------------------------------------- Let us return to the full pasilla data set. Remember that we started of with these data: % <>= head( pasillaCountTable ) pasillaDesign @ When creating a count data set with multiple factors, just pass a data frame instead of the condition factor: <>= cdsFull = newCountDataSet( pasillaCountTable, pasillaDesign ) @ As before, we estimate the size factors and then the dispersions. Here, the default method (\texttt{method=''pooled''} to \Rfunction{estimateDispersion}), means that, as before, one dispersion is computed for each gene, which is now an average over all cells (weighted by the number of samples for each cells), where the term \emph{cell} denotes any of the four combinations of factor levels of the design. An alternative is the option \texttt{method=''pooled-CR''}, which uses a Cox-Reid-adjusted maximum likelihood estimator \cite{CR,edgeR_GLM}. The latter is slower but useful when the cell concept is not applicable (e.g. in paired designs). <>= cdsFull = estimateSizeFactors( cdsFull ) cdsFull = estimateDispersions( cdsFull ) @ \begin{figure}[ht] \centering \includegraphics[width=.6\textwidth]{DESeq-figFitPooled} \caption{Estimated (black) pooled dispersion values for all seven samples, with regression curve (red).} \label{figFitPooled} \end{figure} We check the fit (Fig.~\ref{figFitPooled}): <>= plotDispEsts( cdsFull ) @ %$ For inference, we now specify two \emph{models} by formulas. The \emph{full model} regresses the genes' expression on both the library type and the treatment condition, the \emph{reduced model} regresses them only on the library type. For each gene, we fit generalized linear models (GLMs) according to the two models, and then compare them in order to infer whether the additional specification of the treatment improves the fit and hence, whether the treatment has significant effect. <>= fit1 = fitNbinomGLMs( cdsFull, count ~ libType + condition ) fit0 = fitNbinomGLMs( cdsFull, count ~ libType ) @ These commands take a while to execute. Also, they may produce a few warnings, informing you that the GLM fit failed to converge (and the results from these genes should be interpreted with care). The ``fit'' objects are data frames with three columns: <>= str(fit1) @ To perform the test, we call <>= pvalsGLM = nbinomGLMTest( fit1, fit0 ) padjGLM = p.adjust( pvalsGLM, method="BH" ) @ % \fixme{Can we add a paragraph on what to do if we only want to make specific comparisons, e.g. let \texttt{fac} be a factor with three levels A, B and C, and we want to test pairwise for differences between A and B (without C), between A and C (without B) etc.} The function \Rfunction{nbinomTestGLM} returned simply a vector of $p$ values which we handed to the standard R function \Rfunction{p.adjust} to adjust for multiple testing using the Benjamini-Hochberg (BH) method. \begin{figure}[ht] \centering \includegraphics[width=.5\textwidth]{DESeq-figDispScatter} \caption{Comparison of per-gene estimates of the dispersion in the analysis using only the four paired-end samples ($x$-axis) and in the analysis using all seven samples ($y$-axis). For visualisation, the values are on a logarithm-like scale, defined by the function \Rfunction{trsf}, which is of the form $f(x)=\log\left((x+\sqrt{x^2+1})/2\right)$. For $x>2$, the values of $f(x)$ and $\log(x)$ are approximately the same, whereas for values of $x$ around 0, $f(x)\approx x$ is approximated by a straight line of slope 1.} \label{figDispScatter} \end{figure} Let's compare with the result from the four-samples test: <>= tab1 = table( "paired-end only" = res$padj < .1, "all samples" = padjGLM < .1 ) addmargins( tab1 ) @ We see that the analyses find \Sexpr{tab1[2,2]} genes in common, while \Sexpr{tab1[1,2]} were only found in the analysis using all samples and \Sexpr{tab1[2,1]} were specific for the \emph{paired-end only} analysis. In this case, the improvement in power that we gained from the additional samples is rather modest. This might indicate that the single-end samples (which are presumably older than the paired-end one) are of lower quality. This is supported by the observation that the dispersion estimates in the full data set tend to be larger than in the paired-end only one. So, despite the fact that with 7 samples we gain power from having more degrees of freedom in the estimation of the treatment effect, the additional samples also increase the dispersion (or equivalently, the variance), which loses power. % <>= table(sign(fitInfo(cds)$perGeneDispEsts - fitInfo(cdsFull)$perGeneDispEsts)) @ See also Figure~\ref{figDispScatter}, which is produced by % <>= trsf = function(x) log( (x + sqrt(x*x+1))/2 ) plot( trsf(fitInfo(cds)$perGeneDispEsts), trsf(fitInfo(cdsFull)$perGeneDispEsts), pch=16, cex=0.45, asp=1) abline(a=0, b=1, col="red3") @ Continuing with the analysis, we can now extract the significant genes from the vector \Robject{padjGLM} as before. To see the corresponding fold changes, we have a closer look at the object \Robject{fit1}. <>= head(fit1) @ The first three columns show the fitted coefficients, converted to a logarithm base 2 scale. The log2 fold change due to the condition is shown in the third column. As indicated by the column name, it is the effect of ``untreated'', i.e., the log ratio of ``untreated'' versus ``treated''. (This is unfortunately the other way round as before, due to the peculiarities of contrast coding.) Note that the library type also had noticeable influence on the expression, and hence would have increased the dispersion estimates (and so reduced power) if we had not fitted an effect for it. The column \emph{deviance} is the deviance of the fit. (Comparing the deviances with a $\chi^2$ likelihood ratio test is how \Rfunction{nbinomGLMTest} calculates the $p$ values.) The last column, \emph{converged}, indicates whether the calculation of coefficients and deviance has fully converged. (If it is false too often, you can try to change the GLM control parameters, as explained in the help page to \Rfunction{fitNbinomGLMs}.) \fixme{This is a bit vague, 'too often' should be specified and ideally the remedy be automated.} Finally, we show that taking the library type into account was important to have good detection power by doing the analysis again using the standard workflow, as outlined earlier, and without informing \Rpackage{DESeq} of the library types: <>= cdsFullB = newCountDataSet( pasillaCountTable, pasillaDesign$condition ) cdsFullB = estimateSizeFactors( cdsFullB ) cdsFullB = estimateDispersions( cdsFullB ) resFullB = nbinomTest( cdsFullB, "untreated", "treated" ) <>= tab2 = table( `all samples simple` = resFullB$padj < 0.1, `all samples GLM` = padjGLM < 0.1 ) addmargins(tab2) @ %$ % We see that the two analyses find \Sexpr{tab2[2,2]} genes in common, while in addition \Sexpr{tab2[1,2]} genes were found by the analysis that took library type into account. The small number, namely \Sexpr{tab2[2,1]}, of genes that only made the FDR cutoff in the simple analysis is likely due to sampling variation. %-------------------------------------------------- \section{Independent filtering and multiple testing} \label{sec:indepfilt} \subsection{Filtering by overall count} \label{sec:filtbycount} %-------------------------------------------------- The analyses of the previous sections involve the application of statistical tests, one by one, to each row of the data set, in order to identify those genes that have evidence for differential expression. The idea of \emph{independent filtering} is to filter out those tests from the procedure that have no, or little chance of showing significant evidence, without even looking at their test statistic. Typically, this results in increased detection power at the same experiment-wide type I error. Here, we measure experiment-wide type I error in terms of the false discovery rate. A good choice for a filtering criterion is one that \begin{enumerate} \item\label{it:indp} is statistically independent from the test statistic under the null hypothesis, \item\label{it:corr} is correlated with the test statistic under the alternative, and \item\label{it:joint} does not notably change the dependence structure --if there is any-- between the test statistics of nulls and alternatives. \end{enumerate} The benefit from filtering relies on property~\ref{it:corr}, and we will explore it further in Section~\ref{sec:whyitworks}. Its statistical validity relies on properties~\ref{it:indp} and \ref{it:joint}. We refer to~\cite{Bourgon:2010:PNAS} for further discussion on the mathematical and conceptual background. % <>= rs = rowSums ( counts ( cdsFull )) theta = 0.4 use = (rs > quantile(rs, probs=theta)) table(use) cdsFilt = cdsFull[ use, ] @ <>= stopifnot(!any(is.na(use))) @ % Above, we consider as a filter criterion \Robject{rs}, the overall sum of counts (irrespective of biological condition), and remove the genes in the lowest \Sexpr{theta*100}\% quantile (as indicated by the parameter \Robject{theta}). We perform the testing as before in Section~\ref{sec:GLM}. % <>= fitFilt1 = fitNbinomGLMs( cdsFilt, count ~ libType + condition ) fitFilt0 = fitNbinomGLMs( cdsFilt, count ~ libType ) pvalsFilt = nbinomGLMTest( fitFilt1, fitFilt0 ) padjFilt = p.adjust(pvalsFilt, method="BH" ) @ <>= stopifnot(all.equal(pvalsFilt, pvalsGLM[use])) @ Let us compare the number of genes found at an FDR of 0.1 by this analysis with that from the previous one (\Robject{padjGLM}). <>= padjFiltForComparison = rep(+Inf, length(padjGLM)) padjFiltForComparison[use] = padjFilt tab3 = table( `no filtering` = padjGLM < .1, `with filtering` = padjFiltForComparison < .1 ) addmargins(tab3) @ The analysis with filtering found an additional \Sexpr{tab3[1,2]} genes, an increase in the detection rate by about \Sexpr{round(100*tab3[1,2]/tab3[2,2])}\%, while \Sexpr{tab3[2,1]} genes were only found by the previous analysis. %-------------------------------------------------- \subsection{Why does it work?}\label{sec:whyitworks} %-------------------------------------------------- First, consider Figure~\ref{figscatterindepfilt}, which shows that among the 40--45\% of genes with lowest overall counts, \Robject{rs}, there are essentially none that achieved an (unadjusted) $p$ value less than \Sexpr{signif(quantile(pvalsGLM[!use], 0.0001, na.rm=TRUE), 1)} (this corresponds to about \Sexpr{signif(-log10(quantile(pvalsGLM[!use], 0.0001, na.rm=TRUE)), 2)} on the $-\log_{10}$-scale). % <>= plot(rank(rs)/length(rs), -log10(pvalsGLM), pch=16, cex=0.45) @ \begin{figure}[ht] \centering \includegraphics[width=.5\textwidth]{DESeq-figscatterindepfilt} \caption{Scatterplot of rank of filter criterion (overall sum of counts \Robject{rs}) versus the negative logarithm of the test statistic \Robject{pvalsGLM}.} \label{figscatterindepfilt} \end{figure} This means that by dropping the 40\% genes with lowest \Robject{rs}, we do not loose anything substantial from our subsequent results. Second, consider the $p$ value histogram in Figure~\ref{fighistindepfilt}. It shows how the filtering ameliorates the multiple testing problem -- and thus the severity of a multiple testing adjustment -- by removing a background set of hypotheses whose $p$ values are distributed more or less uniformly in $[0,1]$. <>= h1 = hist(pvalsGLM[!use], breaks=50, plot=FALSE) h2 = hist(pvalsGLM[use], breaks=50, plot=FALSE) colori = c(`do not pass`="khaki", `pass`="powderblue") <>= barplot(height = rbind(h1$counts, h2$counts), beside = FALSE, col = colori, space = 0, main = "", ylab="frequency") text(x = c(0, length(h1$counts)), y = 0, label = paste(c(0,1)), adj = c(0.5,1.7), xpd=NA) legend("topright", fill=rev(colori), legend=rev(names(colori))) @ \begin{figure}[ht] \centering \includegraphics[width=.5\textwidth]{DESeq-fighistindepfilt} \caption{Histogram of $p$ values for all tests (\Robject{pvalsGLM}). The area shaded in blue indicates the subset of those that pass the filtering, the area in khaki those that do not pass.} \label{fighistindepfilt} \end{figure} %-------------------------------------------------- \subsection{How to choose the filter statistic and the cutoff?}\label{sec:indepfilterchoose} %-------------------------------------------------- Please refer to the vignette \emph{Diagnostic plots for independent filtering} in the \Rpackage{genefilter} package for a discussion on \begin{packeditemize} \item best choice of filter criterion and \item the choice of filter cutoff. \end{packeditemize} %--------------------------------------------------- \subsection{Diagnostic plots for multiple testing} %--------------------------------------------------- The Benjamini-Hochberg multiple testing adjustment procedure~\cite{BH:1995} has a simple graphical illustration, which we produce in the following code chunk. Its result is shown in the left panel of Figure~\ref{figmulttest}. % <>= orderInPlot = order(pvalsFilt) showInPlot = (pvalsFilt[orderInPlot] <= 0.08) alpha = 0.1 <>= plot(seq(along=which(showInPlot)), pvalsFilt[orderInPlot][showInPlot], pch=".", xlab = expression(rank(p[i])), ylab=expression(p[i])) abline(a=0, b=alpha/length(pvalsFilt), col="red3", lwd=2) @ <>= whichBH = which(pvalsFilt[orderInPlot] <= alpha*seq(0, 1, length=length(pvalsFilt))) ## Test some assertions: ## - whichBH is a contiguous set of integers from 1 to length(whichBH) ## - the genes selected by this graphical method coincide with those ## from p.adjust (i.e. padjFilt) stopifnot(length(whichBH)>0, identical(whichBH, seq(along=whichBH)), padjFilt[orderInPlot][ whichBH] <= alpha, padjFilt[orderInPlot][-whichBH] > alpha) @ % Schweder and Spj\o{}tvoll~\cite{SchwederSpjotvoll1982} suggested a diagnostic plot of the observed $p$-values which permits estimation of the fraction of true null hypotheses. For a series of hypothesis tests $H_1, \ldots, H_m$ with $p$-values $p_i$, they suggested plotting % \begin{equation} \left( 1-p_i, N(p_i) \right) \mbox{ for } i \in 1, \ldots, m, \end{equation} % where $N(p)$ is the number of $p$-values greater than $p$. An application of this diagnostic plot to \Robject{pvalsFilt} is shown in the right panel of Figure~\ref{figmulttest}. When all null hypotheses are true, the $p$-values are each uniformly distributed in $[0,1]$, Consequently, the cumulative distribution function of $(p_1, \ldots, p_m)$ is expected to be close to the line $F(t)=t$. By symmetry, the same applies to $(1 - p_1, \ldots, 1 - p_m)$. When (without loss of generality) the first $m_0$ null hypotheses are true and the other $m-m_0$ are false, the cumulative distribution function of $(1-p_1, \ldots, 1-p_{m_0})$ is again expected to be close to the line $F_0(t)=t$. The cumulative distribution function of $(1-p_{m_0+1}, \ldots, 1-p_{m})$, on the other hand, is expected to be close to a function $F_1(t)$ which stays below $F_0$ but shows a steep increase towards 