%\VignetteIndexEntry{Analyzing RNA-Seq data with the "DESeq2" package} %\VignettePackage{DESeq2} % To compile this document % library('cacheSweave'); rm(list=ls()); Sweave('DESeq2.Rnw', driver=cacheSweaveDriver()) \documentclass[12pt]{article} <>= BiocStyle::latex() @ <>= library("DESeq2") @ \usepackage{cite} \usepackage{Sweave} \SweaveOpts{keep.source=TRUE,eps=FALSE,pdf=FALSE,png=TRUE,include=FALSE,width=4,height=4.5,resolution=150} \setkeys{Gin}{width=0.5\textwidth} % use a vertical rule for R output instead of prompts for R input \usepackage{fancyvrb} \definecolor{darkgray}{gray}{0.2} \DefineVerbatimEnvironment{Sinput}{Verbatim}{xleftmargin=1em,formatcom={\color{darkgray}}} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=1em,frame=leftline,framerule=.6pt,rulecolor=\color{darkgray},framesep=1em,formatcom={\color{darkgray}}} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} \author{Michael Love$^{1*}$, Simon Anders$^{2}$, Wolfgang Huber$^{2}$ \\[1em] \small{$^{1}$ Max Planck Institute for Molecular Genetics, Berlin, Germany;} \\ \small{$^{2}$ European Molecular Biology Laboratory (EMBL), Heidelberg, Germany} \\ \small{\texttt{$^*$michaelisaiahlove (at) gmail.com}}} \title{Differential analysis of count data -- the DESeq2 package} \begin{document} \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 sequence fragments that have been assigned to each gene. Analogous data also arise for other assay types, including comparative ChIP-Seq, HiC, shRNA screening, mass spectrometry. An important analysis question is the quantification and statistical inference of systematic changes between conditions, as compared to within-condition variability. The package \Biocpkg{DESeq2} provides methods to test for differential expression by use of negative binomial generalized linear models; the estimates of dispersion and logarithmic fold changes incorporate data-driven prior distributions \footnote{Other \Bioconductor{} packages with similar aims are \Biocpkg{edgeR}, \Biocpkg{baySeq} and \Biocpkg{DSS}.}. This vignette explains the use of the package and demonstrates typical work flows. %-- The GB paper is really dated. Let's comment this out until the new ms exists: %For an exposition of the statistical method, please see our paper \cite{Anders:2010:GB}. \vspace{1em} \textbf{DESeq2 version:} \Sexpr{sessionInfo()[["otherPkgs"]][["DESeq2"]][["Version"]]} \end{abstract} <>= options(digits=3, width=80, prompt=" ", continue=" ") @ \newpage \tableofcontents \section{Standard workflow} \subsection{Quick start} Here we show the most basic steps for a differential expression analysis. These steps imply you have a \Rclass{SummarizedExperiment} object \Robject{se} with a column \Robject{condition}. <>= dds <- DESeqDataSet(se = se, design = ~ condition) dds <- DESeq(dds) res <- results(dds) @ \subsection{Input data} \label{sec:prep} \subsubsection{Why raw counts?} As input, the \Biocpkg{DESeq2} package expects count data as obtained, e.\,g., from RNA-Seq or another high-throughput sequencing experiment, in the form of a matrix of integer values. The value in the $i$-th row and the $j$-th column of the matrix tells how many reads have been mapped to gene $i$ in sample $j$. Analogously, for other types of assays, the rows of the matrix 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 \Biocpkg{DESeq2}'s statistical model to hold, as only the actual counts allow assessing the measurement precision correctly. Hence, please do not supply other quantities, such as (rounded) normalized counts, or counts of covered base pairs -- this will only lead to nonsensical results. \subsubsection{\Rclass{SummarizedExperiment} input} \label{sec:sumExpInput} The class used by the \Biocpkg{DESeq2} package to store the read counts is \Rclass{DESeqDataSet} which extends the \Rclass{SummarizedExperiment} class of the \Biocpkg{GenomicRanges} package. This facilitates preparation steps and also downstream exploration of results. For counting aligned reads in genes, the \Rfunction{summarizeOverlaps} function of \Biocpkg{GenomicRanges}/\Biocpkg{Rsamtools} with \Robject{mode="Union"} is encouraged, resulting in a \Rclass{SummarizedExperiment} object (\Biocpkg{easyRNASeq} is another \Bioconductor{} package which can prepare \Rclass{SummarizedExperiment} objects as input for \Biocpkg{DESeq2}). An example of the steps to produce a \Rclass{SummarizedExperiment} can be found in the data package \Biocannopkg{parathyroidSE}, which summarizes RNA-Seq data from experiments on 4 human cell cultures \cite{Haglund2012Evidence}. <>= library("parathyroidSE") data("parathyroidGenesSE") se <- parathyroidGenesSE colnames(se) <- colData(se)$run @ A \Rclass{DESeqDataSet} object must have an associated design formula. The design formula expresses the variables which will be used in modeling. The formula should be a tilde ($\sim$) followed by the variables with plus signs between them (it will be coerced into an \Rclass{formula} if it is not already). An intercept is included, representing the base mean of counts. The design can be changed later, however then all differential analysis steps should be repeated, as the design formula is used to estimate the dispersions and to estimate the $\log_2$ fold changes of the model. The constructor function below shows the generation of a \Rclass{DESeqDataSet} from a \Rclass{SummarizedExperiment} \Robject{se}. Note: In order to benefit from the default settings of the package, you should put the variable of interest at the end of the formula and make sure the control level is the first level. <>= library("DESeq2") ddsPara <- DESeqDataSet(se = se, design = ~ patient + treatment) colData(ddsPara)$treatment <- factor(colData(ddsPara)$treatment, levels=c("Control","DPN","OHT")) ddsPara @ \subsubsection{Count matrix input} Alternatively, if you already have prepared a matrix of read counts, you can use the function \Rfunction{DESeqDataSetFromMatrix}. For this function you should provide the counts matrix, the column information as a \Rclass{DataFrame} or \Rclass{data.frame} and