Quick start

Here we show the most basic steps for a differential expression analysis. There are a variety of steps upstream of DESeq2 that result in the generation of counts or estimated counts for each sample, which we will discuss in the sections below. This code chunk assumes that you have a count matrix called cts and a table of sample information called coldata. The design indicates how to model the samples, here, that we want to measure the effect of the condition, controlling for batch differences. The two factor variables batch and condition should be columns of coldata.

dds <- DESeqDataSetFromMatrix(countData = cts,
                              colData = coldata,
                              design= ~ batch + condition)
dds <- DESeq(dds)
resultsNames(dds) # lists the coefficients
res <- results(dds, name="condition_trt_vs_untrt")
# or to shrink log fold changes association with condition:
res <- lfcShrink(dds, coef="condition_trt_vs_untrt", type="apeglm")

The following starting functions will be explained below:

• If you have performed transcript quantification (with Salmon, kallisto, RSEM, etc.) you could import the data with tximport, which produces a list, and then you can use DESeqDataSetFromTximport().
• If you imported quantification data with tximeta, which produces a SummarizedExperiment with additional metadata, you can then use DESeqDataSet().
• If you have htseq-count files, you can use DESeqDataSetFromHTSeq().

How to get help for DESeq2

Any and all DESeq2 questions should be posted to the Bioconductor support site, which serves as a searchable knowledge base of questions and answers:

https://support.bioconductor.org

Posting a question and tagging with “DESeq2” will automatically send an alert to the package authors to respond on the support site. See the first question in the list of Frequently Asked Questions (FAQ) for information about how to construct an informative post.

You should not email your question to the package authors, as we will just reply that the question should be posted to the Bioconductor support site.

Acknowledgments

Constantin Ahlmann-Eltze has contributed core code for increasing the computational performance of DESeq2 and building an interface to his glmGamPoi package.

We have benefited in the development of DESeq2 from the help and feedback of many individuals, including but not limited to:

The Bionconductor Core Team, Alejandro Reyes, Andrzej Oles, Aleksandra Pekowska, Felix Klein, Nikolaos Ignatiadis (IHW), Anqi Zhu (apeglm), Joseph Ibrahim (apeglm), Vince Carey, Owen Solberg, Ruping Sun, Devon Ryan, Steve Lianoglou, Jessica Larson, Christina Chaivorapol, Pan Du, Richard Bourgon, Willem Talloen, Elin Videvall, Hanneke van Deutekom, Todd Burwell, Jesse Rowley, Igor Dolgalev, Stephen Turner, Ryan C Thompson, Tyr Wiesner-Hanks, Konrad Rudolph, David Robinson, Mingxiang Teng, Mathias Lesche, Sonali Arora, Jordan Ramilowski, Ian Dworkin, Bjorn Gruning, Ryan McMinds, Paul Gordon, Leonardo Collado Torres, Enrico Ferrero, Peter Langfelder, Gavin Kelly, Rob Patro, Charlotte Soneson, Koen Van den Berge, Fanny Perraudeau, Davide Risso, Stephan Engelbrecht, Nicolas Alcala, Jeremy Simon, Travis Ptacek, Rory Kirchner, R. Butler, Ben Keith, Dan Liang, Nil Aygün, Rory Nolan, Michael Schubert, Hugo Tavares, Eric Davis, Wancen Mu, Zhang Cheng, Frederik Ziebell, Luca Menestrina, Hendrik Weisse, I-Hsuan Lin, Rasmus Henningsson, Alexey Sergushichev.

Funding

DESeq2 and its developers have been partially supported by funding from the European Union’s 7th Framework Programme via Project RADIANT, NIH NHGRI R01-HG009937, and by a CZI EOSS award.

Input data

library("tximport")
library("readr")
library("tximportData")
dir <- system.file("extdata", package="tximportData")
samples <- read.table(file.path(dir,"samples.txt"), header=TRUE)
samples$condition <- factor(rep(c("A","B"),each=3))
rownames(samples) <- samples$run
samples[,c("pop","center","run","condition")]

##           pop center       run condition
## ERR188297 TSI  UNIGE ERR188297         A
## ERR188088 TSI  UNIGE ERR188088         A
## ERR188329 TSI  UNIGE ERR188329         A
## ERR188288 TSI  UNIGE ERR188288         B
## ERR188021 TSI  UNIGE ERR188021         B
## ERR188356 TSI  UNIGE ERR188356         B

files <- file.path(dir,"salmon", samples$run, "quant.sf.gz")
names(files) <- samples$run
tx2gene <- read_csv(file.path(dir, "tx2gene.gencode.v27.csv"))

txi <- tximport(files, type="salmon", tx2gene=tx2gene)

library("DESeq2")

## Warning: multiple methods tables found for 'union'

## Warning: multiple methods tables found for 'intersect'

## Warning: multiple methods tables found for 'setdiff'

## Warning: multiple methods tables found for 'setequal'

## Warning: multiple methods tables found for 'union'

## Warning: multiple methods tables found for 'intersect'

## Warning: multiple methods tables found for 'setdiff'

## Warning: multiple methods tables found for 'intersect'

## Warning: multiple methods tables found for 'union'

## Warning: multiple methods tables found for 'intersect'

## Warning: multiple methods tables found for 'setdiff'

## Warning: replacing previous import 'S4Arrays::read_block' by
## 'DelayedArray::read_block' when loading 'SummarizedExperiment'

ddsTxi <- DESeqDataSetFromTximport(txi,
                                   colData = samples,
                                   design = ~ condition)

coldata <- samples
coldata$files <- files
coldata$names <- coldata$run

## Warning: multiple methods tables found for 'union'

## Warning: multiple methods tables found for 'intersect'

## Warning: multiple methods tables found for 'setdiff'

## Warning: multiple methods tables found for 'setequal'

library("tximeta")
se <- tximeta(coldata)
ddsTxi <- DESeqDataSet(se, design = ~ condition)

library("pasilla")
pasCts <- system.file("extdata",
                      "pasilla_gene_counts.tsv",
                      package="pasilla", mustWork=TRUE)
pasAnno <- system.file("extdata",
                       "pasilla_sample_annotation.csv",
                       package="pasilla", mustWork=TRUE)
cts <- as.matrix(read.csv(pasCts,sep="\t",row.names="gene_id"))
coldata <- read.csv(pasAnno, row.names=1)
coldata <- coldata[,c("condition","type")]
coldata$condition <- factor(coldata$condition)
coldata$type <- factor(coldata$type)

head(cts,2)