1 as $t$ approaches $1$. In practice, we do not know which of the null hypotheses are true, so we can only observe a mixture whose cumulative distribution function is expected to be close to % \begin{equation} F(t) = \frac{m_0}{m} F_0(t) + \frac{m-m_0}{m} F_1(t). \end{equation} % <>= j = round(length(pvalsFilt)*c(1, .66)) px = (1-pvalsFilt[orderInPlot[j]]) py = ((length(pvalsFilt)-1):0)[j] slope = diff(py)/diff(px) @ % Such a situation is shown in the right panel of Figure~\ref{figmulttest}. If $F_1(t)/F_0(t)$ is small for small $t$, then the mixture fraction $\frac{m_0}{m}$ can be estimated by fitting a line to the left-hand portion of the plot, and then noting its height on the right. Such a fit is shown by the red line in the right panel of Figure~\ref{figmulttest}. Here we used a value for \Robject{slope} of \Sexpr{round(slope)}, the computation can be seen in the \texttt{.Rnw} source code of this vignette. % <>= plot(1-pvalsFilt[orderInPlot], (length(pvalsFilt)-1):0, pch=".", xlab=expression(1-p[i]), ylab=expression(N(p[i]))) abline(a=0, b=slope, col="red3", lwd=2) @ \begin{figure}[ht] \centering \includegraphics[width=.49\textwidth]{DESeq-sortedP} \includegraphics[width=.49\textwidth]{DESeq-SchwederSpjotvoll} \caption{\emph{Left:} illustration of the Benjamini-Hochberg multiple testing adjustment procedure~\cite{BH:1995}. The black line shows the $p$-values ($y$-axis) versus their rank ($x$-axis), starting with the smallest $p$-value from the left, then the second smallest, and so on. Only the first \Sexpr{sum(showInPlot)} $p$-values are shown. The red line is a straight line with slope $\alpha/n$, where $n=\Sexpr{length(pvalsFilt)}$ is the number of tests, and $\alpha=\Sexpr{alpha}$ is a target false discovery rate (FDR). FDR is controlled at the value $\alpha$ if the genes are selected that lie to the left of the rightmost intersection between the red and black lines: here, this results in \Sexpr{length(whichBH)} genes. \emph{Right:} Schweder and Spj\o{}tvoll plot, as described in the text. For both of these plots, the $p$-values \Robject{pvalsFilt} from Section~\ref{sec:filtbycount} were used as a starting point. Analogously, one can produce these types of plots for any set of $p$-values, for instance those from the previous sections.} \label{figmulttest} \end{figure} %--------------------------------------------------- \section{Variance stabilizing transformation} %--------------------------------------------------- For some applications, it is useful to work with transformed versions of the count data. Maybe the most obvious choice is the logarithmic transformation. Since count values for a gene can be zero in some conditions (and non-zero in others), some advocate the use of \emph{pseudocounts}, i.\,e.\ transformations of the form \begin{equation}\label{eq:shiftedlog} y = \log_2(n + 1)\quad\mbox{or more generally,}\quad y = \log_2(n + n_0), \end{equation} where $n$ represents the count values and $n_0$ is a somehow chosen positive constant. In this section, we discuss a related, alternative approach that offers more theoretical justification and a rational way of choosing the parameter equivalent to $n_0$ above. It is based on error modeling and the concept of variance stabilizing transformations~\cite{Tibshirani1988,sagmb2003,Anders:2010:GB}. We estimate an overall mean-dispersion relationship of the data using \Rfunction{estimateDispersions} with the argument \Robject{method="blind"} and call the function \Rfunction{getVarianceStabilizedData}. % <>= cdsBlind = estimateDispersions( cds, method="blind" ) vsd = varianceStabilizingTransformation( cdsBlind ) @ Here, we have used a parametric fit for the dispersion. In this case, the a closed-form expression for the variance stabilizing transformation is used by \Rfunction{getVarianceStabilizedData}, which is derived in the document \texttt{vst.pdf} (you find it in the \Rpackage{DESeq} package alongside this vignette). If a local fit is used (option \texttt{fittype="local"} to \Rfunction{estimateDispersion}) a numerical integration is used instead. % The resulting transformation is shown in Figure~\ref{figvsd1}. The code that produces the figure is hidden from this vignette for the sake of brevity, but can be seen in the \texttt{.Rnw} or \texttt{.R} source file. % \begin{figure}[ht] \centering \includegraphics[width=.49\textwidth]{DESeq-vsd1} \caption{Graphs of the variance stabilizing transformation for sample 1, in blue, and of the transformation $f(n)=log_2(n/s_1)$, in black. $n$ are the counts and $s_1$ is the size factor for the first sample. } \label{figvsd1} \end{figure} \begin{figure}[ht] \centering \includegraphics[width=\textwidth]{DESeq-vsd2} \caption{Per-gene standard deviation (taken across samples), against the rank of the mean, for the shifted logarithm $\log_2(n+1)$ (left) and \Rpackage{DESeq}'s variance stabilising transformation (right).} \label{figvsd2} \end{figure} <>= ##par(mai=ifelse(1:4 <= 2, par("mai"), 0)) px = counts(cds)[,1] / sizeFactors(cds)[1] ord = order(px) ord = ord[px[ord] < 150] ord = ord[seq(1, length(ord), length=50)] last = ord[length(ord)] vstcol = c("blue", "black") matplot(px[ord], cbind(exprs(vsd)[, 1], log2(px))[ord, ], type="l", lty=1, col=vstcol, xlab="n", ylab="f(n)") legend("bottomright", legend = c( expression("variance stabilizing transformation"), expression(log[2](n/s[1]))), fill=vstcol) @ % Figure~\ref{figvsd2} plots the standard deviation of the transformed data, across samples, against the mean, first using the shifted logarithm transformation~(\ref{eq:shiftedlog}), then using \Rpackage{DESeq}'s variance stabilising transformation. While for the latter, the standard deviation is roughly constant along the whole dynamic range, the shifted logarithm results in a highly elevated standard deviation in the lower count range. % <>= library("vsn") par(mfrow=c(1,2)) notAllZero = (rowSums(counts(cds))>0) meanSdPlot(log2(counts(cds)[notAllZero, ] + 1)) meanSdPlot(vsd[notAllZero, ]) @ %--------------------------------------------------------------- \subsection{Application to moderated fold change estimates} %--------------------------------------------------------------- In the beginning of Section~\ref{sec:DE}, we have seen in the \Rclass{data.frame} \Robject{res} the (logarithm base 2) fold change estimate computed from the size-factor adjusted counts. When the involved counts are small, these (logarithmic) fold-change estimates can be highly variable, and can even be infinite. For some purposes, such as the clustering of samples or genes according to their expression profiles, or for visualisation of the data, this high variability from ratios between low counts tends to drown informative, systematic signal in other parts of the data. The variance stabilizing transformation offers one way to \emph{moderate} the fold change estimates, so that they are more amenable to plotting or clustering. % <>= mod_lfc = (rowMeans( exprs(vsd)[, conditions(cds)=="treated", drop=FALSE] ) - rowMeans( exprs(vsd)[, conditions(cds)=="untreated", drop=FALSE] )) @ % Let us compare these to the original ($\log_2$) fold changes. First we find that many of the latter are infinite (resulting from division of a finite value by 0) or \emph{not a number} (NaN, resulting from division of 0 by 0). % <>= lfc = res$log2FoldChange table(lfc[!is.finite(lfc)], useNA="always") @ % For plotting, let us bin genes by their $\log_{10}$ mean to colour them according to expression strength, % <>= logdecade = 1 + round( log10( 1+rowMeans(counts(cdsBlind, normalized=TRUE)) ) ) lfccol = colorRampPalette( c( "gray", "blue" ) )(6)[logdecade] @ % and then compare their ordinary log-ratios (\Robject{lfc}) against the \emph{moderated} log-ratios (\Robject{mod\_lfc}) in a scatterplot. % <>= ymax = 4.5 plot( pmax(-ymax, pmin(ymax, lfc)), mod_lfc, xlab = "ordinary log-ratio", ylab = "moderated log-ratio", cex=0.45, asp=1, col = lfccol, pch = ifelse(lfc<(-ymax), 60, ifelse(lfc>ymax, 62, 16))) abline( a=0, b=1, col="red3") @ The result is shown in Figure~\ref{figmodlr}. \begin{figure}[htb] \centering \includegraphics[width=.5\textwidth]{DESeq-figmodlr} \caption{Scatterplot of ordinary (\Robject{lfc}) versus \emph{moderated} log-ratios (\Robject{mod\_lfc}). The points are coloured in a scale from grey to blue, representing weakly to strongly expressed genes. For the highly expressed genes (blue), \Robject{lfc} and \Robject{mod\_lfc} agree. Differences arise when the involved counts are small (grey points): in this case, the moderated log-ratio is shrunk towards 0, compared to the ordinary log-ratio. The $>$ and $<$ symbols correspond to values of \Robject{lfc} whose absolute value was larger than \Sexpr{ymax} (including those that were infinite). All values of \Robject{mod\_lfc} vary in a finite range.} \label{figmodlr} \end{figure} %--------------------------------------------------------------- \section{Data quality assessment by sample clustering and visualisation}\label{sec:quality} %--------------------------------------------------------------- Data quality assessment and quality control (i.\,e.\ the removal of insufficiently good data) are essential steps of any data analysis. Even though we present these steps towards the end of this vignette, they should typically be performed very early in the analysis of a new data set, preceding or in parallel to the differential expression testing. We define the term \emph{quality} as \emph{fitness for purpose}\footnote{\url{http://en.wikipedia.org/wiki/Quality_\%28business\%29}}. Our purpose is the detection of differentially expressed genes, and we are looking in particular for samples whose experimental treatment suffered from an anormality that renders the data points obtained from these particular samples detrimental to our purpose. \subsection{Heatmap of the count table}\label{sec:hmc} To explore a count table, it is often instructive to look at it as a heatmap. Below we show how to produce such a heatmap from the variance stabilisation transformed data for all \Sexpr{ncol(cdsFull)} samples. % <>= cdsFullBlind = estimateDispersions( cdsFull, method = "blind" ) vsdFull = varianceStabilizingTransformation( cdsFullBlind ) <>= library("RColorBrewer") library("gplots") select = order(rowMeans(counts(cdsFull)), decreasing=TRUE)[1:30] hmcol = colorRampPalette(brewer.pal(9, "GnBu"))(100) <>= heatmap.2(exprs(vsdFull)[select,], col = hmcol, trace="none", margin=c(10, 6)) @ % \begin{figure} \centering \includegraphics[width=.49\textwidth]{DESeq-figHeatmap2a} \includegraphics[width=.49\textwidth]{DESeq-figHeatmap2b} \caption{Heatmaps showing the expression data of the \Sexpr{length(select)} most highly expressed genes. Left, the variance stabilisation transformed data (\Robject{vsdFull}) are shown, right, the original count data (\Robject{cdsFull}). In the left panel, the sample clustering aligns with the experimental factor (\emph{treated} / \emph{untreated}). The clustering and the colour scale in the right plot is dominated by a small number of data points with large values.} \label{figHeatmap2} \end{figure} % The left panel of Figure~\ref{figHeatmap2} shows the resulting heatmap for the \Sexpr{length(select)} most highly expressed genes. For comparison, let us also do the same with the untransformed counts. % <>= heatmap.2(counts(cdsFull)[select,], col = hmcol, trace="none", margin=c(10,6)) @ \begin{figure} \centering \includegraphics[width=.6\textwidth]{DESeq-figHeatmapSamples} \caption{Heatmap showing the Euclidean distances between the samples as calculated from the variance stabilising transformation of the count data.} \label{figHeatmapSamples} \end{figure} \subsection{Heatmap of the sample-to-sample distances}\label{sec:dists} Another use of variance stabilized data is sample clustering. Here, we apply the \Rfunction{dist} function to the transpose of the transformed count matrix to get sample-to-sample distances. % <>= dists = dist( t( exprs(vsdFull) ) ) @ % A heatmap of this distance matrix gives us an overview over similarities and dissimilarities between samples (Figure~\ref{figHeatmapSamples}): <>= mat = as.matrix( dists ) rownames(mat) = colnames(mat) = with(pData(cdsFullBlind), paste(condition, libType, sep=" : ")) heatmap.2(mat, trace="none", col = rev(hmcol), margin=c(13, 13)) @ % The clustering correctly reflects our experimental design, i.e., samples are more similar when they have the same treatment or the same library type. (To avoid potential circularities in this conclusion, it was important to re-estimate the dispersions with \Robject{method="blind"} in the calculation for \Robject{cdsFullBlind} above, as only then, the variance stabilizing transformation is not informed about the design, and we can be sure that it is not biased towards a result supporting the design.) \subsection{Principal component plot of the samples} Related to the distance matrix of Section~\ref{sec:dists} is the PCA plot of the samples, which we obtain as follows (Figure~\ref{figPCA}). % <>= print(plotPCA(vsdFull, intgroup=c("condition", "libType"))) @ \begin{figure} \centering \includegraphics[width=.6\textwidth]{DESeq-figPCA} \caption{PCA plot. The \Sexpr{ncol(vsdFull)} samples shown in the 2D plane spanned by their first two principal components. This type of plot is useful for visualizing the overall effect of experimental covariates and batch effects. For this data set, no batch effects besides the known effects of \emph{condition} and \emph{libType} are discernible.