the design formula. <>= library("Biobase") library("pasilla") data("pasillaGenes") countData <- counts(pasillaGenes) colData <- pData(pasillaGenes)[,c("condition","type")] @ Now that we have a matrix of counts and the column information, we can construct a \Rclass{DESeqDataSet}: <>= dds <- DESeqDataSetFromMatrix(countData = countData, colData = colData, design = ~ condition) colData(dds)$condition <- factor(colData(dds)$condition, levels=c("untreated","treated")) dds @ \subsubsection{\textit{HTSeq} input} If you have used the \textit{HTSeq} python scripts, you can use the function \Rfunction{DESeqDataSetFromHTSeqCount}. For an example of using the python scripts, see the \Biocannopkg{pasilla} or \Biocannopkg{parathyroid} data package. <>= library("pasilla") directory <- system.file("extdata", package="pasilla", mustWork=TRUE) sampleFiles <- grep("treated",list.files(directory),value=TRUE) sampleCondition <- sub("(.*treated).*","\\1",sampleFiles) sampleTable <- data.frame(sampleName = sampleFiles, fileName = sampleFiles, condition = sampleCondition) ddsHTSeq <- DESeqDataSetFromHTSeqCount(sampleTable = sampleTable, directory = directory, design= ~ condition) colData(ddsHTSeq)$condition <- factor(colData(ddsHTSeq)$condition, levels=c("untreated","treated")) ddsHTSeq @ \subsubsection{Note on factor levels} \label{sec:factorLevels} In the three examples above, we applied the function \Rfunction{factor} to the column of interest in \Robject{colData}, supplying a character vector of levels. It is important to supply levels (otherwise the levels are chosen in alphabetical order) and to put the ``control'' or ``untreated'' level as the first element, so that the $\log_2$ fold changes and results will be most easily interpretable. A helpful \R{} function for easily changing the base level is \Rfunction{relevel}. An example of setting the base level with \Rfunction{relevel} is: <>= colData(dds)$condition <- relevel(colData(dds)$condition, "control") @ The reason for the importance of the specifying the base level is that the function \Rfunction{model.matrix} is used by the \Biocpkg{DESeq2} package to build model matrices, and these matrices will be used to compare all other levels to the base level. See \ref{sec:contrasts} for examples on how to compare factor levels to other levels than the base level. \subsubsection{About the pasilla dataset} We continue with the \Biocannopkg{pasilla} data constructed from the count matrix method above. 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 the production of the \Biocannopkg{pasilla} data is provided in the vignette of the data package \Biocannopkg{pasilla}. \subsection{Differential expression analysis} \label{sec:de} The standard differential expression analysis steps are wrapped into a single function, \Rfunction{DESeq}. The individual functions are still available, described in Section~\ref{sec:steps}. The results are accessed using the function \Rfunction{results}, which extracts a results table for a single variable (by default the last variable in the design formula, and if this is a factor, the last level of this variable). Note that the \Rfunction{results} function performs independent filtering by default using the \Biocpkg{genefilter} package, discussed in Section~\ref{sec:autoFilt}. <>= dds <- DESeq(dds) res <- results(dds) res <- res[order(res$padj),] head(res) @ <>= # this chunk is used to demonstrate the shrinkage # of log fold changes # note: betaPrior can also be used as an argument to DESeq() ddsNoPrior <- nbinomWaldTest(dds,betaPrior=FALSE) @ Extracting results of other variables is discussed in section \ref{sec:multifactor}. All the values calculated by the \Biocpkg{DESeq2} package are stored in the \Rclass{DESeqDataSet} object, and access to these values is discussed in Section~\ref{sec:access}. \subsection{Exploring and exporting results} \subsubsection{MA-plot} For \Biocpkg{DESeq2}, the function \Rfunction{plotMA} shows the $\log_2$ fold changes attributable to a variable over the mean of normalized counts. By default, the last variable in the design formula is chosen, and points will be colored red if the adjusted p-value is less than 0.1. Points which fall out of the window are plotted as open triangles. <>= plotMA(dds,ylim=c(-2,2),main="DESeq2") @ <>= plotMA(ddsNoPrior, ylim=c(-2,2),main=expression(unshrunken~log[2]~fold~changes)) @ \begin{figure} \centering \includegraphics[width=.45\textwidth]{DESeq2-MANoPrior} \includegraphics[width=.45\textwidth]{DESeq2-MA} \caption{ \textbf{MA-plot.} These plots show the $\log_2$ fold changes from the treatment over the mean of normalized counts, i.e. the average of counts normalized by size factors. The left plot shows the ``unshrunken'' $\log_2$ fold changes, while the right plot, produced by the code above, shows the shrinkage of $\log_2$ fold changes resulting from the incorporation of zero-centered normal prior. The shrinkage is greater for the $\log_2$ fold change estimates from genes with low counts and high dispersion, as can be seen by the narrowing of spread of leftmost points in the right plot.} \label{DESeq2-MA} \end{figure} \subsubsection{More information on results columns} \label{sec:moreInfo} Information about which variables and tests were used can be found by calling the function \Rfunction{mcols} on the results object. <>= mcols(res, use.names=TRUE) @ The variable \Robject{condition} and the factor level \Robject{treated} are combined as ``condition\_treated\_vs\_untreated''. For a particular gene, a $\log_2$ fold change of $-1$ for \Robject{condition\_treated\_vs\_untreated} means that the treatment induces a change in observed expression level of $2^{-1} = 0.5$ compared to the untreated condition. If the variable of interest is continuous-valued, then the reported $\log_2$ fold change is per unit of change of that variable. The results for particular genes can be set to \texttt{NA}, for either one of the following reasons: \begin{enumerate} \item If within a row, all samples have zero counts, this is recorded in \texttt{mcols(dds)\$allZero} and $\log_2$ fold change estimates, p-value and adjusted p-value will all be set to \texttt{NA}. \item If a row contains a sample with an extreme count then the p-value and adjusted p-value are set to \texttt{NA}. These outlier counts are detected by Cook's distance. Customization of this outlier filtering is described in Section~\ref{sec:dealingCooks}, along with a method for replacing outlier counts and refitting. \item If a row is filtered by automatic independent filtering, then only the adjusted p-value is set to \texttt{NA}. Description and customization of independent filtering is decribed in Section~\ref{sec:autoFilt}. \end{enumerate} \subsubsection{Exporting results} An HTML report of the results with plots and sortable/filterable columns can be exported using the \Biocpkg{ReportingTools} package (version higher than 2.1.16) on a \Rclass{DESeqDataSet} which has been processed by the \Rfunction{DESeq} function. For a code example, see the ``RNA-seq differential expression'' vignette at the \Biocpkg{ReportingTools} page, or the manual page for the \Rfunction{publish} method for the \Rclass{DESeqDataSet} class. A plain-text file of the results can be exported using the base \R{} functions \Rfunction{write.csv} or \Rfunction{write.delim}, and a descriptive file name indicating the variable which was tested. <>= write.csv(as.data.frame(res), file="condition_treated_results.csv") @ \subsection{Multi-factor designs} \label{sec:multifactor} Experiments with more than one factor influencing the counts can be analyzed using model formulae with additional variables. The data in the \Biocannopkg{pasilla} package have a condition of interest (the column \Robject{condition}), as well as the type of sequencing which was performed (the column \Robject{type}). <>= colData(dds) @ We can account for the different types of sequencing, and get a clearer picture of the differences attributable to the treatment. As \Robject{condition} is the variable of interest, we put it at the end of the formula. Here we <>= design(dds) <- formula(~ type + condition) dds <- DESeq(dds) @ Again, we access the results using the \Rfunction{results} function. <>= res <- results(dds) head(res) @ It is also possible to retrieve the $\log_2$ fold changes, p-values and adjusted p-values of the \Robject{type} variable. The function \Rfunction{results} takes an argument \Robject{name}, which is a combination of the variable, the level (numeratoFr of the fold change) and the base level (denominator of the fold change). In addition, there might be minor changes made by the \Rfunction{make.names} function on column names, e.g. changing \texttt{-} (a dash) to \texttt{.} (a period). The function \Rfunction{resultsNames} will tell you the names of all available results. <>= resultsNames(dds) resType <- results(dds, "type_single.read_vs_paired.end") head(resType) mcols(resType) @ %--------------------------------------------------- \section{Data transformations and visualization} %--------------------------------------------------- \subsection{Count data transformations} %--------------------------------------------------- For testing for differential expression we operate on raw counts and use discrete distributions, however for other downstream analyses -- e.g. for visualization or clustering -- it might be useful to work with transformed versions of the count data. Maybe the most obvious choice of transformation is the logarithm. 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 positive constant. In this section, we discuss two alternative approaches that offer more theoretical justification and a rational way of choosing the parameter equivalent to $n_0$ above. One method incorporates priors on the sample differences, and the other uses the concept of variance stabilizing transformations \cite{Tibshirani1988,sagmb2003,Anders:2010:GB}. The two functions, \Rfunction{rlogTransformation} and \Rfunction{varianceStabilizingTransformation}, have an argument \Robject{blind}, for whether the transformation should be blind to the sample information specified by the design formula. By setting the argument \Robject{blind} to \Robject{TRUE}, the functions will re-estimate the dispersions using only an intercept (design formula $\sim 1$). This setting should be used in order to compare samples in a manner unbiased by the information about experimental groups, for example to perform sample QA (quality assurance) as demonstrated below. By setting \Robject{blind} to \Robject{FALSE}, the dispersions already estimated will be used to perform transformations, or if not present, they will be estimated using the current design formula. This setting should be used for transforming data for downstream analysis. The two functions return \Rclass{SummarizedExperiment} objects, as the data are no longer counts. The \Rfunction{assay} function is used to extract the matrix of normalized values. <>= rld <- rlogTransformation(dds, blind=TRUE) vsd <- varianceStabilizingTransformation(dds, blind=TRUE) @ \subsubsection{Regularized log transformation} The function \Rfunction{rlogTransformation}, stands for \emph{regularized log}, transforming the original count data to the $\log_2$ scale by fitting a model with a term for each sample and a prior distribution on the coefficients which is estimated from the data. This is very similar to the regularization used by the \Rfunction{DESeq} and \Rfunction{nbinomWaldTest}, as seen in Figure \ref{DESeq2-MA}. The resulting data contains elements defined as: $$ \log_2(q_{ij}) = x_{j.} \beta_i $$ where $q_{ij}$ is a parameter proportional to the expected true concentration of fragments for gene $i$ and sample $j$ (see Section~\ref{sec:glm}), $x_{j.