##             untreated1 untreated2 untreated3 untreated4 treated1 treated2
## FBgn0000003          0          0          0          0        0        0
## FBgn0000008         92        161         76         70      140       88
##             treated3
## FBgn0000003        1
## FBgn0000008       70

coldata

##              condition        type
## treated1fb     treated single-read
## treated2fb     treated  paired-end
## treated3fb     treated  paired-end
## untreated1fb untreated single-read
## untreated2fb untreated single-read
## untreated3fb untreated  paired-end
## untreated4fb untreated  paired-end

rownames(coldata) <- sub("fb", "", rownames(coldata))
all(rownames(coldata) %in% colnames(cts))

## [1] TRUE

all(rownames(coldata) == colnames(cts))

## [1] FALSE

cts <- cts[, rownames(coldata)]
all(rownames(coldata) == colnames(cts))

## [1] TRUE

library("DESeq2")
dds <- DESeqDataSetFromMatrix(countData = cts,
                              colData = coldata,
                              design = ~ condition)
dds

## class: DESeqDataSet 
## dim: 14599 7 
## metadata(1): version
## assays(1): counts
## rownames(14599): FBgn0000003 FBgn0000008 ... FBgn0261574 FBgn0261575
## rowData names(0):
## colnames(7): treated1 treated2 ... untreated3 untreated4
## colData names(2): condition type

featureData <- data.frame(gene=rownames(cts))
mcols(dds) <- DataFrame(mcols(dds), featureData)
mcols(dds)

## DataFrame with 14599 rows and 1 column
##                    gene
##             <character>
## FBgn0000003 FBgn0000003
## FBgn0000008 FBgn0000008
## FBgn0000014 FBgn0000014
## FBgn0000015 FBgn0000015
## FBgn0000017 FBgn0000017
## ...                 ...
## FBgn0261571 FBgn0261571
## FBgn0261572 FBgn0261572
## FBgn0261573 FBgn0261573
## FBgn0261574 FBgn0261574
## FBgn0261575 FBgn0261575

directory <- "/path/to/your/files/"

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)
sampleTable$condition <- factor(sampleTable$condition)

library("DESeq2")
ddsHTSeq <- DESeqDataSetFromHTSeqCount(sampleTable = sampleTable,
                                       directory = directory,
                                       design= ~ condition)
ddsHTSeq

## class: DESeqDataSet 
## dim: 70463 7 
## metadata(1): version
## assays(1): counts
## rownames(70463): FBgn0000003:001 FBgn0000008:001 ... FBgn0261575:001
##   FBgn0261575:002
## rowData names(0):
## colnames(7): treated1fb.txt treated2fb.txt ... untreated3fb.txt
##   untreated4fb.txt
## colData names(1): condition

library("airway")
data("airway")
se <- airway

library("DESeq2")
ddsSE <- DESeqDataSet(se, design = ~ cell + dex)
ddsSE

## class: DESeqDataSet 
## dim: 63677 8 
## metadata(2): '' version
## assays(1): counts
## rownames(63677): ENSG00000000003 ENSG00000000005 ... ENSG00000273492
##   ENSG00000273493
## rowData names(10): gene_id gene_name ... seq_coord_system symbol
## colnames(8): SRR1039508 SRR1039509 ... SRR1039520 SRR1039521
## colData names(9): SampleName cell ... Sample BioSample

smallestGroupSize <- 3
keep <- rowSums(counts(dds) >= 10) >= smallestGroupSize
dds <- dds[keep,]

dds$condition <- factor(dds$condition, levels = c("untreated","treated"))

dds$condition <- relevel(dds$condition, ref = "untreated")

dds$condition <- droplevels(dds$condition)

Differential expression analysis

The standard differential expression analysis steps are wrapped into a single function, DESeq. The estimation steps performed by this function are described below, in the manual page for ?DESeq and in the Methods section of the DESeq2 publication (Love, Huber, and Anders 2014).

Results tables are generated using the function results, which extracts a results table with log2 fold changes, p values and adjusted p values. With no additional arguments to results, the log2 fold change and Wald test p value will be for the last variable in the design formula, and if this is a factor, the comparison will be the last level of this variable over the reference level (see previous note on factor levels). However, the order of the variables of the design do not matter so long as the user specifies the comparison to build a results table for, using the name or contrast arguments of results.

Details about the comparison are printed to the console, directly above the results table. The text, condition treated vs untreated, tells you that the estimates are of the logarithmic fold change log2(treated/untreated).

dds <- DESeq(dds)
res <- results(dds)
res

## log2 fold change (MLE): condition treated vs untreated 
## Wald test p-value: condition treated vs untreated 
## DataFrame with 8148 rows and 6 columns
##               baseMean log2FoldChange     lfcSE       stat    pvalue      padj
##              <numeric>      <numeric> <numeric>  <numeric> <numeric> <numeric>
## FBgn0000008   95.28865     0.00399148  0.225010  0.0177391 0.9858470  0.996699
## FBgn0000017 4359.09632    -0.23842494  0.127094 -1.8759764 0.0606585  0.289604
## FBgn0000018  419.06811    -0.10185506  0.146568 -0.6949338 0.4870968  0.822681
## FBgn0000024    6.41105     0.21429657  0.691557  0.3098756 0.7566555  0.939146
## FBgn0000032  990.79225    -0.08896298  0.146253 -0.6082822 0.5430003  0.848881
## ...                ...            ...       ...        ...       ...       ...
## FBgn0261564   1160.028     -0.0857255  0.108354 -0.7911643 0.4288481  0.789246
## FBgn0261565    620.388     -0.2943294  0.140496 -2.0949303 0.0361772  0.206423
## FBgn0261570   3212.969      0.2971841  0.126742  2.3447877 0.0190379  0.133380
## FBgn0261573   2243.936      0.0146611  0.111365  0.1316493 0.8952617  0.977565
## FBgn0261574   4863.807      0.0179729  0.194137  0.0925784 0.9262385  0.986726