} \label{figPCA} \end{figure} \subsection{arrayQualityMetrics} Heatmaps and PCA plots similar to Figures~\ref{figHeatmapSamples} and \ref{figPCA} as well as some further diagnostics are also provided by the package \Rpackage{arrayQualityMetrics}. The package may be particularly useful for larger data set with dozens of samples. You can call its main function, which is also called \Rfunction{arrayQualityMetrics}, with an \Rclass{ExpressionSet} such as \Robject{vsdFull}, which you will have produced from your \Rclass{CountDataSet} with calls to \Rfunction{estimateDispersions} and \Rpackage{varianceStabilizingTransformation} as in the beginning of Section~\ref{sec:hmc}. \clearpage %------------------------------------------------------------ \section{Further reading}\label{sec:further} %------------------------------------------------------------ For more information on the statistical method, see our paper~\cite{Anders:2010:GB}. For more information on how to customize the \Rpackage{DESeq} work flow, see the package help pages, especially the help page for \Rfunction{estimateDispersions}. %------------------------------------------------------------ \section{Changes since publication of the paper}\label{sec:changes} %------------------------------------------------------------ Since our paper on \Rpackage{DESeq} was published in Genome Biology in Oct 2010, we have made a number of changes to algorithm and implementation, which are listed here. \begin{itemize} \item \Rfunction{nbinomTest} calculates a $p$ value by summing up the probabilities of all per-group count sums $a$ and $b$ that sum up to the observed count sum $k_{iS}$ and are more extreme than the observed count sums $k_{iA}$ and $k_{iB}$. Equation~(11) of the paper defined \emph{more extreme} as those pairs of values $(a,b)$ that had smaller probability than the observed pair. This caused problems in cases where the dispersion exceeded 1. Hence, we now sum instead the probabilities of all values pairs that are \emph{further out} in the sense that they cause a more extreme fold change $(a/s_A)/(b/s_B)$, where $s_A$ and $s_B$ are the sums of the size factors of the samples in conditions $A$ and $B$, respectively. We do this in a one-tailed manner and double the result. Furthermore, we no longer approximate the sum, but always calculate it exactly. \item We added the possibility to fit GLMs of the negative binomial family with log link. This new functionality is described in this vignette. $p$ values are calculated by a $\chi^2$ likelihood ratio test. The logarithms of the size factors are provided as offsets to the GLM fitting function. \item The option \texttt{sharingMode='maximum'} was added to \Rfunction{estimateDispersion} and made default. This change makes DESeq robust against variance outliers and was not yet discussed in the paper. \item By default, DESeq now estimates one pooled dispersion estimate across all (replicated) conditions. In the original version, we estimated a separate dispersion-mean relation for each condition. The ``maximum'' sharing mode achieves its goal of making DESeq robust against outliers only with pooled dispersion estimate, and hence, this is now the default. The option \texttt{method='per-condition'} to \Rfunction{estimateDispersions} allows the user to go back to the old method. \item In the paper, the mean-dispersion relation is fitted by local regression. Now, DESeq also offers a parametric regression, as described in this vignette. The option \texttt{fitType} to \Rfunction{estimateDispersions} allows the user to choose between these. If a parametric regression is used, the variance stabilizing transformation is calculated using the closed-form expression given in the vignette supplement file \texttt{vst.pdf}. \item Finally, instead of the term \emph{raw squared coefficient of variance} used in the paper we now prefer the more standard term \emph{dispersion}. \end{itemize} \section{Session Info} <>= sessionInfo() @ \bibliographystyle{unsrt} \bibliography{DESeq} \end{document} DESeq/inst/doc/DESeq.pdf0000644000175500017550000423132313556150210015727 0ustar00biocbuildbiocbuild%PDF-1.5 % 133 0 obj << /Length 2760 /Filter /FlateDecode >> stream xZ[sܶ~ׯ[W3!K$Hc;NIi?pw{.W?s%ʒ;4=-I8;".4,ϲ,2EbME$.*OOy ߜ;3/[.#cجKez/q#+|fG$"FER!dsS0ʒ(}>dėKs9-āe KwHc˝AvY8׎?}6G|qV9PÍmxt4O/w(WT_%a.2g78e/ܮQn|k߭7';P*ħc9Ws7Y`{;D&n'DHc2d8͒b%v8)ѻ"SfGɔpW2?14 oI&̎:PlwdedeRyO֎V^{\NTє Ϻ;E@%6%l.3p~p)(aVZ:mxZگt_nQ{| X;AZÂ;L 2c<2^̺VU"%jW#ZR_tڊ;)z6wRre\\jidhRx(/\PLk ^|!)N Xݕ NmhCԻqId^KY dZ6'U*pSs/.yAt=P5"fb VjA9c Nƶ"^٪%K#` *+`/{$ЖG-=mUih w7#_KY:A!ToU;.|M#bEMž3yAay2\0@p9 Xř'Fy!̇W(e`0?sp`Tz.㏡A OEVxMEZ 6]#Wq09a5Vz/a'S~Gttًw-c w}Xm4^@#oEdS^a?u.z6O#paEQ?Ln0qK<Сpn!قY <eɑSgxǻ.y=OӎA*XjCk* IN-{(4&'"OWR4@Zρ}SFGPeT B|epn= O8Hm%ê;,ߌ}4ݻX$9zo5DΉkX_^2ğpZ\^vCLJ+\݂f'%sge\j:{4 7NzͦhԡZ1Oi/z>ܟF5BmĮnN&[w!kWD2kIᨹ|֌LvƋ!?kJ;)װ~sM, L,)O,0Q>$}HNG^j@y#8 ڎ0Wr_IKL] 9H3roou&Aa¾c@}AYx&I>~Cab +(3GIYe,;֛:g>鷃n .y5 *-ǰb,+/.8fuiqB_\8qL1#dZ}NC7zHcs NT<;UvTdJ !͞kTa:sɁ׼?FR8Q. +w{Sm&:P몲Pk> stream xi #_U r&m~JƖ=n|Œgv?_dyAD{||jNy˻WoTI|rd&)rRen1qқMQS;-7"OT-mk'Y:_&QY\L03&I ofJ9pjw7&C׺#L[ݫ_*MTn?{ðNlY$YV=./KhTRe\֕8dqw `:Po\@}[hMV}4`w8Yf{p mE:)+w_y~=xno`Hrij673Ox1B6衎 ͚u@~O)L89 li?Hx#4f$ÙOKvl?ĺ^IZuB:粆* 9-hVhۅKFܽA%]k7 0 i82?h Y5<桸֑<7jz w 7Ľ W)qUEZ1^b;7*OB i0jfV4F $/{V)t( eHLk6Rǃ51m> E4ڏ<=qPÄȝh@t]5 7iA'a!asiWuI;֠ W{ uAڔ/p6֑w<- –6y_\q@wV%y4 BF싻 ~{7hIG#^q[ڵ27h=]EhY1~( vfk?A'0cu`8t\ ֭Yb#uxYh  j^ܑ~1- u5UTC|G aˊM]-r`Q ڰ4LCxd/Zm \$[bYMŹwLtiLr/VUoh=b]p*k"KJ=U$ ֈY$!j63v8d(]lE:f s #NS[ǎnX!4(xOOWan3NLрɭ(R8,u{{Ƣ=Or*A?s̭D҄sP.,GOㅸd0 p"۰V+ xx,[Xi'PmlqW.s܍HܓB=xv] c"Bc*?|ъֵ[ Q+@YZs.,:P)auh`mT+N[XW0[!5oG(ړE(3_Ptl; `fc4>)Aȅ' v&ݴ5ؐ)QԢ V@@(}0&@5Ã{4;tsjl={Yl"j Z„D)6olIQ>P ▓؎iF3׌Rq-)U1QAVH ]EQ/I]0Œ^G0N:= JǼ; 7yτ iwt,ĉu=33vnRb)@Bݏg9eMCAb]kK6HR҂%N'Cz`QӨ~uRlNn-h8ܷ&D; yV Ux6^߁bNtB&쳒sR`JE/rd= {HVP:DbM,2m3h3-,8vsH;CT1rv31nfP'VbFghS#J}{CEEny)s;J!/+J7$!Tל> Vx^PlV41%ڋ(Re}dT1̜J\Q$^UIf=*%p^'1R%J{竑Mg* b&xǘ+DC9-@PzMBRM: !!zWKLF}1M%u@Fܔ1=mځ6$y.qSDA%U]dg:d]৙~ A!0X!.F E*lswY &P cVb c[g ǰųyR\4tϰMGhzQf=%f,ՙ.vqxU<;oFiP[ʪݯС|w(.ioJz5Y7ܧNEi~ UQ6%Fμ0, ⎉A fX{yfI!3tk"S+} o!28.^} ށfBOz .&KTc5 2lQ&P񲏬M2<%T>iP͍h"9,-oN!FL\F_N5IYK-q& Io62_C)N ŵOo}ϥZ(n8p Xe/4]ǧ9e!BK#H+Z*6_Fz:)&/>]^fwfP?`GZ>5@AWh4tOs9f@]f_sS oF(|zk)p\`,>I':eb _&$ifh\#5ьSfGQR\P^&΍aΈpF&3ښfu?X=P4n[Ʌf眺hjF |XNІlq3fS#JҖ;cy: T2oz> stream x]s~ҙ !tNS5yy{)u"e?_JEA" , j&Oo{GRY/gY0y¬/flͯOOqw'Q4k4 ˠu毆a0|K&%;W7zP[2zI \p-|:w0̈U_e~.|44tPI.c.jw0TqG nYMgu:A`ꁏ(gsUA aǬ#%B;?%J#_";F}D3%iZ64*18<3ЈW(HOis?h;C+z= 'EX+ *= QP!2emhcyc7PzeX@sMP>"0EFz~lccˆj, 5βwSuVpZ&!u8&^<8> eT7_ yi(#< 7ܐ?wS MMa%¬dY4{V2})8bShW.mñ`鼉 M{)`TS|oDb"Rox.Mt`xhu dqo[ ed/_6m,UY;1wu"88d!Bo=IJۛ:[Xx:Lg=FnbD]g$lZH0m.F\6S\Rߌ1䡭XǨ(.#V6u;Ok,?ATh4!%th5Nz*z 3a:U4dͨFn ]ɔHh/9sy%`:X A[]Q%sYe̡щ*dHHXg&`$,ccsSraj$p+h[z8/UNZs@S;@z!+,D?.Zns,K4&f{,1:x/9Glu|z% ~[XZRW:R` ja-c>t>a|ܵR:N[$0M1uctuoEG7UXC{]uc`%B.i٪tlM9 <:*7 \ꑢD>od$C{s Z(<-1٪~2& ~x>B;]ǩXQ_"aW~TbW5cݒM W8͎]ަkK h*`BO7msp$T0U/M+'[{gI? 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It is used for the examples in the package help pages. } \usage{ makeExampleCountDataSet() } \value{ a CountDataSet that has been constructed as follows: First, true base mean values for 10,000 genes are drawn from an exponential distribution with rate 1/250. Then, certain genes are declared (with probability 0.3 per gene) as truly differentially expressed (tDE). For these genes, the true base mean is split into two values, one for condition "A" and one for condition "B", such that the log2 fold change from "A" to "B" follows a zero-centred normal distribution with standard deviation 2. Then, counts are drawn for each gene for 5 samples, the first three corresponding to condition "A" and the remaining two for condition "B". The counts are drawn from a negative binomial with the specified mean, multiplied by the size factor for the sample, with a constant raw SCV (dispersion) of 0.2 (i.e., a 'size' parameter of 1/0.2). The true size factors are fixed to c( 1., 1.3, .7, .9, 1.6 ). All these values were chosen to give data that at least somewhat resembles what one might encounter in an actual experiment. Note that this function is not meant to verify the package by simulation. For this purpose the parameters and distribution choices should be more varied. } \author{ Simon Anders, anders@embl.de } \examples{ cds <- makeExampleCountDataSet() } DESeq/man/nbinomGLMTest.Rd0000644000175500017550000000172313554551773016311 0ustar00biocbuildbiocbuild\name{nbinomGLMTest} \alias{nbinomGLMTest} \title{ Perform chi-squared tests comparing two sets of GLM fits } \description{ For each gene, the function calculates a chi-square p value by simply calculating: \code{1 - pchisq(resReduced$deviance - resFull$deviance, attr(resReduced, "df.residual") - attr(resFull, "df.residual"))} } \usage{ nbinomGLMTest(resFull, resReduced) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{resFull, resReduced}{ GLM fit data frames, as returned by \code{\link{fitNbinomGLMs}}, first the full, then the reduced model. } } \value{ a vector of p values } \author{ Simon Anders, anders@embl.de } \seealso{ \code{\link{fitNbinomGLMs}} } \examples{ cds <- makeExampleCountDataSet()[ 1:100, ] cds <- estimateSizeFactors( cds ) cds <- estimateDispersions( cds, method="pooled" ) fit1 <- fitNbinomGLMs( cds, count ~ condition ) fit0 <- fitNbinomGLMs( cds, count ~ 1 ) nbinomGLMTest( fit1, fit0 ) } DESeq/man/nbinomTest.Rd0000644000175500017550000000336213554551773015752 0ustar00biocbuildbiocbuild\name{nbinomTest} \Rdversion{1.1} \alias{nbinomTest} \title{ Test for differences between the base means for two conditions } \description{ This function tests for differences between the base means of two conditions (i.e., for differential expression in the case of RNA-Seq). } \usage{ nbinomTest(cds, condA, condB, pvals_only = FALSE, eps=NULL ) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{cds}{ a CountDataSet with size factors and raw variance functions } \item{condA}{ one of the conditions in 'cds' } \item{condB}{ another one of the conditions in 'cds' } \item{pvals_only}{ return only a vector of (unadjusted) p values instead of the data frame described below. } \item{eps}{ This argument is no longer used. Do not use it. } } \details{ See \code{\link{nbinomTestForMatrices}} for more technical informations } \value{ A data frame with the following columns: \item{id}{The ID of the observable, taken from the row names of the counts slots.} \item{baseMean}{The base mean (i.e., mean of the counts divided by the size factors) for the counts for both conditions} \item{baseMeanA}{The base mean (i.e., mean of the counts divided by the size factors) for the counts for condition A} \item{baseMeanB}{The base mean for condition B} \item{foldChange}{The ratio meanB/meanA} \item{log2FoldChange}{The log2 of the fold change} \item{pval}{The p value for rejecting the null hypothesis 'meanA==meanB'} \item{padj}{The adjusted p values (adjusted with 'p.adjust( pval, method="BH")')} } \author{ Simon Anders, sanders@fs.tum.de } \examples{ cds <- makeExampleCountDataSet() cds <- estimateSizeFactors( cds ) cds <- estimateDispersions( cds ) head( nbinomTest( cds, "A", "B" ) ) } DESeq/man/nbinomTestForMatrices.Rd0000644000175500017550000000356413554551773020115 0ustar00biocbuildbiocbuild\name{nbinomTestForMatrices} \Rdversion{1.1} \alias{nbinomTestForMatrices} \title{ Perform row-wise tests for differences between the base means of two count matrices. } \description{ This function is called by \code{\link{nbinomTest}}. Call it directly only if the S4 interface is unsuitable for your task. } \usage{ nbinomTestForMatrices(countsA, countsB, sizeFactorsA, sizeFactorsB, dispsA, dispsB ) } \arguments{ \item{countsA}{ A matrix of counts, where each column is a replicate } \item{countsB}{ Another matrix of counts, where each column is a replicate} \item{sizeFactorsA}{ Size factors for the columns of the matrix 'countsA' } \item{sizeFactorsB}{ Size factors for the columns of the matrix 'countsB' } \item{dispsA}{ The dispersions for 'countsA', a vector with one value per gene } \item{dispsB}{ The same for 'countsB' } } \details{ See the vignette for an exact description of the null hypothesis tested. } \value{ A vector of unadjusted p values, one for each row in the counts matrices. } \author{ Simon Anders, sanders@fs.tum.de } \examples{ cds <- makeExampleCountDataSet() cds <- estimateSizeFactors( cds ) cds <- estimateDispersions( cds, method="per-condition" ) colsA <- conditions(cds) == "A" colsB <- conditions(cds) == "B" bmvA <- getBaseMeansAndVariances( counts(cds)[,colsA], sizeFactors(cds)[colsA] ) bmvB <- getBaseMeansAndVariances( counts(cds)[,colsB], sizeFactors(cds)[colsB] ) pvals <- nbinomTestForMatrices( counts(cds)[,colsA], counts(cds)[,colsB], sizeFactors(cds)[colsA], sizeFactors(cds)[colsB], fitInfo(cds,"A")$dispFunc( rowMeans( counts( cds, normalized=TRUE ) ) ), fitInfo(cds,"B")$dispFunc( rowMeans( counts( cds, normalized=TRUE ) ) ) ) names( pvals ) <- row.names( counts(cds) ) head( pvals ) # This here should give the same results: head( nbinomTest( cds, "A", "B" )$pval ) } DESeq/man/nbkd.sf.Rd0000644000175500017550000000146313554551773015155 0ustar00biocbuildbiocbuild\name{nbkd.sf} \alias{nbkd.sf} \title{ GLM family for a negative binomial with known dispersion and log link with size factors } \description{ A distribution family for use with \code{\link{glm}}. It describes a negative binomial (as \code{negative.binomial} in the MASS package), but with a special link function, namely eta[i] = log( mu[i] / sf[i] ), i.e., each count value is divided by its size factor before the log is taken. This is used internally by \code{\link{fitNbinomGLMs}}. } \usage{ nbkd.sf(r, sf) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{r}{ The 'size' argument (see \code{\link{dnbinom}}), i.e., the reciprocal of the dispersion. } \item{sf}{ A vector of size factors. } } \value{ A GLM family object. } \author{ Simon Anders, anders@embl.de } DESeq/man/newCountDataSet.Rd0000644000175500017550000000544113554551773016700 0ustar00biocbuildbiocbuild\name{newCountDataSet} \Rdversion{1.1} \alias{newCountDataSet} \title{ Create a CountDataSet object } \description{ This function creates a CountDataSet object from a matrix or data frame of count data. } \usage{ newCountDataSet(countData, conditions, sizeFactors = NULL, phenoData = NULL, featureData = NULL) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{countData}{ A matrix or data frame of count data, i.e., of non-negative integer values. The rows correspond to observations (e.g., number of reads that were assigned to a gene), the columns correspond to samples (or experiments). Note that biological replicates should each get their own column, while the counts of technical replicates (i.e., several sequencing ruins/lanes from the same sample) have to be summed up into a single column. } \item{conditions}{ A factor of experimental conditions (or treatments, or tissue types, or phenotypes, or the like). The length of the factor has to be equal to the number of columns of the countData matrix, assigning a condition to each sample. If 'conditions' is not a factor, it will be converted to one. Alternatively, you may pass a data frame, that will be placed in pData(cds) as is and can then be used with the modes "pooled" and "blind" in \code{\link{estimateVarianceFunctions}} and its columns can be refered top in a model formula provided to \code{\link{fitNbinomGLMs}}. } \item{sizeFactors}{ This argument is deprecated. Do not use it. (Size factors should always be estimated from the data with \code{\link{estimateSizeFactors}}. If you need to set size factors manually for some reasons, change the \code{pData(cds)$sizeFactor}. } \item{phenoData}{ You may pass an AnnotatedDataFrame here to describe the columns of the count matrix. Note that the package always adds two rows (or creates a new AnnotatedDataFrame with only these two rows in case you do not supply one) with names "condition" and "sizeFactor" to store this information. } \item{featureData}{ You may pass an AnnotatedDataFrame here to describe the rows of the count matrix. The package will just pass through this information without using it. Note that further columns will be added to feature data later, when estimating dispersions. } } \details{ See also \code{\link{CountDataSet-class}} and the documentation of \code{eSet} (package Biobase) for the meaning of the other slots, which CountDataSet inherits from eSet (but which the present package does not use). } \value{ an object of class CountDataSet } \author{ Simon Anders, sanders@fs.tum.de } \examples{ countsTable <- counts( makeExampleCountDataSet() ) cds <- newCountDataSet( countsTable, c( "A", "A", "A", "B", "B" ) ) } DESeq/man/newCountDataSetFromHTSeqCount.Rd0000644000175500017550000000203513554551773021436 0ustar00biocbuildbiocbuild\name{newCountDataSetFromHTSeqCount} \alias{newCountDataSetFromHTSeqCount} \title{ Create a new CountDataSet from count files generated with htseq-count } \description{Use this function to start a DESeq analysis if you used htseq-count to count your reads.