}$ is the $j$-th row of the design matrix $X$, which has a $1$ for the intercept and a $1$ for the sample-specific beta, and $\beta_i$ is the vector of coefficients for gene $i$. Without priors, this design matrix would lead to a non-unique solution, however the addition of a prior on non-intercept betas allows for a unique solution to be found. The regularized log transformation is preferable to the variance stabilizing transformation if the size factors vary widely. \subsubsection{Variance stabilizing transformation} Above, we used a parametric fit for the dispersion. In this case, the closed-form expression for the variance stabilizing transformation is used by \Rfunction{varianceStabilizingTransformation}, which is derived in the file \texttt{vst.pdf}, that is distributed in the package alongside this vignette. If a local fit is used (option \Robject{fitType="locfit"} to \Rfunction{estimateDispersions}) a numerical integration is used instead. The resulting variance stabilizing transformation is shown in Figure \ref{DESeq2-vsd1}. 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. \incfig{DESeq2-vsd1}{.49\textwidth}{VST and log2.}{ 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. } \subsubsection{Effects of transformations on the variance} \begin{figure}[ht] \centering \includegraphics[width=\textwidth]{DESeq2-vsd2} \caption{Per-gene standard deviation (taken across samples), against the rank of the mean, for the shifted logarithm $\log_2(n+1)$ (left), the regularized log transformation (center) and the variance stabilizing transformation (right).} \label{figvsd2} \end{figure} <>= px <- counts(dds)[,1] / sizeFactors(dds)[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(assay(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, using the shifted logarithm transformation (\ref{eq:shiftedlog}), the regularized log transformation and the variance stabilizing transformation. The shifted logarithm has elevated standard deviation in the lower count range, and the regularized log to a lesser extent, while for the variance stabilized data the standard deviation is roughly constant along the whole dynamic range. <>= library("vsn") par(mfrow=c(1,3)) notAllZero <- (rowSums(counts(dds))>0) meanSdPlot(log2(counts(dds,normalized=TRUE)[notAllZero,] + 1), ylim = c(0,2.5)) meanSdPlot(assay(rld[notAllZero,]), ylim = c(0,2.5)) meanSdPlot(assay(vsd[notAllZero,]), ylim = c(0,2.5)) @ %--------------------------------------------------------------- \subsection{Data quality assessment by sample clustering and visualization}\label{sec:quality} %--------------------------------------------------------------- Data quality assessment and quality control (i.\,e.\ the removal of insufficiently good data) are essential steps of any data analysis. These steps 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. \subsubsection{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 raw and transformed data. <>= library("RColorBrewer") library("gplots") select <- order(rowMeans(counts(dds,normalized=TRUE)),decreasing=TRUE)[1:30] hmcol <- colorRampPalette(brewer.pal(9, "GnBu"))(100) @ <>= heatmap.2(counts(dds,normalized=TRUE)[select,], col = hmcol, Rowv = FALSE, Colv = FALSE, scale="none", dendrogram="none", trace="none", margin=c(10,6)) @ <>= heatmap.2(assay(rld)[select,], col = hmcol, Rowv = FALSE, Colv = FALSE, scale="none", dendrogram="none", trace="none", margin=c(10, 6)) @ <>= heatmap.2(assay(vsd)[select,], col = hmcol, Rowv = FALSE, Colv = FALSE, scale="none", dendrogram="none", trace="none", margin=c(10, 6)) @ \begin{figure} \centering \includegraphics[width=.32\textwidth]{DESeq2-figHeatmap2a} \includegraphics[width=.32\textwidth]{DESeq2-figHeatmap2b} \includegraphics[width=.32\textwidth]{DESeq2-figHeatmap2c} \caption{Heatmaps showing the expression data of the \Sexpr{length(select)} most highly expressed genes. The data is of raw counts (left), from regularized log transformation (center) and from variance stabilizing transformation (right).} \label{figHeatmap2} \end{figure} \incfig{DESeq2-figHeatmapSamples}{.6\textwidth}{Sample-to-sample distances.}{ Heatmap showing the Euclidean distances between the samples as calculated from the regularized log transformation. } \subsubsection{Heatmap of the sample-to-sample distances}\label{sec:dists} Another use of the transformed 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. We could alternatively use the variance stabilized transformation here. <>= distsRL <- dist(t(assay(rld))) @ A heatmap of this distance matrix gives us an overview over similarities and dissimilarities between samples (Figure \ref{DESeq2-figHeatmapSamples}): <>= mat <- as.matrix(distsRL) rownames(mat) <- colnames(mat) <- with(colData(dds), paste(condition, type, sep=" : ")) heatmap.2(mat, trace="none", col = rev(hmcol), margin=c(13, 13)) @ \subsubsection{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{DESeq2-figPCA}). <>= print(plotPCA(rld, intgroup=c("condition", "type"))) @ \incfig{DESeq2-figPCA}{.5\textwidth}{PCA plot.}{ PCA plot. The \Sexpr{ncol(rld)} 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. } \newpage \section{Variations to the standard workflow} \subsection{Wald test individual steps} \label{sec:steps} The function \Rfunction{DESeq} runs the following functions in order: <>= dds <- estimateSizeFactors(dds) dds <- estimateDispersions(dds) dds <- nbinomWaldTest(dds) @ \subsection{Contrasts} \label{sec:contrasts} A contrast is a linear combination of factor level means, which can be used to test if combinations of variables are different than zero. The simplest use case for contrasts is the case of a factor with three levels, say A,B and C, where A is the base level. While the standard \Biocpkg{DESeq2} workflow generates p-values for the null hypotheses that the $\log_2$ fold change of B vs A is zero, and that the $\log_2$ fold change of C vs A is zero, a contrast is needed to compare if the $\log_2$ fold change of C vs B is zero. Here we show how to make all three pairwise comparisons using the parathyroid dataset which was built in Section~\ref{sec:sumExpInput}. The three levels of the factor \Robject{treatment} are: Control, DPN and OHT. The samples are also split according to the patient from which the cell cultures were derived, so we include this in the design formula. <>= ddsCtrst <- ddsPara[, colData(ddsPara)$time == "48h"] as.data.frame(colData(ddsCtrst)[,c("patient","treatment")]) design(ddsCtrst) <- ~ patient + treatment @ First we run \Rfunction{DESeq} and show how to extract one of the two comparisons of the treatment factor with the base level: the comparison of DPN vs Control or the comparison of OHT vs Control. <>= ddsCtrst <- DESeq(ddsCtrst) resultsNames(ddsCtrst) resPara <- results(ddsCtrst,"treatment_OHT_vs_Control") head(resPara,2) mcols(resPara) @ Using the \Robject{contrast} argument of the \Rfunction{results} function, we can specify a test of OHT vs DPN. The contrast argument takes a character vector of length three, containing the name of the factor, the name of the numerator level, and the name of the denominator level, where we test the $\log_2$ fold change of numerator vs denominator. Here we extract the results for the $\log_2$ fold change of OHT vs DPN for the treatment factor. <>= resCtrst <- results(ddsCtrst, contrast=c("treatment","OHT","DPN")) head(resCtrst,2) mcols(resCtrst) @ For advanced users, a numeric contrast vector can also be provided with one element for each element provided by \Rfunction{resultsNames}, i.e. columns of the model matrix. Note that the following contrast is the same as specified by the character vector in the previous code chunk. <>= resCtrst <- results(ddsCtrst, contrast=c(0,0,0,0,-1,1)) head(resCtrst,2) mcols(resCtrst) @ The formula that is used to generate the contrasts can be found in Section~\ref{sec:ctrstTheory}. \subsection{Dealing with count outliers} \label{sec:dealingCooks} RNA-Seq data sometimes contain isolated instances of very large counts that are apparently unrelated to the experimental or study design, and which may be considered outliers. There are many reasons why outliers can arise, including rare technical or experimental artifacts, read mapping problems in the case of genetically differing samples, and genuine, but rare biological events. In many cases, users appear primarily interested in genes that show a consistent behaviour, and this is the reason why by default, genes that are affected by such outliers are set aside by \Biocpkg{DESeq2}. The function calculates, for every gene and for every sample, a diagnostic test for outliers called \emph{Cook's distance}. Cook's distance is a measure of how much a single sample is influencing the fitted coefficients for a gene, and a large value of Cook's distance is intended to indicate an outlier count. \Biocpkg{DESeq2} automatically flags genes with Cook's distance above a cutoff and sets their p-values and adjusted p-values to \Robject{NA}. The default cutoff depends on the sample size and number of parameters to be estimated. The default is to use the $99\%$ quantile of the $F(p,m-p)$ distribution (with $p$ the number of parameters including the intercept and $m$ number of samples). The default can be modified using the \Robject{cooksCutoff} argument to the \Rfunction{results} function. The outlier removal functionality can be disabled by setting \Robject{cooksCutoff} to \Robject{FALSE} or \Robject{Inf}. If the removal of a sample would mean that a coefficient cannot be fitted (e.g. if there is only one sample for a given group), then the Cook's distance for this sample is not counted towards the flagging. The Cook's distances are stored as a matrix available in \Robject{assays(dds)[["cooks"]]}. These values are the same as those produced by the \Rfunction{cooks.distance} function of the \Rpackage{stats} package, except using the fitted dispersion and taking into account the size factors. With many degrees of freedom --i.\,e., many more samples than number of parameters to be estimated-- it might be undesirable to remove entire genes from the analysis just because their data include a single count outlier. An alternate strategy is to replace the outlier counts with the trimmed mean over all samples, adjusted by the size factor for that sample. This approach is conservative, it will not lead to false positives, as it replaces the outlier value with the value predicted by the null hypothesis. The \Rfunction{DESeq} function (or \Rfunction{nbinomWaldTest} and \Rfunction{nbinomLRT}) calculates Cook's distance for every gene and sample. After an initial fit has been performed, the following function replaces count outliers by the trimmed mean. Here we demonstrate with the \Robject{pasilla} dataset, although there are not many extra degrees of freedom for this dataset. <>= ddsClean <- replaceOutliersWithTrimmedMean(dds) @ Finally we rerun all the steps of \Rfunction{DESeq}. <>= ddsClean <- DESeq(ddsClean) tab <- table(initial = results(dds)$padj < .1, cleaned = results(ddsClean)$padj < .1) addmargins(tab) @ \subsection{Likelihood ratio test} One reason to use the likelihood ratio test is in order to test the null hypothesis that $\log_2$ fold changes for multiple levels of a factor, or for multiple variables, such as all interactions between two variables, are equal to zero. The likelihood ratio test can also be specified using the \Robject{test} argument to \Rfunction{DESeq}, which substitutes \Rfunction{nbinomWaldTest} with \Rfunction{nbinomLRT}. In this case, the user provides the full formula (the formula stored in \Robject{design(dds)}), and a reduced formula, e.g. one which does not contain the variable of interest. The degrees of freedom for the test is obtained from the number of parameters in the two models. The Wald test and the likelihood ratio test share many of the same genes with adjusted p-value < .1 for this experiment. As we already have an object \Robject{dds} with dispersions calculated for the design formula \texttt{~ type + condition}, we only need to run the function \Rfunction{nbinomLRT}, with a reduced formula including only the type of sequencing, in order to test the $\log_2$ fold change attributable to the condition: <>= ddsLRT <- nbinomLRT(dds, reduced = ~ type) resLRT <- results(ddsLRT) head(resLRT,2) mcols(resLRT) tab <- table(Wald=res$padj < .1, LRT=resLRT$padj < .1) addmargins(tab) @ \subsection{Dispersion plot and fitting alternatives} Plotting the dispersion estimates is a useful diagnostic. The dispersion plot in Figure \ref{DESeq2-dispFit} is typical, with the final estimates shrunk from the gene-wise estimates towards the fitted estimates. Some gene-wise estimates are flagged as outliers and not shrunk towards the fitted value, (this outlier detection is described in the man page for \Rfunction{estimateDispersionsMAP}). The amount of shrinkage can be more or less than seen here, depending on the sample size, the number of coefficients, the row mean and the variability of the gene-wise estimates. <>= plotDispEsts(dds) @ \incfig{DESeq2-dispFit}{.5\textwidth}{Dispersion plot.