Note that we could have specified the coefficient or contrast we want to build a results table for, using either of the following equivalent commands:

res <- results(dds, name="condition_treated_vs_untreated")
res <- results(dds, contrast=c("condition","treated","untreated"))

One exception to the equivalence of these two commands, is that, using contrast will additionally set to 0 the estimated LFC in a comparison of two groups, where all of the counts in the two groups are equal to 0 (while other groups have positive counts). As this may be a desired feature to have the LFC in these cases set to 0, one can use contrast to build these results tables. More information about extracting specific coefficients from a fitted DESeqDataSet object can be found in the help page ?results. The use of the contrast argument is also further discussed below.

resultsNames(dds)

## [1] "Intercept"                      "condition_treated_vs_untreated"

resLFC <- lfcShrink(dds, coef="condition_treated_vs_untreated", type="apeglm")
resLFC

## log2 fold change (MAP): condition treated vs untreated 
## Wald test p-value: condition treated vs untreated 
## DataFrame with 8148 rows and 5 columns
##               baseMean log2FoldChange     lfcSE    pvalue      padj
##              <numeric>      <numeric> <numeric> <numeric> <numeric>
## FBgn0000008   95.28865     0.00195376  0.152654 0.9858470  0.996699
## FBgn0000017 4359.09632    -0.18810628  0.120870 0.0606585  0.289604
## FBgn0000018  419.06811    -0.06893831  0.122805 0.4870968  0.822681
## FBgn0000024    6.41105     0.01786546  0.199499 0.7566555  0.939146
## FBgn0000032  990.79225    -0.06001511  0.121962 0.5430003  0.848881
## ...                ...            ...       ...       ...       ...
## FBgn0261564   1160.028     -0.0669829 0.0976567 0.4288481  0.789246
## FBgn0261565    620.388     -0.2284564 0.1362122 0.0361772  0.206423
## FBgn0261570   3212.969      0.2395981 0.1237304 0.0190379  0.133380
## FBgn0261573   2243.936      0.0115395 0.0981689 0.8952617  0.977565
## FBgn0261574   4863.807      0.0101618 0.1417667 0.9262385  0.986726

library("BiocParallel")
register(MulticoreParam(4))

resOrdered <- res[order(res$pvalue),]

summary(res)

## 
## out of 8148 with nonzero total read count
## adjusted p-value < 0.1
## LFC > 0 (up)       : 533, 6.5%
## LFC < 0 (down)     : 536, 6.6%
## outliers [1]       : 0, 0%
## low counts [2]     : 0, 0%
## (mean count < 5)
## [1] see 'cooksCutoff' argument of ?results
## [2] see 'independentFiltering' argument of ?results

sum(res$padj < 0.1, na.rm=TRUE)

## [1] 1069

res05 <- results(dds, alpha=0.05)
summary(res05)

## 
## out of 8148 with nonzero total read count
## adjusted p-value < 0.05
## LFC > 0 (up)       : 416, 5.1%
## LFC < 0 (down)     : 437, 5.4%
## outliers [1]       : 0, 0%
## low counts [2]     : 0, 0%
## (mean count < 5)
## [1] see 'cooksCutoff' argument of ?results
## [2] see 'independentFiltering' argument of ?results

sum(res05$padj < 0.05, na.rm=TRUE)

## [1] 853

# (unevaluated code chunk)
library("IHW")
resIHW <- results(dds, filterFun=ihw)
summary(resIHW)
sum(resIHW$padj < 0.1, na.rm=TRUE)
metadata(resIHW)$ihwResult

Exploring and exporting results

plotMA(res, ylim=c(-2,2))

plotMA(resLFC, ylim=c(-2,2))

idx <- identify(res$baseMean, res$log2FoldChange)
rownames(res)[idx]

resultsNames(dds)

## [1] "Intercept"                      "condition_treated_vs_untreated"

# because we are interested in treated vs untreated, we set 'coef=2'
resNorm <- lfcShrink(dds, coef=2, type="normal")
resAsh <- lfcShrink(dds, coef=2, type="ashr")

par(mfrow=c(1,3), mar=c(4,4,2,1))
xlim <- c(1,1e5); ylim <- c(-3,3)
plotMA(resLFC, xlim=xlim, ylim=ylim, main="apeglm")
plotMA(resNorm, xlim=xlim, ylim=ylim, main="normal")
plotMA(resAsh, xlim=xlim, ylim=ylim, main="ashr")

plotCounts(dds, gene=which.min(res$padj), intgroup="condition")

d <- plotCounts(dds, gene=which.min(res$padj), intgroup="condition", 
                returnData=TRUE)
library("ggplot2")
ggplot(d, aes(x=condition, y=count)) + 
  geom_point(position=position_jitter(w=0.1,h=0)) + 
  scale_y_log10(breaks=c(25,100,400))

mcols(res)$description

## [1] "mean of normalized counts for all samples"             
## [2] "log2 fold change (MLE): condition treated vs untreated"
## [3] "standard error: condition treated vs untreated"        
## [4] "Wald statistic: condition treated vs untreated"        
## [5] "Wald test p-value: condition treated vs untreated"     
## [6] "BH adjusted p-values"

write.csv(as.data.frame(resOrdered), 
          file="condition_treated_results.csv")