} \usage{ newCountDataSetFromHTSeqCount(sampleTable, directory = ".") } \arguments{ \item{sampleTable}{ A data frame with three or more columns. Each row describes one sample. The first column is the sample name, the seond column the file name of the count file generated by htseq-count, and the remaining columns are sample meta data. If the meta data consists of only a single column (i.e., three columns in total), this is used as 'condition' factor. } \item{directory}{ The directory relative to which the filenames are specified. } } \value{ A CountDataSet object.} \references{ See http://www-huber.embl.de/users/anders/HTSeq/ for htseq-count.} \author{ Simon Anders} %% ~Make other sections like Warning with \section{Warning }{....} ~ \seealso{ \code{\link{newCountDataSet}}} DESeq/man/plotDispEsts.Rd0000644000175500017550000000255313554551773016266 0ustar00biocbuildbiocbuild\name{plotDispEsts} \alias{plotDispEsts} \title{Plot dispersion estimates and fitted values} \description{ A simple helper function that plots the per-gene dispersion estimates together with the fitted mean-dispersion relationship. } \usage{ plotDispEsts(cds, name=NULL, ymin, linecol="#ff000080", xlab = "mean of normalized counts", ylab = "dispersion", log = "xy", cex = 0.45, ... ) } \arguments{ \item{cds}{a \code{CountDataSet}.} \item{name}{this argument, together with \code{cds}, is passed on to \code{\link{fitInfo}}.} \item{ymin}{a scalar numeric, indicating the lower limit of the y-axis. The y-axis is plotted on the logarithmic scale. For the purpose of this plot, per-gene dispersion estimates that are below this value (in particular, those that happen to be zero) are shifted up to this value. If missing, the function attempts to guess a reasonable default.} \item{linecol}{colour used for the regression line} \item{xlab, ylab, log, cex, ...}{arguments that are passed on to \code{plot.default}.} } \details{This is a trivial helper function. Do not be afraid to edit and modify it to your needs.} \value{ The function is called for its side effect. } \author{ Simon Anders, sanders@fs.tum.de } \examples{ cds <- makeExampleCountDataSet() cds <- estimateSizeFactors( cds ) cds <- estimateDispersions( cds ) plotDispEsts(cds) } DESeq/man/plotMA.Rd0000644000175500017550000000210013554551773015011 0ustar00biocbuildbiocbuild\name{plotMA} \alias{plotMA} \title{Makes a so-called "MA-plot"} \description{ A simple helper function that makes a so-called "MA-plot", i.e. a scatter plot of logarithmic fold changes (on the y-axis) versus the mean of normalized counts (on the x-axis).} \usage{ plotMA(x, ylim, col = ifelse(x$padj>=0.1, "gray32", "red3"), linecol = "#ff000080", xlab = "mean of normalized counts", ylab = expression(log[2]~fold~change), log = "x", cex=0.45, ...) } \arguments{ \item{x}{a \code{data.frame} with columns \code{baseMean}, and \code{log2FoldChange}. In addition, if the argument \code{col} is left at its default, this \code{data.frame} also needs to have a column named \code{padj}.} \item{linecol}{colour used for the horizontal line at y=0.} \item{ylim, col, xlab, ylab, log, cex, ...}{arguments that are passed on to \code{plot.default}.} } \details{This is a trivial helper function. Do not be afraid to edit and modify it to your needs.} \value{ The function is called for its side effect. } \author{ Wolfgang Huber } \examples{ ## see vignette } DESeq/man/plotPCA.Rd0000644000175500017550000000154313554551773015131 0ustar00biocbuildbiocbuild\name{plotPCA} \alias{plotPCA} %- Also NEED an '\alias' for EACH other topic documented here. \title{ Sample PCA plot from variance-stabilized data } \description{This plot helps to check for batch effects and the like.} \usage{ plotPCA(x, intgroup = "condition", ntop = 500) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{x}{ an ExpressionSet, as obtained from \code{\link{varianceStabilizingTransformation}} } \item{intgroup}{ } \item{ntop}{ how many of the most variable genes should be used in calculating the PCA } } \value{ a plot is produced } \author{ Wolfgang Huber} \seealso{ \code{\link{varianceStabilizingTransformation}} } \examples{ cds <- makeExampleCountDataSet() cds <- estimateSizeFactors( cds ) cds <- estimateDispersions( cds, method="blind" ) vsd <- varianceStabilizingTransformation( cds ) plotPCA( vsd ) } DESeq/man/residualsEcdfPlot.Rd0000644000175500017550000000045013554551773017237 0ustar00biocbuildbiocbuild\name{residualsEcdfPlot} \Rdversion{1.1} \alias{residualsEcdfPlot} \title{ REMOVED } \description{ This function has been removed. Please see the vignette for our newer suggestions on how to check fit quality. } \usage{ residualsEcdfPlot(...) } \arguments{ \item{...}{ dummy argument} } DESeq/man/scvPlot.Rd0000644000175500017550000000037413554551773015262 0ustar00biocbuildbiocbuild\name{scvPlot} \alias{scvPlot} \title{ REMOVED } \description{ This function has been removed. Please see the vignette for our newer suggestions on how to check fit quality. } \usage{ scvPlot( ... ) } \arguments{ \item{...}{ dummy argument} } DESeq/man/sizeFactors.Rd0000644000175500017550000000167613554551773016132 0ustar00biocbuildbiocbuild\name{sizeFactors} \Rdversion{1.1} \docType{methods} \alias{sizeFactors,CountDataSet-method} \alias{sizeFactors<-,CountDataSet,numeric-method} \alias{sizeFactors} \title{ Accessor functions for the 'sizeFactors' information in a CountDataSet object. } \description{ The sizeFactors vector assigns to each column of the count data a value, the size factor, such that count values in the columns can be brought to a common scale by dividing by the corresponding size factor. } \usage{ \S4method{sizeFactors}{CountDataSet}(object) \S4method{sizeFactors}{CountDataSet,numeric}(object) <- value } \arguments{ \item{object}{a \code{CountDataSet} object.} \item{value}{a numeric vector, one size factor for each column in the count data.} } \seealso{ \code{\link{estimateSizeFactors}} } \examples{ cds <- makeExampleCountDataSet() cds <- estimateSizeFactors( cds ) sizeFactors(cds) } \author{ Simon Anders, sanders@fs.tum.de } DESeq/man/varianceFitDiagnostics.Rd0000644000175500017550000000047213554551773020252 0ustar00biocbuildbiocbuild\name{varianceFitDiagnostics} \Rdversion{1.1} \alias{varianceFitDiagnostics} \title{ REMOVED } \description{ This function has been removed. Please see the vignette for our newer suggestions on how to check fit quality. } \usage{ varianceFitDiagnostics( ... ) } \arguments{ \item{...}{ dummy argument} } DESeq/src/0000755000175500017550000000000013556150211013331 5ustar00biocbuildbiocbuildDESeq/src/pval.c0000644000175500017550000000755013554551773014466 0ustar00biocbuildbiocbuild#include #include #include #include #include #define MAX( a, b ) ( a > b ? a : b ) #define MIN( a, b ) ( a < b ? a : b ) void add_from_both_sides( long int left, long int right, long int kS, double pobs, double muA, double vA, double muB, double vB, double eps, double * res_total, double * res_obstotal) { double sizeA = muA*muA / (vA-muA); double probA = muA/vA; double sizeB = muB*muB / (vB-muB); double probB = muB/vB; long int kl = left; long int kr = right; double lval = Rf_dnbinom( kl, sizeA, probA, 0 ) * Rf_dnbinom( kS-kl, sizeB, probB, 0 ); double rval = Rf_dnbinom( kr, sizeA, probA, 0 ) * Rf_dnbinom( kS-kr, sizeB, probB, 0 ); double prevlval = lval; double prevrval = rval; double total = lval + rval; double esttotalperlength = total/2; double obstotal = 0; long int step = 1; long int steps = 0; int do_left; if( lval <= pobs ) obstotal += lval; if( rval <= pobs ) obstotal += rval; while( kl < kr ) { steps ++; if( fabs( ( prevrval - rval ) ) / prevrval > .01 ) do_left = 1; else if( fabs( ( prevlval - lval ) ) / prevlval > .01 ) do_left = 0; else do_left = lval > rval; if( do_left ) { prevlval = lval; if( kl + step > kr ) step = kr - kl; kl += step; lval = Rf_dnbinom( kl, sizeA, probA, 0 ) * Rf_dnbinom( kS-kl, sizeB, probB, 0 ); if( step == 1 ) total += lval; else total += MIN( lval, prevlval ) * step; if( lval <= pobs ) { if( step == 1 ) obstotal += lval; else { if( prevlval <= pobs ) obstotal += MAX( lval, prevlval ) * step; else obstotal += MAX( lval, prevlval ) * step * fabs( (pobs-lval) / (prevlval-lval) ); } } if( fabs( prevlval - lval ) / prevlval < eps ) step = MAX( step + 1, (long int) step * 1.5 ); } else { prevrval = rval; if( kr - step < kl ) step = kr - kl; kr -= step; rval = Rf_dnbinom( kr, sizeA, probA, 0 ) * Rf_dnbinom( kS-kr, sizeB, probB, 0 ); if( step == 1 ) total += rval; else total += MIN( rval, prevrval ) * step; if( rval <= pobs ) { if( step == 1 ) obstotal += rval; else { if( prevrval <= pobs ) obstotal += MAX( rval, prevrval ) * step; else obstotal += MAX( rval, prevrval ) * step * fabs( (pobs-rval) / (prevrval-rval) ); } } if( fabs( ( prevrval - rval ) ) / prevrval < eps ) step = MAX( step + 1, (long int) step * 1.5 ); } } //assert( kl == kr ); *res_total = total; *res_obstotal = obstotal; } SEXP calc_pvals( SEXP kS, SEXP pobs, SEXP muA, SEXP vA, SEXP muB, SEXP vB, SEXP eps ) { double totall, totalr, obstotall, obstotalr; long int kexp = INTEGER(kS)[0] * REAL(muA)[0] / ( REAL(muA)[0] + REAL(muB)[0] ); add_from_both_sides( 0, kexp, INTEGER(kS)[0], REAL(pobs)[0], REAL(muA)[0], REAL(vA)[0], REAL(muB)[0], REAL(vB)[0], REAL(eps)[0], &totall, &obstotall); add_from_both_sides( kexp+1, INTEGER(kS)[0], INTEGER(kS)[0], REAL(pobs)[0], REAL(muA)[0], REAL(vA)[0], REAL(muB)[0], REAL(vB)[0], REAL(eps)[0], &totalr, &obstotalr); SEXP res = Rf_allocVector( REALSXP, 2 ); REAL(res)[0] = totall + totalr; REAL(res)[1] = obstotall + obstotalr; return res; } R_CallMethodDef callMethods[] = { { "calc_pvals", (DL_FUNC) &calc_pvals, 7 }, { NULL, NULL, 0 } }; void R_init_DESeq( DllInfo *info ) { R_registerRoutines(info, NULL, callMethods, NULL, NULL); } DESeq/vignettes/0000755000175500017550000000000013556150211014552 5ustar00biocbuildbiocbuildDESeq/vignettes/DESeq.Rnw0000644000175500017550000016674113554551773016242 0ustar00biocbuildbiocbuild%\VignetteIndexEntry{Analysing RNA-Seq data with the "DESeq" package} %\VignettePackage{DESeq} % To compile this document % library('cacheSweave');rm(list=ls());Sweave('DESeq.Rnw',driver=cacheSweaveDriver());system("pdflatex DESeq") \documentclass[10pt,oneside]{article} \newcommand{\thetitle}{Differential expression of RNA-Seq data at the gene level -- the DESeq package} %\usepackage[pdftitle={\thetitle},pdfauthor={Wolfgang Huber}]{whbiocvignette} \usepackage{whbiocvignette} \title{\textsf{\textbf{\thetitle}}} \author{Simon Anders$^1$, Wolfgang Huber\\[1em]European Molecular Biology Laboratory (EMBL),\\ Heidelberg, Germany\\ \texttt{$^1$sanders@fs.tum.de}} % The following command makes use of SVN's 'Date' keyword substitution % To activate this, I used: svn propset svn:keywords Date DESeq.Rnw \date{\Rpackage{DESeq} version \Sexpr{packageDescription("DESeq")$Version} (Last revision \StrMid{$Date$}{8}{18})} \SweaveOpts{keep.source=TRUE,eps=FALSE,pdf=FALSE,png=TRUE,include=FALSE,width=5.4,height=3.7,resolution=180} \begin{document} <>= options(digits=3, width=100) @ \maketitle \begin{abstract} A basic task in the analysis of count data from RNA-Seq is the detection of differentially expressed genes. The count data are presented as a table which reports, for each sample, the number of reads that have been assigned to a gene. Analogous analyses also arise for other assay types, such as comparative ChIP-Seq. The package \Rpackage{DESeq} provides methods to test for differential expression by use of the negative binonial distribution and a shrinkage estimator for the distribution's variance\footnote{Other Bioconductor packages with similar aims are \Rpackage{edgeR} and \Rpackage{baySeq}.}. This vignette explains the use of the package. For an exposition of the statistical method, please see our paper~\cite{Anders:2010:GB} and the additional information in Section~\ref{sec:changes}. \end{abstract} \tableofcontents %-------------------------------------------------- \section{Input data and preparations} \label{sec:prep} %-------------------------------------------------- \subsection{The count table} %-------------------------------------------------- As input, the \Rpackage{DESeq} package expects count data as obtained, e.\,g., from RNA-Seq or another high-throughput sequencing experiment, in the form of a rectangular table of integer values. The table cell in the $i$-th row and the $j$-th column of the table tells how many reads have been mapped to gene $i$ in sample $j$. Analogously, for other types of assays, the rows of the table might correspond e.\,g.\ to binding regions (with ChIP-Seq) or peptide sequences (with quantitative mass spectrometry). The count values must be raw counts of sequencing reads. This is important for \Rpackage{DESeq}'s statistical model to hold, as only the actual counts allow assessing the measurement precision correctly. Hence, please do do not supply other quantities, such as (rounded) normalized counts, or counts of covered base pairs -- this will only lead to nonsensical results. Furthermore, it is important that each column stems from an independent biological replicate. For technical replicates (e.\,g.