}{ The dispersion estimate plot shows the gene-wise estimates (black), the fitted values (red), and the final maximum \textit{a posteriori} estimates used in testing (blue). } \subsubsection{Local dispersion fit} The local dispersion fit is available in case the parametric fit fails to converge. A warning will be printed that one should use \Rfunction{plotDispEsts} to check the quality of the fit, whether the curve is pulled dramatically by a few outlier points. <>= ddsLocal <- estimateDispersions(dds, fitType="local") @ \subsubsection{Mean dispersion} While RNA-Seq data tend to demonstrate a dispersion-mean dependence, this assumption is not appropriate for all assays. An alternative is to use the mean of all gene-wise dispersion estimates. <>= ddsMean <- estimateDispersions(dds, fitType="mean") @ \subsubsection{Supply a custom dispersion fit} Any fitted values can be provided during dispersion estimation, using the lower-level functions described in the manual page for \Rfunction{estimateDispersionsGeneEst}. In the first line of the code below, the function \Rfunction{estimateDispersionsGeneEst} stores the gene-wise estimates in the metadata column \Robject{dispGeneEst}. In the last line, the function \Rfunction{estimateDispersionsMAP}, uses this column and the column \Robject{dispFit} to generate maximum \textit{a posteriori} (MAP) estimates of dispersion. The modeling assumption is that the true dispersions are distributed according to a log-normal prior around the fitted values in the column \Robject{fitDisp}. The width of this prior is calculated from the data. <>= ddsMed <- estimateDispersionsGeneEst(dds) useForMedian <- mcols(ddsMed)$dispGeneEst > 1e-7 medianDisp <- median(mcols(ddsMed)$dispGeneEst[useForMedian],na.rm=TRUE) mcols(ddsMed)$dispFit <- medianDisp ddsMed <- estimateDispersionsMAP(ddsMed) @ \subsection{Independent filtering of results}\label{sec:autoFilt} The \Rfunction{results} function of the \Biocpkg{DESeq2} package performs independent filtering by default using the mean of normalized counts as a filter statistic. A threshold on the filter statistic is found which optimizes the number of adjusted p-values lower than a significance level \Robject{alpha} (we use the standard variable name for significance level, though it is unrelated to the dispersion parameter $\alpha$). The theory behind independent filtering is discussed in greater detail in Section~\ref{sec:indepfilt}. The adjusted p-values for the genes which do not pass the filter threshold are set to \Robject{NA}. The independent filtering is performed using the \Rfunction{filtered\_p} function of the \Biocpkg{genefilter} package, and all of the arguments of \Rfunction{filtered\_p} can be passed to the \Rfunction{results} function. The filter threshold value and the number of rejections at each quantile of the filter statistic are available as attributes of the object returned by \Rfunction{results}. For example, we can easily visualize the optimization by plotting the \Robject{filterNumRej} attribute of the results object, as seen in Figure \ref{DESeq2-filtByMean}. <>= attr(res,"filterThreshold") plot(attr(res,"filterNumRej"),type="b", ylab="number of rejections") @ \incfig{DESeq2-filtByMean}{.5\textwidth}{Independent filtering.}{ The \Rfunction{results} function maximizes the number of rejections (adjusted p-value less than a significance level), over theta, the quantiles of a filtering statistic (in this case, the mean of normalized counts). } Independent filtering can be turned off by setting \Robject{independentFiltering} to \Robject{FALSE}. Alternative filtering statistics can be easily provided as an argument to the \Rfunction{results} function. <>= resNoFilt <- results(dds, independentFiltering=FALSE) table(filtering=(res$padj < .1), noFiltering=(resNoFilt$padj < .1)) library(genefilter) rv <- rowVars(counts(dds,normalized=TRUE)) resFiltByVar <- results(dds, filter=rv) table(rowMean=(res$padj < .1), rowVar=(resFiltByVar$padj < .1)) @ \subsection{Access to all calculated values}\label{sec:access} All row-wise calculated values (intermediate dispersion calculations, coefficients, standard errors, etc.) are stored in the \Rclass{DESeqDataSet} object, e.g. \Robject{dds} in this vignette. These values are accessible by calling \Rfunction{mcols} on \Robject{dds}. Descriptions of the columns are accessible by two calls to \Rfunction{mcols}. <>= mcols(dds,use.names=TRUE)[1:4,1:4] mcols(mcols(dds), use.names=TRUE)[1:4,] @ \subsection{Sample-/gene-dependent normalization factors}\label{sec:normfactors} In some experiments, there might be gene-dependent dependencies which vary across samples. For instance, GC-content bias or length bias might vary across samples coming from different labs or processed at different times. We use the terms ``normalization factors'' for a gene $\times$ sample matrix, and ``size factors'' for a single number per sample. Incorporating normalization factors, the mean parameter $\mu_{ij}$ from Section~\ref{sec:glm} becomes: $$ \mu_{ij} = NF_{ij} q_{ij} $$ with normalization factor matrix $NF$ having the same dimensions as the counts matrix $K$. This matrix can be incorporated as shown below. We recommend providing a matrix with a mean of 1, which can be accomplished by dividing out the mean of the matrix. <>= normFactors <- normFactors / mean(normFactors) normalizationFactors(dds) <- normFactors @ These steps then replace \Rfunction{estimateSizeFactors} in the steps described in Section~\ref{sec:steps}. Normalization factors, if present, will always be used in the place of size factors. The methods provided by the \Biocpkg{cqn} or \Biocpkg{EDASeq} packages can help correct for GC or length biases. They both describe in their vignettes how to create matrices which can be used by \Biocpkg{DESeq2}. From the formula above, we see that normalization factors should be on the scale of the counts, like size factors, and unlike offsets which are typically on the scale of the predictors (i.e. the logarithmic scale for the negative binomial GLM). At the time of writing, the transformation from the matrices provided by these packages should be: <>= cqnOffset <- cqnObject$glm.offset cqnNormFactors <- exp(cqnOffset) EDASeqNormFactors <- exp(-1 * EDASeqOffset) @ \section{Theory behind \Biocpkg{DESeq2}} \subsection{Generalized linear model} \label{sec:glm} The differential expression analysis in \Biocpkg{DESeq2} uses a generalized linear model of the form: $$ K_{ij} \sim \textrm{NB}(\mu_{ij}, \alpha_i) $$ $$ \mu_{ij} = s_j q_{ij} $$ $$ \log_2(q_{ij}) = x_{j.} \beta_i $$ where counts $K_{ij}$ for gene $i$, sample $j$ are modeled using a negative binomial distribution with fitted mean $\mu_{ij}$ and a gene-specific dispersion parameter $\alpha_i$. The fitted mean is composed of a sample-specific size factor $s_j$\footnote{The model can be generalised to use sample- \textbf{and} gene-dependent normalisation factors, see Appendix~\ref{sec:normfactors}.} and a parameter $q_{ij}$ proportional to the expected true concentration of fragments for sample $j$. The coefficients $\beta_i$ give the $\log_2$ fold changes for gene $i$ for each column of the model matrix $X$. Dispersions are estimated using a Cox-Reid adjusted profile likelihood, as first implemented for RNA-Seq data in \Biocpkg{edgeR} \cite{CR,edgeR_GLM}. For further details on dispersion estimation and inference, please see the manual pages for the functions \Rfunction{DESeq} and \Rfunction{estimateDispersions}. For access to the calculated values see Section~\ref{sec:access} \subsection{Changes compared to the \Biocpkg{DESeq} package} The main changes in the package \Biocpkg{DESeq2}, compared to the (older) version \Biocpkg{DESeq}, are as follows: \begin{itemize} \item \Rclass{SummarizedExperiment} is used as the superclass for storage of input data, intermediate calculations and results. \item Maximum \textit{a posteriori} estimation of GLM coefficients incorporating a zero-mean normal prior with variance estimated from data (equivalent to Tikhonov/ridge regularization). This adjustment has little effect on genes with high counts, yet it helps to moderate the otherwise large spread in $\log_2$ fold changes for genes with low counts (e.\,g.\ single digits per condition). \item Maximum \textit{a posteriori} estimation of dispersion replaces the \Robject{sharingMode} options \Robject{fit-only} or \Robject{maximum} of the previous version of the package.\cite{Wu2012New} \item All estimation and inference is based on the generalized linear model, which includes the two condition case (previously the \textit{exact test} was used). \item The Wald test for significance of GLM coefficients is provided as the default inference method, with the likelihood ratio test of the previous version still available. \item It is possible to provide a matrix of sample-/gene-dependent normalization factors. \end{itemize} \subsection{Count outlier detection} \label{sec:cooks} \Biocpkg{DESeq2} relies on the negative binomial distribution to make estimates and perform statistical inference on differences. While the negative binomial is versatile in having a mean and dispersion parameter, extreme counts in individual samples might not fit well to the negative binomial. For this reason, we perform automatic detection of count outliers. We use Cook's distance, which is a measure of how much the fitted coefficients would change if an individual sample were removed \cite{Cook1977Detection}. For more on the implementation of Cook's distance see Section~\ref{sec:dealingCooks} and the manual page for the \Rfunction{results} function. Below we plot the maximum value of Cook's distance for each row over the rank of the test statistic to justify its use as a filtering criterion. <>= W <- mcols(dds)$WaldStatistic_condition_treated_vs_untreated maxCooks <- apply(assays(dds)[["cooks"]],1,max) idx <- !is.na(W) plot(rank(W[idx]), maxCooks[idx], xlab="rank of Wald statistic", ylab="maximum Cook's distance per gene", ylim=c(0,5), cex=.4, col=rgb(0,0,0,.3)) m <- ncol(dds) p <- 3 abline(h=qf(.99, p, m - p)) @ \incfig{DESeq2-cooksPlot}{.5\textwidth}{Cook's distance.}{ Plot of the maximum Cook's distance per gene over the rank of the Wald statistics for the condition. The two regions with small Cook's distances are genes with a single count in one sample. The horizontal line is the default cutoff used for 7 samples and 3 estimated parameters. } \subsection{Contrasts} \label{sec:ctrstTheory} Contrasts can be calculated for a \Rclass{DESeqDataSet} object for which the GLM coefficients have already been fit using the Wald test steps (\Rfunction{DESeq} with \texttt{test="Wald"} or using \Rfunction{nbinomWaldTest}). The vector of coefficients $\beta$ is left multiplied by the contrast vector $c$ to form the numerator of the test statistic. The denominator is formed by multiplying the covariance matrix $\Sigma$ for the coefficients on either side by the contrast vector $c$. The square root of this product is an estimate of the standard error for the contrast. The contrast statistic is then compared to a normal distribution as are the Wald statistics for the \Biocpkg{DESeq2} package. $$ W = \frac{c^t \beta}{\sqrt{c^t \Sigma c}} $$ %-------------------------------------------------- \subsection{Independent filtering and multiple testing} \label{sec:indepfilt} \subsubsection{Filtering criteria} \label{sec:filtbycount} %-------------------------------------------------- The