resSig <- subset(resOrdered, padj < 0.1)
resSig

## log2 fold change (MLE): condition treated vs untreated 
## Wald test p-value: condition treated vs untreated 
## DataFrame with 1069 rows and 6 columns
##              baseMean log2FoldChange     lfcSE      stat       pvalue
##             <numeric>      <numeric> <numeric> <numeric>    <numeric>
## FBgn0039155   730.992       -4.61695 0.1667827  -27.6824 1.13645e-168
## FBgn0025111  1504.272        2.90205 0.1261989   22.9958 5.13138e-117
## FBgn0029167  3709.741       -2.19491 0.0957474  -22.9240 2.68012e-116
## FBgn0003360  4344.597       -3.17683 0.1416166  -22.4326 1.89322e-111
## FBgn0035085   638.757       -2.55819 0.1359972  -18.8106  6.18405e-79
## ...               ...            ...       ...       ...          ...
## FBgn0003890 1644.2002      -0.495185  0.199269  -2.48501    0.0129549
## FBgn0010053  178.3259      -0.516894  0.208034  -2.48466    0.0129675
## FBgn0034997 5125.8312       0.250348  0.100801   2.48360    0.0130063
## FBgn0004359   84.1178       0.646359  0.260308   2.48306    0.0130260
## FBgn0027604  283.2465      -0.578675  0.233077  -2.48277    0.0130366
##                     padj
##                <numeric>
## FBgn0039155 9.25981e-165
## FBgn0025111 2.09052e-113
## FBgn0029167 7.27919e-113
## FBgn0003360 3.85649e-108
## FBgn0035085  1.00775e-75
## ...                  ...
## FBgn0003890    0.0991143
## FBgn0010053    0.0991176
## FBgn0034997    0.0993210
## FBgn0004359    0.0993659
## FBgn0027604    0.0993659

Multi-factor designs

Experiments with more than one factor influencing the counts can be analyzed using design formulas that include the additional variables. In fact, DESeq2 can analyze any possible experimental design that can be expressed with fixed effects terms (multiple factors, designs with interactions, designs with continuous variables, splines, and so on are all possible).

By adding variables to the design, one can control for additional variation in the counts. For example, if the condition samples are balanced across experimental batches, by including the batch factor to the design, one can increase the sensitivity for finding differences due to condition. There are multiple ways to analyze experiments when the additional variables are of interest and not just controlling factors (see section on interactions).

Experiments with many samples: in experiments with many samples (e.g. 50, 100, etc.) it is highly likely that there will be technical variation affecting the observed counts. Failing to model this additional technical variation will lead to spurious results. Many methods exist that can be used to model technical variation, which can be easily included in the DESeq2 design to control for technical variation while estimating effects of interest. See the RNA-seq workflow for examples of using RUV or SVA in combination with DESeq2. For more details on why it is important to control for technical variation in large sample experiments, see the following thread, also archived here by Frederik Ziebell.

The data in the pasilla package have a condition of interest (the column condition), as well as information on the type of sequencing which was performed (the column type), as we can see below:

colData(dds)

## DataFrame with 7 rows and 3 columns
##            condition        type sizeFactor
##             <factor>    <factor>  <numeric>
## treated1   treated   single-read   1.629707
## treated2   treated   paired-end    0.761162
## treated3   treated   paired-end    0.830312
## untreated1 untreated single-read   1.143904
## untreated2 untreated single-read   1.791281
## untreated3 untreated paired-end    0.645994
## untreated4 untreated paired-end    0.750728

We create a copy of the DESeqDataSet, so that we can rerun the analysis using a multi-factor design.

ddsMF <- dds

We change the levels of type so it only contains letters (numbers, underscore and period are also allowed in design factor levels). Be careful when changing level names to use the same order as the current levels.

levels(ddsMF$type)

## [1] "paired-end"  "single-read"

levels(ddsMF$type) <- sub("-.*", "", levels(ddsMF$type))
levels(ddsMF$type)

## [1] "paired" "single"

We can account for the different types of sequencing, and get a clearer picture of the differences attributable to the treatment. As condition is the variable of interest, we put it at the end of the formula. Thus the results function will by default pull the condition results unless contrast or name arguments are specified.

Then we can re-run DESeq:

design(ddsMF) <- formula(~ type + condition)
ddsMF <- DESeq(ddsMF)

Again, we access the results using the results function.

resMF <- results(ddsMF)
head(resMF)

## log2 fold change (MLE): condition treated vs untreated 
## Wald test p-value: condition treated vs untreated 
## DataFrame with 6 rows and 6 columns
##               baseMean log2FoldChange     lfcSE      stat    pvalue      padj
##              <numeric>      <numeric> <numeric> <numeric> <numeric> <numeric>
## FBgn0000008   95.28865     -0.0390130  0.218997 -0.178144 0.8586100  0.947833
## FBgn0000017 4359.09632     -0.2548984  0.113535 -2.245099 0.0247617  0.131475
## FBgn0000018  419.06811     -0.0625571  0.129956 -0.481372 0.6302523  0.852180
## FBgn0000024    6.41105      0.3097331  0.750231  0.412850 0.6797164  0.877741
## FBgn0000032  990.79225     -0.0465134  0.120215 -0.386918 0.6988171  0.886082
## FBgn0000037   14.11443      0.4541562  0.523436  0.867644 0.3855893  0.691941

It is also possible to retrieve the log2 fold changes, p values and adjusted p values of variables other than the last one in the design. While in this case, type is not biologically interesting as it indicates differences across sequencing protocol, for other hypothetical designs, such as ~genotype + condition + genotype:condition, we may actually be interested in the difference in baseline expression across genotype, which is not the last variable in the design.

In any case, the contrast argument of the function results takes a character vector of length three: the name of the variable, the name of the factor level for the numerator of the log2 ratio, and the name of the factor level for the denominator. The contrast argument can also take other forms, as described in the help page for results and below

resMFType <- results(ddsMF,
                     contrast=c("type", "single", "paired"))
head(resMFType)

## log2 fold change (MLE): type single vs paired 
## Wald test p-value: type single vs paired 
## DataFrame with 6 rows and 6 columns
##               baseMean log2FoldChange     lfcSE      stat    pvalue      padj
##              <numeric>      <numeric> <numeric> <numeric> <numeric> <numeric>
## FBgn0000008   95.28865      -0.265123  0.217459 -1.219189 0.2227725  0.492729
## FBgn0000017 4359.09632      -0.103203  0.113399 -0.910090 0.3627748  0.642817
## FBgn0000018  419.06811       0.225857  0.128864  1.752669 0.0796589  0.271610
## FBgn0000024    6.41105       0.302083  0.745703  0.405099 0.6854049        NA
## FBgn0000032  990.79225       0.233891  0.119646  1.954855 0.0506002  0.206081
## FBgn0000037   14.11443      -0.053260  0.521939 -0.102043 0.9187228  0.969866

If the variable is continuous or an interaction term (see section on interactions) then the results can be extracted using the name argument to results, where the name is one of elements returned by resultsNames(dds).