\ when the same library preparation was distributed over multiple lanes of the sequencer), please sum up their counts to get a single column, corresponding to a unique biological replicate. This is needed in order to allow \Rpackage{DESeq} to estimate variability in the experiment correctly. To obtain such a count table for your own data, you will need to create it from your sequence alignments and suitable annotation. In Bioconductor, you can use the function \Rfunction{summarizeOverlaps} in the \Rpackage{GenomicRanges} package. See the vignette, reference~\cite{summarizeOverlaps}, for a worked example. Another possibility is provided by the Bioconductor package \Rpackage{easyRNASeq}. Another easy way to produce such a table from the output of the aligner is to use the \texttt{htseq-count} script distributed with the \emph{HTSeq} Python package. Even though \emph{HTSeq} is written in Python, you do not need to know any Python to use \texttt{htseq-count}. See \url{http://www-huber.embl.de/users/anders/HTSeq/doc/count.html}. HTSeq-count produces one count file for each sample. \Rpackage{DESeq} offers the function \Rfunction{newCountDataSetFromHTSeqCount}, described below, to get an analysis started from these files. In this vignette, we will work with the gene level read counts from the \Rpackage{pasilla} data package. This data set is from an experiment on \emph{Drosophila melanogaster} cell cultures and investigated the effect of RNAi knock-down of the splicing factor \emph{pasilla}~\cite{Brooks2010}. The detailed transcript of how we produced the \Rpackage{pasilla} count table from second generation sequencing (Illumina) FASTQ files is provided in the vignette of the data package \Rpackage{pasilla}. The table is supplied by the \Rpackage{pasilla} package as a text file of tab-separated values. The function \Rfunction{system.file} tells us where this file is stored on your computer. % <>= datafile = system.file( "extdata/pasilla_gene_counts.tsv", package="pasilla" ) datafile @ % Have a look at the file with a text editor to see how it is formatted. To read this file with R, we use the function \Rfunction{read.table}. % <>= pasillaCountTable = read.table( datafile, header=TRUE, row.names=1 ) head( pasillaCountTable ) @ % Here, \texttt{header=TRUE} indicates that the first line contains column names and \texttt{row.names=1} means that the first column should be used as row names. This leaves us with a \Rclass{data.frame} containing integer count values. %-------------------------------------------------- \subsection{The metadata} %-------------------------------------------------- The best data are useless without metadata. \Rpackage{DESeq} uses familiar idioms in Bioconductor to manage the metadata that go with the count table. The metadata can be divided into three groups: information about the samples (table colums), about the features (table rows), and about the overall experiment. First, we need a description of the samples, which we keep in a \Rclass{data.frame} whose columns correspond to different types of information, and whose rows correspond to the \Sexpr{ncol(pasillaCountTable)} samples: <>= pasillaDesign = data.frame( row.names = colnames( pasillaCountTable ), condition = c( "untreated", "untreated", "untreated", "untreated", "treated", "treated", "treated" ), libType = c( "single-end", "single-end", "paired-end", "paired-end", "single-end", "paired-end", "paired-end" ) ) pasillaDesign @ % Here, simply use a chunk of R code to set up this define. More often, you will read this into R from a spreadsheet table, using the R functions \Rfunction{read.table} or \Rfunction{read.csv}; or perhaps even from a relational database table using R's database access facilities. To analyse these samples, we will have to account for the fact that we have both single-end and paired-end method. To keep things simple at the start, we defer the discussion of this to Section~\ref{sec:GLM} and first demonstrate a simple analysis by using only the paired-end samples. % <>= pairedSamples = pasillaDesign$libType == "paired-end" countTable = pasillaCountTable[ , pairedSamples ] condition = pasillaDesign$condition[ pairedSamples ] @ % Now, we have data input as follows. % <<>>= head(countTable) condition @ % For your own data, create such a factor simply with <>= #not run condition = factor( c( "untreated", "untreated", "treated", "treated" ) ) @ <>= stopifnot( identical( condition, factor( c( "untreated", "untreated", "treated", "treated" ) ) ) ) @ % We can now instantiate a \Rclass{CountDataSet}, which is the central data structure in the \Rpackage{DESeq} package: % <>= library( "DESeq" ) cds = newCountDataSet( countTable, condition ) @ If you have used \emph{htseq-count} (see above) to obtain your read counts, you can use the funtion \Rfunction{newCountDataSetFromHTSeqCount} to obtain a CountDataSe directly from the count files produced by \emph{htseq-count}. To this end, produce a data frame, similar to \emph{pasillaDesign} constructed above, with the sample names in the first column, the file names in the scond column, and the condition in the third column (or, if you have more than one factor in your design matrix, all these factors in the third and folling columns), and pass this data frame to the function. See the help page (``\texttt{?newCountDataSetFromHTSeqCount}'') for further details. The \Rclass{CountDataSet} class is derived from \Rpackage{Biobase}'s \Rclass{eSet} class and so shares all features of this standard Bioconductor class. Furthermore, accessors are provided for its data slots\footnote{In fact, the object \Robject{pasillaGenes} from the \Rpackage{pasilla} package is of class \Rclass{CountDataSet}, and we could do the subsequent analysis on the basis of this object. Here we re-create \Robject{cds} from elementary data types, a \Rclass{data.frame} and a \Rclass{factor}, for pedagogic effect.}. For example, the counts can be accessed with the \Rfunction{counts} function, as we will see in the next section. %------------------------------------------------------------ \subsection{Normalisation} %------------------------------------------------------------ As a first processing step, we need to estimate the effective library size. This step is sometimes also called \emph{normalisation}, even though there is no relation to normality or a normal distribution. The effective library size information is called the \emph{size factors} vector, since the package only needs to know the relative library sizes. If the counts of non-differentially expressed genes in one sample are, on average, twice as high as in another (because the library was sequenced twice as deeply), the size factor for the first sample should be twice that of the other sample~\cite{Anders:2010:GB,Anders:2012:GR}. The function \Rfunction{estimateSizeFactors} estimates the size factors from the count data. (See the man page of \Rfunction{estimateSizeFactorsForMatrix} for technical details on the calculation.) % <>= cds = estimateSizeFactors( cds ) sizeFactors( cds ) @ If we divide each column of the count table by the size factor for this column, the count values are brought to a common scale, making them comparable. When called with \texttt{normalized=TRUE}, the \texttt{counts} accessor function performs this calculation. This is useful, e.g., for visualization. % <>= head( counts( cds, normalized=TRUE ) ) @ %------------------------------------------------------------ \section{Variance estimation} %------------------------------------------------------------ The inference in \Rpackage{DESeq} relies on an estimation of the typical relationship between the data's variance and their mean, or, equivalently, between the data's dispersion and their mean. The \emph{dispersion} can be understood as the square of the coefficient of biological variation. So, if a gene's expression typically differs from replicate to replicate sample by 20\%, this gene's dispersion is $0.2^2=.04$. Note that the variance seen between counts is the sum of two components: the sample-to-sample variation just mentioned, and the uncertainty in measuring a concentration by counting reads. The latter, known as shot noise or Poisson noise, is the dominating noise source for lowly expressed genes. The former dominates for highly expressed genes. The sum of both, shot noise and dispersion, is considered in the differential expression inference. Hence, the variance $v$ of count values is modelled as \[ v = s \mu + \alpha s^2\mu^2, \] where $\mu$ is the expected normalized count value (estimated by the average normalized count value), $s$ is the size factor for the sample under consideration, and $\alpha$ is the dispersion value for the gene under consideration. To estimate the dispersions, use this command. <>= cds = estimateDispersions( cds ) @ We could now proceed straight to the testing for differetial expression in Section~\ref{sec:DE}. However, let us first spend a little more time with looking at the results of \Rfunction{estimateDispersions}, in order to better understand the subsequent inference. Also, verification of the dispersion plot Figure~\ref{figFit}, explained below, is an aspect of data quality control: how well do the data accord to the expectations of our analytic approach? Quality assessment is a crucial step of the data analysis, and we will see further quality diagnostics in Section~\ref{sec:quality}. The function \Rfunction{estimateDispersions} performs three steps. First, it estimates a dispersion value for each gene, then it fits a curve through the estimates. Finally, it assigns to each gene a dispersion value, using a choice between the per-gene estimate and the fitted value. To allow the user to inspect the intermediate steps, a \Robject{fitInfo} object is stored, which contains the per-gene estimate, the fitted curve and the values that will subsequently be used for inference. % <>= str( fitInfo(cds) ) @ % \label{fitInfo} It is useful to inspect the results of these steps visually. We can plot the per-gene estimates against the mean normalized counts per gene and overlay the fitted curve by using the function \Rfunction{plotDispEsts} (Fig.~\ref{figFit}). % \begin{figure} \centering \includegraphics[width=.6\textwidth]{DESeq-figFit} \caption{Empirical (black dots) and fitted (red lines) dispersion values plotted against the mean of the normalised counts.} \label{figFit} \end{figure} % <>= plotDispEsts( cds ) @ % check a claim made in the paragraph below. <>= all(table(conditions(cds))==2) @ As we estimated the dispersions from a small number of replicates, the estimates scatter with quite some sampling variance around their true values. An initial assumption that one could make is that the regression line shown in Figure~\ref{figFit} models the true underlying dispersions, and that the variation of the point estimates around simply reflects sampling variance. This is the assumption that we put forward in the first paper on \Rpackage{DESeq}~\cite{Anders:2010:GB}. However, subsequent experience with larger data sets indicates that not all of the variability of the points around the regression line seen in Figure~\ref{figFit} is sampling variance: some of it reflects differences of the true, underlying variance between different genes. Hence, the default behaviour of \Rpackage{DESeq} now uses a more prudent or conservative approach: if a per-gene estimates lies below the regression line, we assume that this might indeed be sampling variance, and shift the estimate upwards to the value predicted by the regression line. If, however, the per-gene estimate lies above the line, we do not shift it downwards to the line, but rather keep it as is. The option \texttt{sharingMode} of the function \Rfunction{estimateDispersions} can be used to control this behaviour. The value \texttt{sharingMode="maximum"} corresponds to the default. If you have many replicates (where \emph{many} starts at around 7), the choice \texttt{sharingMode="gene-est-only"} will typically be more adequate. If you would like to use the behaviour described in~\cite{Anders:2010:GB}, this is achieved by specifying \texttt{sharingMode="fit-only"}. Another difference of the current \Rpackage{DESeq} version to the original method described in the paper is the way how the mean-dispersion relation is fitted. By default, \Rfunction{estimateDispersions} now performs a parametric fit: Using a gamma-family GLM, two coefficients $\alpha_0, \alpha_1$ are found to parametrize the fit as $\alpha = \alpha_0 + \alpha_1/\mu$. (The values of the two coefficients can be found in the \texttt{fitInfo} object, as attribute \texttt{coefficients} to \texttt{dispFunc}.) For some data sets, the parametric fit may give bad results, in which case one should try a local fit (the method described in the paper), which is available via the option \texttt{fitType="local"} to \Rfunction{estimateDispersions}. In any case, the dispersion values which will be used by the subsequent testing are stored in the feature data slot of \texttt{cds}: % <>= head( fData(cds) ) @ % \fixme{Why is the value for FBgn00000014 Inf and not 0 (given that all counts are 0)?} You can verify that these values are indeed the maxima from the two value vectors in \Robject{fitInfo(cds)}, which we saw on page~\pageref{fitInfo}. Advanced users who want to fiddle with the dispersion estimation can change the values in \texttt{fData(cds)} prior to calling the testing function. %------------------------------------------------------------ \section{Inference: Calling differential expression} \label{sec:DE} %------------------------------------------------------------ \subsection{Standard comparison between two experimental conditions} Having estimated the dispersion for each gene, it is straight-forward to look for differentially expressed genes. To contrast two conditions, e.g., to see whether there is differential expression between conditions ``untreated'' and ``treated'', we simply call the function \Rfunction{nbinomTest}. It performs the tests as described in~\cite{Anders:2010:GB} and returns a data frame with the $p$ values and other useful information. % <>= res = nbinomTest( cds, "untreated", "treated" ) <>= head(res) @ % <>= stopifnot(identical(colnames(res), c("id", "baseMean", "baseMeanA", "baseMeanB", "foldChange", "log2FoldChange", "pval", "padj"))) @ The interpretation of the columns of \Rclass{\Sexpr{class(res)}} is as follows. \noindent \begin{tabular}{lp{0.8\textwidth}} \texttt{id}&feature identifier\\ \texttt{baseMean}&mean normalised counts, averaged over all samples from both conditions\\ \texttt{baseMeanA}&mean normalised counts from condition A\\ \texttt{baseMeanB}&mean normalised counts from condition B\\ \texttt{foldChange}&fold change from condition A to B\\ \texttt{log2FoldChange}&the logarithm (to basis 2) of the fold change\\ \texttt{pval}&$p$ value for the statistical significance of this change\\ \texttt{padj}&$p$ value adjusted for multiple testing with the Benjamini-Hochberg procedure (see the R function \Rfunction{p.adjust}), which controls false discovery rate (FDR)\\ \end{tabular} \begin{figure}[ht] \centering \includegraphics[width=.6\textwidth]{DESeq-figDE} \caption{Plot of normalised mean versus $log_2$ fold change for the contrast \emph{untreated} versus \emph{treated}.} \label{figDE} \end{figure} \vspace{1.5ex} Let us first plot the $\log_2$ fold changes against the mean normalised counts, colouring in red those genes that are significant at 10\% FDR (Figure~\ref{figDE}). % <>= plotMA(res) @ %$ % \begin{figure}[ht] \centering \includegraphics[width=.6\textwidth]{DESeq-histp} \caption{Histogram of $p$-values from the call to nbinomTest.