goal of 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 tests that pass the filter, compared to the dependence structure between the tests before filtering. \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 property \ref{it:indp} -- which is simple to formally prove for many combinations of filter criteria with test statistics-- and \ref{it:joint}, which is less easy to theoretically imply from first principles, but rarely a problem in practice. We refer to \cite{Bourgon:2010:PNAS} for further discussion of this topic. A simple filtering criterion readily available in the results object is the mean of normalized counts irrespective of biological condition (Figure \ref{DESeq2-indFilt}). Genes with very low counts are not likely to see significant differences typically due to high dispersion. For example, we can plot the $-\log_{10}$ p-values from all genes over the normalized mean counts. <>= plot(res$baseMean+1, -log10(res$pvalue), log="x", xlab="mean of normalized counts", ylab=expression(-log[10](pvalue)), ylim=c(0,30), cex=.4, col=rgb(0,0,0,.3)) @ \incfig{DESeq2-indFilt}{.5\textwidth}{Mean counts as a filter statistic.}{ The mean of normalized counts provides an independent statistic for filtering the tests. It is independent because the information about the variables in the design formula is not used. By filtering out genes which fall on the left side of the plot, the majority of the low p-values are kept. } %-------------------------------------------------- \subsubsection{Why does it work?}\label{sec:whyitworks} %-------------------------------------------------- Consider the $p$ value histogram in Figure \ref{DESeq2-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 $[0,1]$. <>= use <- res$baseMean > attr(res,"filterThreshold") table(use) h1 <- hist(res$pvalue[!use], breaks=0:50/50, plot=FALSE) h2 <- hist(res$pvalue[use], breaks=0:50/50, plot=FALSE) colori <- c(`do not pass`="khaki", `pass`="powderblue") <>= barplot(height = rbind(h1$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))) @ \incfig{DESeq2-fighistindepfilt}{.5\textwidth}{Histogram of p-values}{ for all tests (\Robject{res\$pvalue}). The area shaded in blue indicates the subset of those that pass the filtering, the area in khaki those that do not pass. } %--------------------------------------------------- \subsubsection{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}. % <>= resFilt <- res[use & !is.na(res$pvalue),] orderInPlot <- order(resFilt$pvalue) showInPlot <- (resFilt$pvalue[orderInPlot] <= 0.08) alpha <- 0.1 <>= plot(seq(along=which(showInPlot)), resFilt$pvalue[orderInPlot][showInPlot], pch=".", xlab = expression(rank(p[i])), ylab=expression(p[i])) abline(a=0, b=alpha/length(resFilt$pvalue), col="red3", lwd=2) @ <>= whichBH <- which(resFilt$pvalue[orderInPlot] <= alpha*seq(along=resFilt$pvalue)/length(resFilt$pvalue)) ## 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)), resFilt$padj[orderInPlot][ whichBH] <= alpha, resFilt$padj[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{resFilt\$pvalue} 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} % 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}. % <>= j <- round(length(resFilt$pvalue)*c(1, .66)) px <- (1-resFilt$pvalue[orderInPlot[j]]) py <- ((length(resFilt$pvalue)-1):0)[j] slope <- diff(py)/diff(px) @ <>= plot(1-resFilt$pvalue[orderInPlot], (length(resFilt$pvalue)-1):0, pch=".", xlab=expression(1-p[i]), ylab=expression(N(p[i]))) abline(a=0, slope, col="red3", lwd=2) @ \begin{figure}[ht] \centering \includegraphics[width=.49\textwidth]{DESeq2-sortedP} \includegraphics[width=.49\textwidth]{DESeq2-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 $n=\Sexpr{length(resFilt[["pvalue"]])}$ 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{resFilt\$pvalues} 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{Frequently asked questions} \subsection{How should I email a question?} We welcome emails with questions about our software, and want to ensure that we eliminate issues if and when they appear. We have a few requests to optimize the process: \begin{itemize} \item all emails and follow-up questions should take place over the Bioconductor list, which serves as a repository of information and helps saves the developers' time in responding to similar questions. The subject line should contain ``DESeq2'' and a few words describing the problem. \item first search the Bioconductor list, \url{http://bioconductor.org/help/mailing-list/}, for past threads which might have answered your question. \item if you have a question about the behavior of a function, read the sections of the manual page for this function by typing a question mark and the function name, e.g. \Robject{?results}. We spend a lot of time documenting individual functions and the exact steps that the software is performing. \item include all of your R code, especially the creation of the \Rclass{DESeqDataSet} and the design formula. Include complete warning or error messages, and conclude your message with the full output of \Robject{sessionInfo()}. \item if possible, include the output of \Robject{as.data.frame(colData(dds))}, so that we can have a sense of the experimental setup. If this contains confidential information, you can replace the levels of those factors using \Rfunction{levels()}. \end{itemize} \subsection{Why are some p-values set to \texttt{NA}?} See the details in Section~\ref{sec:moreInfo}. \subsection{How do I use the variance stabilized or rlog transformed data for differential testing?} The variance stabilizing and rlog transformations are provided for applications other than differential testing, for example clustering of samples or other machine learning applications. For differential testing we recommend the \Rfunction{DESeq} function applied to raw counts as outlined in Section~\ref{sec:de}. \section{Session Info} <>= toLatex(sessionInfo()) @ <>= options(prompt="> ", continue="+ ") @ \bibliographystyle{unsrt} \bibliography{library} \end{document}