Count data transformations

In order to test for differential expression, we operate on raw counts and use discrete distributions as described in the previous section on differential expression. 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 pseudocounts, i.e. transformations of the form:

y = log₂(n + n₀)

where n represents the count values and n₀ is a positive constant.

In this section, we discuss two alternative approaches that offer more theoretical justification and a rational way of choosing parameters equivalent to n₀ above. One makes use of the concept of variance stabilizing transformations (VST) (Tibshirani 1988; Huber et al. 2003; Anders and Huber 2010), and the other is the regularized logarithm or rlog, which incorporates a prior on the sample differences (Love, Huber, and Anders 2014). Both transformations produce transformed data on the log2 scale which has been normalized with respect to library size or other normalization factors.

The point of these two transformations, the VST and the rlog, is to remove the dependence of the variance on the mean, particularly the high variance of the logarithm of count data when the mean is low. Both VST and rlog use the experiment-wide trend of variance over mean, in order to transform the data to remove the experiment-wide trend. Note that we do not require or desire that all the genes have exactly the same variance after transformation. Indeed, in a figure below, you will see that after the transformations the genes with the same mean do not have exactly the same standard deviations, but that the experiment-wide trend has flattened. It is those genes with row variance above the trend which will allow us to cluster samples into interesting groups.

Note on running time: if you have many samples (e.g. 100s), the rlog function might take too long, and so the vst function will be a faster choice. The rlog and VST have similar properties, but the rlog requires fitting a shrinkage term for each sample and each gene which takes time. See the DESeq2 paper for more discussion on the differences (Love, Huber, and Anders 2014).

vsd <- vst(dds, blind=FALSE)
rld <- rlog(dds, blind=FALSE)
head(assay(vsd), 3)

##              treated1  treated2  treated3 untreated1 untreated2 untreated3
## FBgn0000008  7.777746  7.984491  7.765448   7.735026   7.807720   7.997378
## FBgn0000017 11.954934 12.035700 12.028610  12.049838  12.295662  12.471723
## FBgn0000018  9.219162  9.089390  9.028791   9.374577   9.173538   9.052143
##             untreated4
## FBgn0000008   7.832458
## FBgn0000017  12.089675
## FBgn0000018   9.142848

# this gives log2(n + 1)
ntd <- normTransform(dds)
library("vsn")
meanSdPlot(assay(ntd))

## Warning: Computation failed in `stat_binhex()`.
## Caused by error in `compute_group()`:
## ! The package "hexbin" is required for `stat_bin_hex()`.

meanSdPlot(assay(vsd))

## Warning: Computation failed in `stat_binhex()`.
## Caused by error in `compute_group()`:
## ! The package "hexbin" is required for `stat_bin_hex()`.

meanSdPlot(assay(rld))

## Warning: Computation failed in `stat_binhex()`.
## Caused by error in `compute_group()`:
## ! The package "hexbin" is required for `stat_bin_hex()`.

Data quality assessment by sample clustering and visualization

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 quality as fitness for purpose. 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.

library("pheatmap")
select <- order(rowMeans(counts(dds,normalized=TRUE)),
                decreasing=TRUE)[1:20]
df <- as.data.frame(colData(dds)[,c("condition","type")])
pheatmap(assay(ntd)[select,], cluster_rows=FALSE, show_rownames=FALSE,
         cluster_cols=FALSE, annotation_col=df)

pheatmap(assay(vsd)[select,], cluster_rows=FALSE, show_rownames=FALSE,
         cluster_cols=FALSE, annotation_col=df)

pheatmap(assay(rld)[select,], cluster_rows=FALSE, show_rownames=FALSE,
         cluster_cols=FALSE, annotation_col=df)

sampleDists <- dist(t(assay(vsd)))

library("RColorBrewer")
sampleDistMatrix <- as.matrix(sampleDists)
rownames(sampleDistMatrix) <- paste(vsd$condition, vsd$type, sep="-")
colnames(sampleDistMatrix) <- NULL
colors <- colorRampPalette( rev(brewer.pal(9, "Blues")) )(255)
pheatmap(sampleDistMatrix,
         clustering_distance_rows=sampleDists,
         clustering_distance_cols=sampleDists,
         col=colors)

plotPCA(vsd, intgroup=c("condition", "type"))

pcaData <- plotPCA(vsd, intgroup=c("condition", "type"), returnData=TRUE)
percentVar <- round(100 * attr(pcaData, "percentVar"))
ggplot(pcaData, aes(PC1, PC2, color=condition, shape=type)) +
  geom_point(size=3) +
  xlab(paste0("PC1: ",percentVar[1],"% variance")) +
  ylab(paste0("PC2: ",percentVar[2],"% variance")) + 
  coord_fixed()

Wald test individual steps

The function DESeq runs the following functions in order:

dds <- estimateSizeFactors(dds)
dds <- estimateDispersions(dds)
dds <- nbinomWaldTest(dds)

Control features for estimating size factors

In some experiments, it may not be appropriate to assume that a minority of features (genes) are affected greatly by the condition, such that the standard median-ratio method for estimating the size factors will not provide correct inference (the log fold changes for features that were truly un-changing will not centered on zero). This is a difficult inference problem for any method, but there is an important feature that can be used: the controlGenes argument of estimateSizeFactors. If there is any prior information about features (genes) that should not be changing with respect to the condition, providing this set of features to controlGenes will ensure that the log fold changes for these features will be centered around 0. The paradigm then becomes:

dds <- estimateSizeFactors(dds, controlGenes=ctrlGenes)
dds <- DESeq(dds)

Contrasts

A contrast is a linear combination of estimated log2 fold changes, which can be used to test if differences between groups are equal to zero. The simplest use case for contrasts is an experimental design containing a factor with three levels, say A, B and C. Contrasts enable the user to generate results for all 3 possible differences: log2 fold change of B vs A, of C vs A, and of C vs B. The contrast argument of results function is used to extract test results of log2 fold changes of interest, for example:

results(dds, contrast=c("condition","C","B"))

Log2 fold changes can also be added and subtracted by providing a list to the contrast argument which has two elements: the names of the log2 fold changes to add, and the names of the log2 fold changes to subtract. The names used in the list should come from resultsNames(dds). Alternatively, a numeric vector of the length of resultsNames(dds) can be provided, for manually specifying the linear combination of terms. A tutorial describing the use of numeric contrasts for DESeq2 explains a general approach to comparing across groups of samples. Demonstrations of the use of contrasts for various designs can be found in the examples section of the help page ?results. The mathematical formula that is used to generate the contrasts can be found below.