} \label{fighistp} \end{figure} It is also instructive to look at the histogram of $p$ values (Figure~\ref{fighistp}). The enrichment of low $p$ values stems from the differentially expressed genes, while those not differentially expressed are spread uniformly over the range from zero to one (except for the $p$ values from genes with very low counts, which take discrete values and so give rise to high counts for some bins at the right.) % <>= hist(res$pval, breaks=100, col="skyblue", border="slateblue", main="") @ We can filter for significant genes, according to some chosen threshold for the false dicovery rate (FDR), <>= resSig = res[ res$padj < 0.1, ] @ and list, e.\,g., the most significantly differentially expressed genes: <>= head( resSig[ order(resSig$pval), ] ) @ We may also want to look at the most strongly down-regulated of the significant genes, <>= head( resSig[ order( resSig$foldChange, -resSig$baseMean ), ] ) @ or at the most strongly up-regulated ones: <>= head( resSig[ order( -resSig$foldChange, -resSig$baseMean ), ] ) @ To save the output to a file, use the R functions \Rfunction{write.table} and \Rfunction{write.csv}. (The latter is useful if you want to load the table in a spreadsheet program such as Excel.) <>= write.csv( res, file="My Pasilla Analysis Result Table.csv" ) @ \begin{figure}[ht] \centering \includegraphics[width=.6\textwidth]{DESeq-MArepl} \caption{Plot of the log2 fold change between the untreated replicates versus average expression strength.} \label{figMArepl} \end{figure} Note in Fig.~\ref{figDE} how the power to detect significant differential expression depends on the expression strength. For weakly expressed genes, stronger changes are required for the gene to be called significantly expressed. To understand the reason for this let, us compare the normalized counts between two replicate samples, here taking the two untreated samples as an example: % <>= ncu = counts( cds, normalized=TRUE )[ , conditions(cds)=="untreated" ] @ \Robject{ncu} is now a matrix with two columns. % <>= plotMA(data.frame(baseMean = rowMeans(ncu), log2FoldChange = log2( ncu[,2] / ncu[,1] )), col = "black") @ % As one can see in Figure~\ref{figMArepl}, the log fold changes between replicates are stronger for lowly expressed genes than for highly expressed ones. We ought to conclude that a gene's expression is influenced by the treatment only if the change between treated and untreated samples is stronger than what we see between replicates, and hence, the dividing line between red and black in Figure~\ref{figDE} mimics the shape seen in Figure~\ref{figMArepl}. %------------------------------------------------------------ \subsection{Working partially without replicates} %------------------------------------------------------------ If you have replicates for one condition but not for the other, you can still proceed as before. In such cases only the conditions with replicates will be used to estimate the dispersion. Of course, this is only valid if you have good reason to believe that the unreplicated condition does not have larger variation than the replicated one. To demonstrate, we subset our data object to only three samples: <>= cdsUUT = cds[ , 1:3] pData( cdsUUT ) @ \begin{figure}[ht] \centering \includegraphics[width=.6\textwidth]{DESeq-figDE_Tb} \caption{MvA plot for the contrast ``treated'' vs.\ ``untreated'', using two treated and only one untreated sample.} \label{figDE_Tb} \end{figure} Now, we do the analysis as before. <>= cdsUUT = estimateSizeFactors( cdsUUT ) cdsUUT = estimateDispersions( cdsUUT ) resUUT = nbinomTest( cdsUUT, "untreated", "treated" ) @ We produce the analogous plot as before, again with <>= plotMA(resUUT) @ %$ Figure~\ref{figDE_Tb} shows the same symmetry in up- and down-regulation as in Fig.~\ref{figDE}, but a certain asymmetry in the boundary line for significance. This has an easy explanation: low counts suffer from proportionally stronger shot noise than high counts, and since there is only one ``untreated'' sample versus two ``treated'' ones, a stronger downward fold-change is required to be called significant than for the upward direction. %-------------------------------------------------- \subsection{Working without any replicates} %-------------------------------------------------- Proper replicates are essential to interpret a biological experiment. After all, if one compares two conditions and finds a difference, how else can one know that this difference is due to the different conditions and would not have arisen between replicates, as well, just due to experimental or biological noise? Hence, any attempt to work without replicates will lead to conclusions of very limited reliability. Nevertheless, such experiments are sometimes undertaken, and the \Rpackage{DESeq} package can deal with them, even though the soundness of the results may depend much on the circumstances. Our primary assumption is now that the mean is a good predictor for the dispersion. Once we accept this assumption, we may argue as follows: Given two samples from different conditions and a number of genes with comparable expression levels, of which we expect only a minority to be influenced by the condition, we may take the dispersion estimated from comparing their counts \emph{across} conditions as ersatz for a proper estimate of the variance across replicates. After all, we assume most genes to behave the same within replicates as across conditions, and hence, the estimated variance should not be affected too much by the influence of the hopefully few differentially expressed genes. Furthermore, the differentially expressed genes will only cause the dispersion estimate to be too high, so that the test will err to the side of being too conservative. We shall now see how well this works for our example data. We reduce our count data set to just two columns, one ``untreated'' and one ``treated'' sample: <>= cds2 = cds[ ,c( "untreated3", "treated3" ) ] @ Now, without any replicates at all, the \Rfunction{estimateDispersions} function will refuse to proceed unless we instruct it to ignore the condition labels and estimate the variance by treating all samples as if they were replicates of the same condition: <>= cds2 = estimateDispersions( cds2, method="blind", sharingMode="fit-only" ) @ Note the option \texttt{sharingMode="fit-only"}. Remember that the default, \texttt{sharingMode="maximum"}, takes care of outliers, i.e., genes with dispersion much larger than the fitted values. Without replicates, we cannot catch such outliers and so have to disable this functionality. Now, we can attempt to find differential expression: <>= res2 = nbinomTest( cds2, "untreated", "treated" ) @ \begin{figure}[ht] \centering \includegraphics[width=.6\textwidth]{DESeq-figDE2} \caption{MvA plot, from a test using no replicates.} \label{figDE2} \end{figure} Unsurprisingly, we find much fewer hits, as can be seen from the plot (Fig.\ \ref{figDE2}) <>= plotMA(res2) @ and from this table, tallying the number of significant hits in our previous and our new, restricted analysis: <>= addmargins( table( res_sig = res$padj < .1, res2_sig = res2$padj < .1 ) ) @ %------------------------------------------------------------------------------------------------- \section{Multi-factor designs} \label{sec:GLM} %------------------------------------------------------------------------------------------------- Let us return to the full pasilla data set. Remember that we started of with these data: % <>= head( pasillaCountTable ) pasillaDesign @ When creating a count data set with multiple factors, just pass a data frame instead of the condition factor: <>= cdsFull = newCountDataSet( pasillaCountTable, pasillaDesign ) @ As before, we estimate the size factors and then the dispersions. Here, the default method (\texttt{method=''pooled''} to \Rfunction{estimateDispersion}), means that, as before, one dispersion is computed for each gene, which is now an average over all cells (weighted by the number of samples for each cells), where the term \emph{cell} denotes any of the four combinations of factor levels of the design. An alternative is the option \texttt{method=''pooled-CR''}, which uses a Cox-Reid-adjusted maximum likelihood estimator \cite{CR,edgeR_GLM}. The latter is slower but useful when the cell concept is not applicable (e.g. in paired designs). <>= cdsFull = estimateSizeFactors( cdsFull ) cdsFull = estimateDispersions( cdsFull ) @ \begin{figure}[ht] \centering \includegraphics[width=.6\textwidth]{DESeq-figFitPooled} \caption{Estimated (black) pooled dispersion values for all seven samples, with regression curve (red).} \label{figFitPooled} \end{figure} We check the fit (Fig.~\ref{figFitPooled}): <>= plotDispEsts( cdsFull ) @ %$ For inference, we now specify two \emph{models} by formulas. The \emph{full model} regresses the genes' expression on both the library type and the treatment condition, the \emph{reduced model} regresses them only on the library type. For each gene, we fit generalized linear models (GLMs) according to the two models, and then compare them in order to infer whether the additional specification of the treatment improves the fit and hence, whether the treatment has significant effect. <>= fit1 = fitNbinomGLMs( cdsFull, count ~ libType + condition ) fit0 = fitNbinomGLMs( cdsFull, count ~ libType ) @ These commands take a while to execute. Also, they may produce a few warnings, informing you that the GLM fit failed to converge (and the results from these genes should be interpreted with care). The ``fit'' objects are data frames with three columns: <>= str(fit1) @ To perform the test, we call <>= pvalsGLM = nbinomGLMTest( fit1, fit0 ) padjGLM = p.adjust( pvalsGLM, method="BH" ) @ % \fixme{Can we add a paragraph on what to do if we only want to make specific comparisons, e.g. let \texttt{fac} be a factor with three levels A, B and C, and we want to test pairwise for differences between A and B (without C), between A and C (without B) etc.} The function \Rfunction{nbinomTestGLM} returned simply a vector of $p$ values which we handed to the standard R function \Rfunction{p.adjust} to adjust for multiple testing using the Benjamini-Hochberg (BH) method. \begin{figure}[ht] \centering \includegraphics[width=.5\textwidth]{DESeq-figDispScatter} \caption{Comparison of per-gene estimates of the dispersion in the analysis using only the four paired-end samples ($x$-axis) and in the analysis using all seven samples ($y$-axis). For visualisation, the values are on a logarithm-like scale, defined by the function \Rfunction{trsf}, which is of the form $f(x)=\log\left((x+\sqrt{x^2+1})/2\right)$. For $x>2$, the values of $f(x)$ and $\log(x)$ are approximately the same, whereas for values of $x$ around 0, $f(x)\approx x$ is approximated by a straight line of slope 1.} \label{figDispScatter} \end{figure} Let's compare with the result from the four-samples test: <>= tab1 = table( "paired-end only" = res$padj < .1, "all samples" = padjGLM < .1 ) addmargins( tab1 ) @ We see that the analyses find \Sexpr{tab1[2,2]} genes in common, while \Sexpr{tab1[1,2]} were only found in the analysis using all samples and \Sexpr{tab1[2,1]} were specific for the \emph{paired-end only} analysis. In this case, the improvement in power that we gained from the additional samples is rather modest. This might indicate that the single-end samples (which are presumably older than the paired-end one) are of lower quality. This is supported by the observation that the dispersion estimates in the full data set tend to be larger than in the paired-end only one. So, despite the fact that with 7 samples we gain power from having more degrees of freedom in the estimation of the treatment effect, the additional samples also increase the dispersion (or equivalently, the variance), which loses power. % <>= table(sign(fitInfo(cds)$perGeneDispEsts - fitInfo(cdsFull)$perGeneDispEsts)) @ See also Figure~\ref{figDispScatter}, which is produced by % <>= trsf = function(x) log( (x + sqrt(x*x+1))/2 ) plot( trsf(fitInfo(cds)$perGeneDispEsts), trsf(fitInfo(cdsFull)$perGeneDispEsts), pch=16, cex=0.45, asp=1) abline(a=0, b=1, col="red3") @ Continuing with the analysis, we can now extract the significant genes from the vector \Robject{padjGLM} as before. To see the corresponding fold changes, we have a closer look at the object \Robject{fit1}. <>= head(fit1) @ The first three columns show the fitted coefficients, converted to a logarithm base 2 scale. The log2 fold change due to the condition is shown in the third column. As indicated by the column name, it is the effect of ``untreated'', i.e., the log ratio of ``untreated'' versus ``treated''. (This is unfortunately the other way round as before, due to the peculiarities of contrast coding.) Note that the library type also had noticeable influence on the expression, and hence would have increased the dispersion estimates (and so reduced power) if we had not fitted an effect for it. The column \emph{deviance} is the deviance of the fit. (Comparing the deviances with a $\chi^2$ likelihood ratio test is how \Rfunction{nbinomGLMTest} calculates the $p$ values.) The last column, \emph{converged}, indicates whether the calculation of coefficients and deviance has fully converged. (If it is false too often, you can try to change the GLM control parameters, as explained in the help page to \Rfunction{fitNbinomGLMs}.) \fixme{This is a bit vague, 'too often' should be specified and ideally the remedy be automated.} Finally, we show that taking the library type into account was important to have good detection power by doing the analysis again using the standard workflow, as outlined earlier, and without informing \Rpackage{DESeq} of the library types: <>= cdsFullB = newCountDataSet( pasillaCountTable, pasillaDesign$condition ) cdsFullB = estimateSizeFactors( cdsFullB ) cdsFullB = estimateDispersions( cdsFullB ) resFullB = nbinomTest( cdsFullB, "untreated", "treated" ) <