Interactions

Interaction terms can be added to the design formula, in order to test, for example, if the log2 fold change attributable to a given condition is different based on another factor, for example if the condition effect differs across genotype.

Initial note: Many users begin to add interaction terms to the design formula, when in fact a much simpler approach would give all the results tables that are desired. We will explain this approach first, because it is much simpler to perform. If the comparisons of interest are, for example, the effect of a condition for different sets of samples, a simpler approach than adding interaction terms explicitly to the design formula is to perform the following steps:

• combine the factors of interest into a single factor with all combinations of the original factors
• change the design to include just this factor, e.g. ~ group

Using this design is similar to adding an interaction term, in that it models multiple condition effects which can be easily extracted with results. Suppose we have two factors genotype (with values I, II, and III) and condition (with values A and B), and we want to extract the condition effect specifically for each genotype. We could use the following approach to obtain, e.g. the condition effect for genotype I:

dds$group <- factor(paste0(dds$genotype, dds$condition))
design(dds) <- ~ group
dds <- DESeq(dds)
resultsNames(dds)
results(dds, contrast=c("group", "IB", "IA"))

Adding interactions to the design: The following two plots diagram genotype-specific condition effects, which could be modeled with interaction terms by using a design of ~genotype + condition + genotype:condition.

In the first plot (Gene 1), note that the condition effect is consistent across genotypes. Although condition A has a different baseline for I,II, and III, the condition effect is a log2 fold change of about 2 for each genotype. Using a model with an interaction term genotype:condition, the interaction terms for genotype II and genotype III will be nearly 0.

Here, the y-axis represents log2(n+1), and each group has 20 samples (black dots). A red line connects the mean of the groups within each genotype.

In the second plot (Gene 2), we can see that the condition effect is not consistent across genotype. Here the main condition effect (the effect for the reference genotype I) is again 2. However, this time the interaction terms will be around 1 for genotype II and -4 for genotype III. This is because the condition effect is higher by 1 for genotype II compared to genotype I, and lower by 4 for genotype III compared to genotype I. The condition effect for genotype II (or III) is obtained by adding the main condition effect and the interaction term for that genotype. Such a plot can be made using the plotCounts function as shown above.

Now we will continue to explain the use of interactions in order to test for differences in condition effects. We continue with the example of condition effects across three genotypes (I, II, and III).

The key point to remember about designs with interaction terms is that, unlike for a design ~genotype + condition, where the condition effect represents the overall effect controlling for differences due to genotype, by adding genotype:condition, the main condition effect only represents the effect of condition for the reference level of genotype (I, or whichever level was defined by the user as the reference level). The interaction terms genotypeII.conditionB and genotypeIII.conditionB give the difference between the condition effect for a given genotype and the condition effect for the reference genotype.

This genotype-condition interaction example is examined in further detail in Example 3 in the help page for results, which can be found by typing ?results. In particular, we show how to test for differences in the condition effect across genotype, and we show how to obtain the condition effect for non-reference genotypes.

Time-series experiments

There are a number of ways to analyze time-series experiments, depending on the biological question of interest. In order to test for any differences over multiple time points, once can use a design including the time factor, and then test using the likelihood ratio test as described in the following section, where the time factor is removed in the reduced formula. For a control and treatment time series, one can use a design formula containing the condition factor, the time factor, and the interaction of the two. In this case, using the likelihood ratio test with a reduced model which does not contain the interaction terms will test whether the condition induces a change in gene expression at any time point after the reference level time point (time 0). An example of the later analysis is provided in our RNA-seq workflow.

Likelihood ratio test

DESeq2 offers two kinds of hypothesis tests: the Wald test, where we use the estimated standard error of a log2 fold change to test if it is equal to zero, and the likelihood ratio test (LRT). The LRT examines two models for the counts, a full model with a certain number of terms and a reduced model, in which some of the terms of the full model are removed. The test determines if the increased likelihood of the data using the extra terms in the full model is more than expected if those extra terms are truly zero.

The LRT is therefore useful for testing multiple terms at once, for example testing 3 or more levels of a factor at once, or all interactions between two variables. The LRT for count data is conceptually similar to an analysis of variance (ANOVA) calculation in linear regression, except that in the case of the Negative Binomial GLM, we use an analysis of deviance (ANODEV), where the deviance captures the difference in likelihood between a full and a reduced model.

The likelihood ratio test can be performed by specifying test="LRT" when using the DESeq function, and providing a reduced design formula, e.g. one in which a number of terms from design(dds) are removed. The degrees of freedom for the test is obtained from the difference between the number of parameters in the two models. A simple likelihood ratio test, if the full design was ~condition would look like:

dds <- DESeq(dds, test="LRT", reduced=~1)
res <- results(dds)

If the full design contained other variables, such as a batch variable, e.g. ~batch + condition then the likelihood ratio test would look like:

dds <- DESeq(dds, test="LRT", reduced=~batch)
res <- results(dds)

Extended section on shrinkage estimators

Here we extend the discussion of shrinkage estimators. Below is a summary table of differences between methods available in lfcShrink via the type argument (and for further technical reference on use of arguments please see ?lfcShrink):

References: 1. Zhu, Ibrahim, and Love (2018); 2. Stephens (2016); 3. Love, Huber, and Anders (2014)

Beginning with the first row, all shrinkage methods provided by DESeq2 are good for ranking genes by “effect size”, that is the log2 fold change (LFC) across groups, or associated with an interaction term. It is useful to contrast ranking by effect size with ranking by a p-value or adjusted p-value associated with a null hypothesis: while increasing the number of samples will tend to decrease the associated p-value for a gene that is differentially expressed, the estimated effect size or LFC becomes more precise. Also, a gene can have a small p-value although the change in expression is not great, as long as the standard error associated with the estimated LFC is small.

The next two rows point out that apeglm and ashr shrinkage methods help to preserve the size of large LFC, and can be used to compute s-values. These properties are related. As noted in the previous section, the original DESeq2 shrinkage estimator used a Normal distribution, with a scale that adapts to the spread of the observed LFCs. Because the tails of the Normal distribution become thin relatively quickly, it was important when we designed the method that the prior scaling is sensitive to the very largest observed LFCs. As you can read in the DESeq2 paper, under the section, “Empirical prior estimate”, we used the top 5% of the LFCs by absolute value to set the scale of the Normal prior (we later added weighting the quantile by precision). ashr, published in 2016, and apeglm use wide-tailed priors to avoid shrinking large LFCs. While a typical RNA-seq experiment may have many LFCs between -1 and 1, we might consider a LFC of >4 to be very large, as they represent 16-fold increases or decreases in expression. ashr and apeglm can adapt to the scale of the entirety of LFCs, while not over-shrinking the few largest LFCs. The potential for over-shrinking LFC is also why DESeq2’s shrinkage estimator is not recommended for designs with interaction terms.

What are s-values? This quantity proposed by Stephens (2016) gives the estimated rate of false sign among genes with equal or smaller s-value. Stephens (2016) points out they are analogous to the q-value of Storey (2003). The s-value has a desirable property relative to the adjusted p-value or q-value, in that it does not require supposing there to be a set of null genes with LFC = 0 (the most commonly used null hypothesis). Therefore, it can be benchmarked by comparing estimated LFC and s-value to the “true LFC” in a setting where this can be reasonably defined. For these estimated probabilities to be accurate, the scale of the prior needs to match the scale of the distribution of effect sizes, and so the original DESeq2 shrinkage method is not really compatible with computing s-values.

The last four rows explain differences in whether coefficients or contrasts can have shrinkage applied by the various methods. All three methods can use coef with either the name or numeric index from resultsNames(dds) to specify which coefficient to shrink. All three methods allow for a positive lfcThreshold to be specified, in which case, they will return p-values and adjusted p-values or s-values for the LFC being greater in absolute value than the threshold (see this section for normal). For apeglm and ashr, setting a threshold means that the s-values will give the “false sign or small” rate (FSOS) among genes with equal or small s-value. We found FSOS to be a useful description for when the LFC is either the wrong sign or less than the threshold distance from 0.

resApeT <- lfcShrink(dds, coef=2, type="apeglm", lfcThreshold=1)
plotMA(resApeT, ylim=c(-3,3), cex=.8)
abline(h=c(-1,1), col="dodgerblue", lwd=2)

resAshT <- lfcShrink(dds, coef=2, type="ashr", lfcThreshold=1)
plotMA(resAshT, ylim=c(-3,3), cex=.8)
abline(h=c(-1,1), col="dodgerblue", lwd=2)

Finally, normal and ashr can be used with arbitrary specified contrast because normal shrinks multiple coefficients simultaneously (apeglm does not), and because ashr does not estimate a vector of coefficients but models estimated coefficients and their standard errors from upstream methods (here, DESeq2’s MLE). Although apeglm cannot be used with contrast, we note that many designs can be easily rearranged such that what was a contrast becomes its own coefficient. In this case, the dispersion does not have to be estimated again, as the designs are equivalent, up to the meaning of the coefficients. Instead, one need only run nbinomWaldTest to re-estimate MLE coefficients – these are necessary for apeglm – and then run lfcShrink specifying the coefficient of interest in resultsNames(dds).

We give some examples below of producing equivalent designs for use with coef. We show how the coefficients change with model.matrix, but the user would, for example, either change the levels of dds$condition or replace the design using design(dds)<-, then run nbinomWaldTest followed by lfcShrink.

Three groups:

condition <- factor(rep(c("A","B","C"),each=2))
model.matrix(~ condition)

##   (Intercept) conditionB conditionC
## 1           1          0          0
## 2           1          0          0
## 3           1          1          0
## 4           1          1          0
## 5           1          0          1
## 6           1          0          1
## attr(,"assign")
## [1] 0 1 1
## attr(,"contrasts")
## attr(,"contrasts")$condition
## [1] "contr.treatment"

# to compare C vs B, make B the reference level,
# and select the last coefficient
condition <- relevel(condition, "B")
model.matrix(~ condition)

##   (Intercept) conditionA conditionC
## 1           1          1          0
## 2           1          1          0
## 3           1          0          0
## 4           1          0          0
## 5           1          0          1
## 6           1          0          1
## attr(,"assign")
## [1] 0 1 1
## attr(,"contrasts")
## attr(,"contrasts")$condition
## [1] "contr.treatment"

Three groups, compare condition effects:

grp <- factor(rep(1:3,each=4))
cnd <- factor(rep(rep(c("A","B"),each=2),3))
model.matrix(~ grp + cnd + grp:cnd)

##    (Intercept) grp2 grp3 cndB grp2:cndB grp3:cndB
## 1            1    0    0    0         0         0
## 2            1    0    0    0         0         0
## 3            1    0    0    1         0         0
## 4            1    0    0    1         0         0
## 5            1    1    0    0         0         0
## 6            1    1    0    0         0         0
## 7            1    1    0    1         1         0
## 8            1    1    0    1         1         0
## 9            1    0    1    0         0         0
## 10           1    0    1    0         0         0
## 11           1    0    1    1         0         1
## 12           1    0    1    1         0         1
## attr(,"assign")
## [1] 0 1 1 2 3 3
## attr(,"contrasts")
## attr(,"contrasts")$grp
## [1] "contr.treatment"
## 
## attr(,"contrasts")$cnd
## [1] "contr.treatment"

# to compare condition effect in group 3 vs 2,
# make group 2 the reference level,
# and select the last coefficient
grp <- relevel(grp, "2")
model.matrix(~ grp + cnd + grp:cnd)