>= tab2 = table( `all samples simple` = resFullB$padj < 0.1, `all samples GLM` = padjGLM < 0.1 ) addmargins(tab2) @ %$ % We see that the two analyses find \Sexpr{tab2[2,2]} genes in common, while in addition \Sexpr{tab2[1,2]} genes were found by the analysis that took library type into account. The small number, namely \Sexpr{tab2[2,1]}, of genes that only made the FDR cutoff in the simple analysis is likely due to sampling variation. %-------------------------------------------------- \section{Independent filtering and multiple testing} \label{sec:indepfilt} \subsection{Filtering by overall count} \label{sec:filtbycount} %-------------------------------------------------- The analyses of the previous sections involve the application of statistical tests, one by one, to each row of the data set, in order to identify those genes that have evidence for differential expression. The idea of \emph{independent filtering} is to filter out those tests from the procedure that have no, or little chance of showing significant evidence, without even looking at their test statistic. Typically, this results in increased detection power at the same experiment-wide type I error. Here, we measure experiment-wide type I error in terms of the false discovery rate. A good choice for a filtering criterion is one that \begin{enumerate} \item\label{it:indp} is statistically independent from the test statistic under the null hypothesis, \item\label{it:corr} is correlated with the test statistic under the alternative, and \item\label{it:joint} does not notably change the dependence structure --if there is any-- between the test statistics of nulls and alternatives. \end{enumerate} The benefit from filtering relies on property~\ref{it:corr}, and we will explore it further in Section~\ref{sec:whyitworks}. Its statistical validity relies on properties~\ref{it:indp} and \ref{it:joint}. We refer to~\cite{Bourgon:2010:PNAS} for further discussion on the mathematical and conceptual background. % <>= rs = rowSums ( counts ( cdsFull )) theta = 0.4 use = (rs > quantile(rs, probs=theta)) table(use) cdsFilt = cdsFull[ use, ] @ <>= stopifnot(!any(is.na(use))) @ % Above, we consider as a filter criterion \Robject{rs}, the overall sum of counts (irrespective of biological condition), and remove the genes in the lowest \Sexpr{theta*100}\% quantile (as indicated by the parameter \Robject{theta}). We perform the testing as before in Section~\ref{sec:GLM}. % <>= fitFilt1 = fitNbinomGLMs( cdsFilt, count ~ libType + condition ) fitFilt0 = fitNbinomGLMs( cdsFilt, count ~ libType ) pvalsFilt = nbinomGLMTest( fitFilt1, fitFilt0 ) padjFilt = p.adjust(pvalsFilt, method="BH" ) @ <>= stopifnot(all.equal(pvalsFilt, pvalsGLM[use])) @ Let us compare the number of genes found at an FDR of 0.1 by this analysis with that from the previous one (\Robject{padjGLM}). <>= padjFiltForComparison = rep(+Inf, length(padjGLM)) padjFiltForComparison[use] = padjFilt tab3 = table( `no filtering` = padjGLM < .1, `with filtering` = padjFiltForComparison < .1 ) addmargins(tab3) @ The analysis with filtering found an additional \Sexpr{tab3[1,2]} genes, an increase in the detection rate by about \Sexpr{round(100*tab3[1,2]/tab3[2,2])}\%, while \Sexpr{tab3[2,1]} genes were only found by the previous analysis. %-------------------------------------------------- \subsection{Why does it work?}\label{sec:whyitworks} %-------------------------------------------------- First, consider Figure~\ref{figscatterindepfilt}, which shows that among the 40--45\% of genes with lowest overall counts, \Robject{rs}, there are essentially none that achieved an (unadjusted) $p$ value less than \Sexpr{signif(quantile(pvalsGLM[!use], 0.0001, na.rm=TRUE), 1)} (this corresponds to about \Sexpr{signif(-log10(quantile(pvalsGLM[!use], 0.0001, na.rm=TRUE)), 2)} on the $-\log_{10}$-scale). % <>= plot(rank(rs)/length(rs), -log10(pvalsGLM), pch=16, cex=0.45) @ \begin{figure}[ht] \centering \includegraphics[width=.5\textwidth]{DESeq-figscatterindepfilt} \caption{Scatterplot of rank of filter criterion (overall sum of counts \Robject{rs}) versus the negative logarithm of the test statistic \Robject{pvalsGLM}.} \label{figscatterindepfilt} \end{figure} This means that by dropping the 40\% genes with lowest \Robject{rs}, we do not loose anything substantial from our subsequent results. Second, consider the $p$ value histogram in Figure~\ref{fighistindepfilt}. It shows how the filtering ameliorates the multiple testing problem -- and thus the severity of a multiple testing adjustment -- by removing a background set of hypotheses whose $p$ values are distributed more or less uniformly in $[0,1]$. <>= h1 = hist(pvalsGLM[!use], breaks=50, plot=FALSE) h2 = hist(pvalsGLM[use], breaks=50, plot=FALSE) colori = c(`do not pass`="khaki", `pass`="powderblue") <>= barplot(height = rbind(h1$counts, h2$counts), beside = FALSE, col = colori, space = 0, main = "", ylab="frequency") text(x = c(0, length(h1$counts)), y = 0, label = paste(c(0,1)), adj = c(0.5,1.7), xpd=NA) legend("topright", fill=rev(colori), legend=rev(names(colori))) @ \begin{figure}[ht] \centering \includegraphics[width=.5\textwidth]{DESeq-fighistindepfilt} \caption{Histogram of $p$ values for all tests (\Robject{pvalsGLM}). The area shaded in blue indicates the subset of those that pass the filtering, the area in khaki those that do not pass.} \label{fighistindepfilt} \end{figure} %-------------------------------------------------- \subsection{How to choose the filter statistic and the cutoff?}\label{sec:indepfilterchoose} %-------------------------------------------------- Please refer to the vignette \emph{Diagnostic plots for independent filtering} in the \Rpackage{genefilter} package for a discussion on \begin{packeditemize} \item best choice of filter criterion and \item the choice of filter cutoff. \end{packeditemize} %--------------------------------------------------- \subsection{Diagnostic plots for multiple testing} %--------------------------------------------------- The Benjamini-Hochberg multiple testing adjustment procedure~\cite{BH:1995} has a simple graphical illustration, which we produce in the following code chunk. Its result is shown in the left panel of Figure~\ref{figmulttest}. % <>= orderInPlot = order(pvalsFilt) showInPlot = (pvalsFilt[orderInPlot] <= 0.08) alpha = 0.1 <>= plot(seq(along=which(showInPlot)), pvalsFilt[orderInPlot][showInPlot], pch=".", xlab = expression(rank(p[i])), ylab=expression(p[i])) abline(a=0, b=alpha/length(pvalsFilt), col="red3", lwd=2) @ <>= whichBH = which(pvalsFilt[orderInPlot] <= alpha*seq(0, 1, length=length(pvalsFilt))) ## Test some assertions: ## - whichBH is a contiguous set of integers from 1 to length(whichBH) ## - the genes selected by this graphical method coincide with those ## from p.adjust (i.e. padjFilt) stopifnot(length(whichBH)>0, identical(whichBH, seq(along=whichBH)), padjFilt[orderInPlot][ whichBH] <= alpha, padjFilt[orderInPlot][-whichBH] > alpha) @ % Schweder and Spj\o{}tvoll~\cite{SchwederSpjotvoll1982} suggested a diagnostic plot of the observed $p$-values which permits estimation of the fraction of true null hypotheses. For a series of hypothesis tests $H_1, \ldots, H_m$ with $p$-values $p_i$, they suggested plotting % \begin{equation} \left( 1-p_i, N(p_i) \right) \mbox{ for } i \in 1, \ldots, m, \end{equation} % where $N(p)$ is the number of $p$-values greater than $p$. An application of this diagnostic plot to \Robject{pvalsFilt} is shown in the right panel of Figure~\ref{figmulttest}. When all null hypotheses are true, the $p$-values are each uniformly distributed in $[0,1]$, Consequently, the cumulative distribution function of $(p_1, \ldots, p_m)$ is expected to be close to the line $F(t)=t$. By symmetry, the same applies to $(1 - p_1, \ldots, 1 - p_m)$. When (without loss of generality) the first $m_0$ null hypotheses are true and the other $m-m_0$ are false, the cumulative distribution function of $(1-p_1, \ldots, 1-p_{m_0})$ is again expected to be close to the line $F_0(t)=t$. The cumulative distribution function of $(1-p_{m_0+1}, \ldots, 1-p_{m})$, on the other hand, is expected to be close to a function $F_1(t)$ which stays below $F_0$ but shows a steep increase towards 1 as $t$ approaches $1$. In practice, we do not know which of the null hypotheses are true, so we can only observe a mixture whose cumulative distribution function is expected to be close to % \begin{equation} F(t) = \frac{m_0}{m} F_0(t) + \frac{m-m_0}{m} F_1(t). \end{equation} % <>= j = round(length(pvalsFilt)*c(1, .66)) px = (1-pvalsFilt[orderInPlot[j]]) py = ((length(pvalsFilt)-1):0)[j] slope = diff(py)/diff(px) @ % Such a situation is shown in the right panel of Figure~\ref{figmulttest}. If $F_1(t)/F_0(t)$ is small for small $t$, then the mixture fraction $\frac{m_0}{m}$ can be estimated by fitting a line to the left-hand portion of the plot, and then noting its height on the right. Such a fit is shown by the red line in the right panel of Figure~\ref{figmulttest}. Here we used a value for \Robject{slope} of \Sexpr{round(slope)}, the computation can be seen in the \texttt{.Rnw} source code of this vignette. % <>= plot(1-pvalsFilt[orderInPlot], (length(pvalsFilt)-1):0, pch=".", xlab=expression(1-p[i]), ylab=expression(N(p[i]))) abline(a=0, b=slope, col="red3", lwd=2) @ \begin{figure}[ht] \centering \includegraphics[width=.49\textwidth]{DESeq-sortedP} \includegraphics[width=.49\textwidth]{DESeq-SchwederSpjotvoll} \caption{\emph{Left:} illustration of the Benjamini-Hochberg multiple testing adjustment procedure~\cite{BH:1995}. The black line shows the $p$-values ($y$-axis) versus their rank ($x$-axis), starting with the smallest $p$-value from the left, then the second smallest, and so on. Only the first \Sexpr{sum(showInPlot)} $p$-values are shown. The red line is a straight line with slope $\alpha/n$, where $n=\Sexpr{length(pvalsFilt)}$ is the number of tests, and $\alpha=\Sexpr{alpha}$ is a target false discovery rate (FDR). FDR is controlled at the value $\alpha$ if the genes are selected that lie to the left of the rightmost intersection between the red and black lines: here, this results in \Sexpr{length(whichBH)} genes. \emph{Right:} Schweder and Spj\o{}tvoll plot, as described in the text. For both of these plots, the $p$-values \Robject{pvalsFilt} from Section~\ref{sec:filtbycount} were used as a starting point. Analogously, one can produce these types of plots for any set of $p$-values, for instance those from the previous sections.} \label{figmulttest} \end{figure} %--------------------------------------------------- \section{Variance stabilizing transformation} %--------------------------------------------------- For some applications, it is useful to work with transformed versions of the count data. Maybe the most obvious choice is the logarithmic transformation. Since count values for a gene can be zero in some conditions (and non-zero in others), some advocate the use of \emph{pseudocounts}, i.\,e.\ transformations of the form \begin{equation}\label{eq:shiftedlog} y = \log_2(n + 1)\quad\mbox{or more generally,}\quad y = \log_2(n + n_0), \end{equation} where $n$ represents the count values and $n_0$ is a somehow chosen positive constant. In this section, we discuss a related, alternative approach that offers more theoretical justification and a rational way of choosing the parameter equivalent to $n_0$ above. It is based on error modeling and the concept of variance stabilizing transformations~\cite{Tibshirani1988,sagmb2003,Anders:2010:GB}. We estimate an overall mean-dispersion relationship of the data using \Rfunction{estimateDispersions} with the argument \Robject{method="blind"} and call the function \Rfunction{getVarianceStabilizedData}. % <>= cdsBlind = estimateDispersions( cds, method="blind" ) vsd = varianceStabilizingTransformation( cdsBlind ) @ Here, we have used a parametric fit for the dispersion. In this case, the a closed-form expression for the variance stabilizing transformation is used by \Rfunction{getVarianceStabilizedData}, which is derived in the document \texttt{vst.pdf} (you find it in the \Rpackage{DESeq} package alongside this vignette). If a local fit is used (option \texttt{fittype="local"} to \Rfunction{estimateDispersion}) a numerical integration is used instead. % The resulting transformation is shown in Figure~\ref{figvsd1}. The code that produces the figure is hidden from this vignette for the sake of brevity, but can be seen in the \texttt{.Rnw} or \texttt{.R} source file. % \begin{figure}[ht] \centering \includegraphics[width=.49\textwidth]{DESeq-vsd1} \caption{Graphs of the variance stabilizing transformation for sample 1, in blue, and of the transformation $f(n)=log_2(n/s_1)$, in black. $n$ are the counts and $s_1$ is the size factor for the first sample. } \label{figvsd1} \end{figure} \begin{figure}[ht] \centering \includegraphics[width=\textwidth]{DESeq-vsd2} \caption{Per-gene standard deviation (taken across samples), against the rank of the mean, for the shifted logarithm $\log_2(n+1)$ (left) and \Rpackage{DESeq}'s variance stabilising transformation (right).} \label{figvsd2} \end{figure} <>= ##par(mai=ifelse(1:4 <= 2, par("mai"), 0)) px = counts(cds)[,1] / sizeFactors(cds)[1] ord = order(px) ord = ord[px[ord] < 150] ord = ord[seq(1, length(ord), length=50)] last = ord[length(ord)] vstcol = c("blue", "black") matplot(px[ord], cbind(exprs(vsd)[, 1], log2(px))[ord, ], type="l", lty=1, col=vstcol, xlab="n", ylab="f(n)") legend("bottomright", legend = c( expression("variance stabilizing transformation"), expression(log[2](n/s[1]))), fill=vstcol) @ % Figure~\ref{figvsd2} plots the standard deviation of the transformed data, across samples, against the mean, first using the shifted logarithm transformation~(\ref{eq:shiftedlog}), then using \Rpackage{DESeq}'s variance stabilising transformation. While for the latter, the standard deviation is roughly constant along the whole dynamic range, the shifted logarithm results in a highly elevated standard deviation in the lower count range. % <>= library("vsn") par(mfrow=c(1,2)) notAllZero = (rowSums(counts(cds))>0) meanSdPlot(log2(counts(cds)[notAllZero, ] + 1)) meanSdPlot(vsd[notAllZero, ]) @ %--------------------------------------------------------------- \subsection{Application to moderated fold change estimates} %--------------------------------------------------------------- In the beginning of Section~\ref{sec:DE}, we have seen in the \Rclass{data.frame} \Robject{res} the (logarithm base 2) fold change estimate computed from the size-factor adjusted counts. When the involved counts are small, these (logarithmic) fold-change estimates can be highly variable, and can even be infinite. For some purposes, such as the clustering of samples or genes according to their expression profiles, or for visualisation of the data, this high variability from ratios between low counts tends to drown informative, systematic signal in other parts of the data. The variance stabilizing transformation offers one way to \emph{moderate} the fold change estimates, so that they are more amenable to plotting or clustering. % <>= mod_lfc = (rowMeans( exprs(vsd)[, conditions(cds)=="treated", drop=FALSE] ) - rowMeans( exprs(vsd)[, conditions(cds)=="untreated", drop=FALSE] )) @ % Let us compare these to the original ($\log_2$) fold changes. First we find that many of the latter are infinite (resulting from division of a finite value by 0) or \emph{not a number} (NaN, resulting from division of 0 by 0). % <>= lfc = res$log2FoldChange table(lfc[!is.finite(lfc)], useNA="always") @ % For plotting, let us bin genes by their $\log_{10}$ mean to colour them according to expression strength, % <>= logdecade = 1 + round( log10( 1+rowMeans(counts(cdsBlind, normalized=TRUE)) ) ) lfccol = colorRampPalette( c( "gray", "blue" ) )(6)[logdecade] @ % and then compare their ordinary log-ratios (\Robject{lfc}) against the \emph{moderated} log-ratios (\Robject{mod\_lfc}) in a scatterplot. % <>= ymax = 4.5 plot( pmax(-ymax, pmin(ymax, lfc)), mod_lfc, xlab = "ordinary log-ratio", ylab = "moderated log-ratio", cex=0.45, asp=1, col = lfccol, pch = ifelse(lfc<(-ymax), 60, ifelse(lfc>ymax, 62, 16))) abline( a=0, b=1, col="red3") @ The result is shown in Figure~\ref{figmodlr}. \begin{figure}[htb] \centering \includegraphics[width=.5\textwidth]{DESeq-figmodlr} \caption{Scatterplot of ordinary (\Robject{lfc}) versus \emph{moderated} log-ratios (\Robject{mod\_lfc}). The points are coloured in a scale from grey to blue, representing weakly to strongly expressed genes. For the highly expressed genes (blue), \Robject{lfc} and \Robject{mod\_lfc} agree. Differences arise when the involved counts are small (grey points): in this case, the moderated log-ratio is shrunk towards 0, compared to the ordinary log-ratio. The $>$ and $<$ symbols correspond to values of \Robject{lfc} whose absolute value was larger than \Sexpr{ymax} (including those that were infinite). All values of \Robject{mod\_lfc} vary in a finite range.} \label{figmodlr} \end{figure} %--------------------------------------------------------------- \section{Data quality assessment by sample clustering and visualisation}\label{sec:quality} %--------------------------------------------------------------- Data quality assessment and quality control (i.\,e.\ the removal of insufficiently good data) are essential steps of any data analysis. Even though we present these steps towards the end of this vignette, they should typically be performed very early in the analysis of a new data set, preceding or in parallel to the differential expression testing. We define the term \emph{quality} as \emph{fitness for purpose}\footnote{\url{http://en.wikipedia.org/wiki/Quality_\%28business\%29}}. Our purpose is the detection of differentially expressed genes, and we are looking in particular for samples whose experimental treatment suffered from an anormality that renders the data points obtained from these particular samples detrimental to our purpose. \subsection{Heatmap of the count table}\label{sec:hmc} To explore a count table, it is often instructive to look at it as a heatmap. Below we show how to produce such a heatmap from the variance stabilisation transformed data for all \Sexpr{ncol(cdsFull)} samples. % <>= cdsFullBlind = estimateDispersions( cdsFull, method = "blind" ) vsdFull = varianceStabilizingTransformation( cdsFullBlind ) <>= library("RColorBrewer") library("gplots") select = order(rowMeans(counts(cdsFull)), decreasing=TRUE)[1:30] hmcol = colorRampPalette(brewer.pal(9, "GnBu"))(100) <>= heatmap.2(exprs(vsdFull)[select,], col = hmcol, trace="none", margin=c(10, 6)) @ % \begin{figure} \centering \includegraphics[width=.49\textwidth]{DESeq-figHeatmap2a} \includegraphics[width=.49\textwidth]{DESeq-figHeatmap2b} \caption{Heatmaps showing the expression data of the \Sexpr{length(select)} most highly expressed genes. Left, the variance stabilisation transformed data (\Robject{vsdFull}) are shown, right, the original count data (\Robject{cdsFull}). In the left panel, the sample clustering aligns with the experimental factor (\emph{treated} / \emph{untreated}). The clustering and the colour scale in the right plot is dominated by a small number of data points with large values.} \label{figHeatmap2} \end{figure} % The left panel of Figure~\ref{figHeatmap2} shows the resulting heatmap for the \Sexpr{length(select)} most highly expressed genes. For comparison, let us also do the same with the untransformed counts. % <>= heatmap.2(counts(cdsFull)[select,], col = hmcol, trace="none", margin=c(10,6)) @ \begin{figure} \centering \includegraphics[width=.6\textwidth]{DESeq-figHeatmapSamples} \caption{Heatmap showing the Euclidean distances between the samples as calculated from the variance stabilising transformation of the count data.} \label{figHeatmapSamples} \end{figure} \subsection{Heatmap of the sample-to-sample distances}\label{sec:dists} Another use of variance stabilized data is sample clustering. Here, we apply the \Rfunction{dist} function to the transpose of the transformed count matrix to get sample-to-sample distances. % <>= dists = dist( t( exprs(vsdFull) ) ) @ % A heatmap of this distance matrix gives us an overview over similarities and dissimilarities between samples (Figure~\ref{figHeatmapSamples}): <>= mat = as.matrix( dists ) rownames(mat) = colnames(mat) = with(pData(cdsFullBlind), paste(condition, libType, sep=" : ")) heatmap.2(mat, trace="none", col = rev(hmcol), margin=c(13, 13)) @ % The clustering correctly reflects our experimental design, i.e., samples are more similar when they have the same treatment or the same library type. (To avoid potential circularities in this conclusion, it was important to re-estimate the dispersions with \Robject{method="blind"} in the calculation for \Robject{cdsFullBlind} above, as only then, the variance stabilizing transformation is not informed about the design, and we can be sure that it is not biased towards a result supporting the design.) \subsection{Principal component plot of the samples} Related to the distance matrix of Section~\ref{sec:dists} is the PCA plot of the samples, which we obtain as follows (Figure~\ref{figPCA}). % <>= print(plotPCA(vsdFull, intgroup=c("condition", "libType"))) @ \begin{figure} \centering \includegraphics[width=.6\textwidth]{DESeq-figPCA} \caption{PCA plot. The \Sexpr{ncol(vsdFull)} samples shown in the 2D plane spanned by their first two principal components. This type of plot is useful for visualizing the overall effect of experimental covariates and batch effects. For this data set, no batch effects besides the known effects of \emph{condition} and \emph{libType} are discernible.} \label{figPCA} \end{figure} \subsection{arrayQualityMetrics} Heatmaps and PCA plots similar to Figures~\ref{figHeatmapSamples} and \ref{figPCA} as well as some further diagnostics are also provided by the package \Rpackage{arrayQualityMetrics}. The package may be particularly useful for larger data set with dozens of samples. You can call its main function, which is also called \Rfunction{arrayQualityMetrics}, with an \Rclass{ExpressionSet} such as \Robject{vsdFull}, which you will have produced from your \Rclass{CountDataSet} with calls to \Rfunction{estimateDispersions} and \Rpackage{varianceStabilizingTransformation} as in the beginning of Section~\ref{sec:hmc}. \clearpage %------------------------------------------------------------ \section{Further reading}\label{sec:further} %------------------------------------------------------------ For more information on the statistical method, see our paper~\cite{Anders:2010:GB}. For more information on how to customize the \Rpackage{DESeq} work flow, see the package help pages, especially the help page for \Rfunction{estimateDispersions}. %------------------------------------------------------------ \section{Changes since publication of the paper}\label{sec:changes} %------------------------------------------------------------ Since our paper on \Rpackage{DESeq} was published in Genome Biology in Oct 2010, we have made a number of changes to algorithm and implementation, which are listed here. \begin{itemize} \item \Rfunction{nbinomTest} calculates a $p$ value by summing up the probabilities of all per-group count sums $a$ and $b$ that sum up to the observed count sum $k_{iS}$ and are more extreme than the observed count sums $k_{iA}$ and $k_{iB}$. Equation~(11) of the paper defined \emph{more extreme} as those pairs of values $(a,b)$ that had smaller probability than the observed pair. This caused problems in cases where the dispersion exceeded 1. Hence, we now sum instead the probabilities of all values pairs that are \emph{further out} in the sense that they cause a more extreme fold change $(a/s_A)/(b/s_B)$, where $s_A$ and $s_B$ are the sums of the size factors of the samples in conditions $A$ and $B$, respectively. We do this in a one-tailed manner and double the result. Furthermore, we no longer approximate the sum, but always calculate it exactly. \item We added the possibility to fit GLMs of the negative binomial family with log link. This new functionality is described in this vignette. $p$ values are calculated by a $\chi^2$ likelihood ratio test. The logarithms of the size factors are provided as offsets to the GLM fitting function. \item The option \texttt{sharingMode='maximum'} was added to \Rfunction{estimateDispersion} and made default. This change makes DESeq robust against variance outliers and was not yet discussed in the paper. \item By default, DESeq now estimates one pooled dispersion estimate across all (replicated) conditions. In the original version, we estimated a separate dispersion-mean relation for each condition. The ``maximum'' sharing mode achieves its goal of making DESeq robust against outliers only with pooled dispersion estimate, and hence, this is now the default. The option \texttt{method='per-condition'} to \Rfunction{estimateDispersions} allows the user to go back to the old method. \item In the paper, the mean-dispersion relation is fitted by local regression. Now, DESeq also offers a parametric regression, as described in this vignette. The option \texttt{fitType} to \Rfunction{estimateDispersions} allows the user to choose between these. If a parametric regression is used, the variance stabilizing transformation is calculated using the closed-form expression given in the vignette supplement file \texttt{vst.pdf}. \item Finally, instead of the term \emph{raw squared coefficient of variance} used in the paper we now prefer the more standard term \emph{dispersion}. \end{itemize} \section{Session Info} <>= sessionInfo() @ \bibliographystyle{unsrt} \bibliography{DESeq} \end{document} DESeq/vignettes/DESeq.bib0000644000175500017550000001017213554551773016212 0ustar00biocbuildbiocbuild@Article{Anders:2010:GB, url = {http://genomebiology.com/2010/11/10/R106}, author = {Simon Anders and Wolfgang Huber}, Title = {{D}ifferential expression analysis for sequence count data}, Journal = {Genome Biology}, Year = 2010, Volume = 11, Pages = {R106}, } @article{BH:1995, author = {Y. Benjamini and Y. Hochberg}, title = {Controlling the false discovery rate: a practical and powerful approach to multiple testing}, journal = "Journal of the Royal Statistical Society B", year = 1995, volume = 57, pages = "289--300" } @Article{Bourgon:2010:PNAS, ISI = {ISI:000278054700015}, URL = {http://www.pnas.org/content/107/21/9546.long}, PDF = {PNAS-2010-Bourgon-9546-51.pdf}, author = {Richard Bourgon and Robert Gentleman and Wolfgang Huber}, Title = {Independent filtering increases detection power for high-throughput experiments}, journal = {PNAS}, Year = 2010, volume = 107, number = 21, pages = {9546--9551}, } @article{Brooks2010, author = {Brooks, A. N. and Yang, L. and Duff, M. O. and Hansen, K. D. and Park, J. W. and Dudoit, S. and Brenner, S. E. and Graveley, B. R.}, doi = {10.1101/gr.108662.110}, issn = {1088-9051}, journal = {Genome Research}, pages = {193--202}, title = {{Conservation of an RNA regulatory map between Drosophila and mammals}}, url = {http://genome.cshlp.org/cgi/doi/10.1101/gr.108662.110}, year = 2011 } @Article{Tibshirani1988, author = {Robert Tibshirani}, title = {Estimating transformations for regression via additivity and variance stabilization}, journal = {Journal of the American Statistical Association}, year = 1988, volume = 83, pages = {394--405} } @misc{htseq, author = {Simon Anders}, title = {{HTSeq: Analysing high-throughput sequencing data with Python}}, year = 2011, howpublished = {\url{http://www-huber.embl.de/users/anders/HTSeq/}} } @article{sagmb2003, title = {Parameter estimation for the calibration and variance stabilization of microarray data}, author = {Wolfgang Huber and Anja von Heydebreck and Holger {S\"ultmann} and Annemarie Poustka and Martin Vingron}, journal = {Statistical Applications in Genetics and Molecular Biology}, year = 2003, volume = 2, number = 1, pages = {Article 3} } @misc{summarizeOverlaps, author = {Valerie Obenchain}, title = {Counting with \texttt{summarizeOverlaps}}, year = 2011, howpublished = {Vignette, distributed as part of the Bioconductor package \emph{GenomicRanges}, as file \emph{summarizeOverlaps.pdf}} } @article{Anders:2012:GR, author = {Simon Anders and Alejandro Reyes and Wolfgang Huber}, title = {Detecting differential usage of exons from {RNA-seq} data }, year = {2012}, journal = {Genome Research}, doi = {10.1101/gr.133744.111}, } @article{CR, author = {Cox, D. R. and Reid, N.}, journal = {Journal of the Royal Statistical Society, Series B}, keywords = {CML,Cox-Reid,ML,dispersion}, mendeley-tags = {CML,Cox-Reid,ML,dispersion}, number = {1}, pages = {1--39}, title = {{Parameter orthogonality and approximate conditional inference}}, url = {http://www.jstor.org/stable/2345476}, volume = {49}, year = {1987} } @article{edgeR_GLM, author = {McCarthy, Davis J and Chen, Yunshun and Smyth, Gordon K}, doi = {10.1093/nar/gks042}, issn = {1362-4962}, journal = {Nucleic Acids Research}, keywords = {edgeR}, mendeley-tags = {edgeR}, month = jan, pmid = {22287627}, title = {{Differential expression analysis of multifactor RNA-Seq experiments with respect to biological variation}}, url = {http://www.ncbi.nlm.nih.gov/pubmed/22287627}, year = {2012}, volume={40}, pages={4288-4297} } @article{SchwederSpjotvoll1982, author={Schweder, T. and Spj\/{o}tvoll, E.}, title={Plots of {P-values} to evaluate many tests simultaneously}, journal={Biometrika}, year={1982}, volume=69, pages={493-502}, doi={10.1093/biomet/69.3.493} } DESeq/vignettes/vst.nb0000644000175500017550000010475613554551773015744 0ustar00biocbuildbiocbuild(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 35124, 991] NotebookOptionsPosition[ 32281, 895] NotebookOutlinePosition[ 32848, 915] CellTagsIndexPosition[ 32805, 912] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Variance-stabilizing transformation for DESeq", "Subtitle", CellChangeTimes->{{3.540622683759346*^9, 3.5406226961574497`*^9}, { 3.540815669170343*^9, 3.540815673334532*^9}}], Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"For", " ", "parametrized", " ", "dispersion", " ", "fit"}], "\[IndentingNewLine]"}], "Subsubtitle"]], "Input", CellChangeTimes->{{3.540815676143361*^9, 3.5408157093482103`*^9}}], Cell[TextData[{ "This file describes the variance stabilizing transformation (VST) used by \ DESeq when parametric dispersion estimation is used.\nThis is a ", StyleBox["Mathematica", FontSlant->"Italic"], " notebook. 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