##    (Intercept) grp1 grp3 cndB grp1:cndB grp3:cndB
## 1            1    1    0    0         0         0
## 2            1    1    0    0         0         0
## 3            1    1    0    1         1         0
## 4            1    1    0    1         1         0
## 5            1    0    0    0         0         0
## 6            1    0    0    0         0         0
## 7            1    0    0    1         0         0
## 8            1    0    0    1         0         0
## 9            1    0    1    0         0         0
## 10           1    0    1    0         0         0
## 11           1    0    1    1         0         1
## 12           1    0    1    1         0         1
## attr(,"assign")
## [1] 0 1 1 2 3 3
## attr(,"contrasts")
## attr(,"contrasts")$grp
## [1] "contr.treatment"
## 
## attr(,"contrasts")$cnd
## [1] "contr.treatment"

Two groups, two individuals per group, compare within-individual condition effects:

grp <- factor(rep(1:2,each=4))
ind <- factor(rep(rep(1:2,each=2),2))
cnd <- factor(rep(c("A","B"),4))
model.matrix(~grp + grp:ind + grp:cnd)

##   (Intercept) grp2 grp1:ind2 grp2:ind2 grp1:cndB grp2:cndB
## 1           1    0         0         0         0         0
## 2           1    0         0         0         1         0
## 3           1    0         1         0         0         0
## 4           1    0         1         0         1         0
## 5           1    1         0         0         0         0
## 6           1    1         0         0         0         1
## 7           1    1         0         1         0         0
## 8           1    1         0         1         0         1
## attr(,"assign")
## [1] 0 1 2 2 3 3
## attr(,"contrasts")
## attr(,"contrasts")$grp
## [1] "contr.treatment"
## 
## attr(,"contrasts")$ind
## [1] "contr.treatment"
## 
## attr(,"contrasts")$cnd
## [1] "contr.treatment"

# to compare condition effect across group,
# add a main effect for 'cnd',
# and select the last coefficient
model.matrix(~grp + cnd + grp:ind + grp:cnd)

##   (Intercept) grp2 cndB grp1:ind2 grp2:ind2 grp2:cndB
## 1           1    0    0         0         0         0
## 2           1    0    1         0         0         0
## 3           1    0    0         1         0         0
## 4           1    0    1         1         0         0
## 5           1    1    0         0         0         0
## 6           1    1    1         0         0         1
## 7           1    1    0         0         1         0
## 8           1    1    1         0         1         1
## attr(,"assign")
## [1] 0 1 2 3 3 4
## attr(,"contrasts")
## attr(,"contrasts")$grp
## [1] "contr.treatment"
## 
## attr(,"contrasts")$cnd
## [1] "contr.treatment"
## 
## attr(,"contrasts")$ind
## [1] "contr.treatment"

Recommendations for single-cell analysis

The DESeq2 developers and collaborating groups have published recommendations for the best use of DESeq2 for single-cell datasets, which have been described first in Van den Berge et al. (2018). Default values for DESeq2 were designed for bulk data and will not be appropriate for single-cell datasets. These settings and additional improvements have also been tested subsequently and published in Zhu, Ibrahim, and Love (2018) and Ahlmann-Eltze and Huber (2020).

• Use test="LRT" for significance testing when working with single-cell data, over the Wald test. This has been observed across multiple single-cell benchmarks.
• Set the following DESeq arguments to these values: useT=TRUE, minmu=1e-6, and minReplicatesForReplace=Inf. The default setting of minmu was benchmarked on bulk RNA-seq and is not appropriate for single cell data when the expected count is often much less than 1.
• The default size factors are not optimal for single cell count matrices, instead consider setting sizeFactors from scran::computeSumFactors.
• One important concern for single-cell data analysis is the size of the datasets and associated processing time. To address the speed concerns, DESeq2 provides an interface to glmGamPoi, which implements faster dispersion and parameter estimation routines for single-cell data (Ahlmann-Eltze and Huber 2020). To use this feature, set fitType = "glmGamPoi". Alternatively, one can use glmGamPoi as a standalone package. This provides the additional option to process data on-disk if the full dataset does not fit in memory, a quasi-likelihood framework for differential testing, and the ability to form pseudobulk samples (more details how to use glmGamPoi are in its README).

Optionally, one can consider using the zinbwave package to directly model the zero inflation of the counts, and take account of these in the DESeq2 model. This allows for the DESeq2 inference to apply to the part of the data which is not due to zero inflation. Not all single cell datasets exhibit zero inflation, and instead may just reflect low conditional estimated counts (conditional on cell type or cell state).There is example code for combining zinbwave and DESeq2 package functions in the zinbwave vignette. We also have an example of ZINB-WaVE + DESeq2 integration using the splatter package for simulation at the zinbwave-deseq2 GitHub repository.

Approach to count outliers

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 behavior, and this is the reason why by default, genes that are affected by such outliers are set aside by DESeq2, or if there are sufficient samples, outlier counts are replaced for model fitting. These two behaviors are described below.

The DESeq function calculates, for every gene and for every sample, a diagnostic test for outliers called 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. The Cook’s distances are stored as a matrix available in assays(dds)[["cooks"]].

The results function automatically flags genes which contain a Cook’s distance above a cutoff for samples which have 3 or more replicates. The p values and adjusted p values for these genes are set to NA. At least 3 replicates are required for flagging, as it is difficult to judge which sample might be an outlier with only 2 replicates. This filtering can be turned off with results(dds, cooksCutoff=FALSE).

With many degrees of freedom – i.,e., many more samples than number of parameters to be estimated – it is undesirable to remove entire genes from the analysis just because their data include a single count outlier. When there are 7 or more replicates for a given sample, the DESeq function will automatically replace counts with large Cook’s distance with the trimmed mean over all samples, scaled up by the size factor or normalization 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. This outlier replacement only occurs when there are 7 or more replicates, and can be turned off with DESeq(dds, minReplicatesForReplace=Inf).

The default Cook’s distance cutoff for the two behaviors described above 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 for gene flagging can be modified using the cooksCutoff argument to the results function. For outlier replacement, DESeq preserves the original counts in counts(dds) saving the replacement counts as a matrix named replaceCounts in assays(dds). Note that with continuous variables in the design, outlier detection and replacement is not automatically performed, as our current methods involve a robust estimation of within-group variance which does not extend easily to continuous covariates. However, users can examine the Cook’s distances in assays(dds)[["cooks"]], in order to perform manual visualization and filtering if necessary.

Note on many outliers: if there are very many outliers (e.g. many hundreds or thousands) reported by summary(res), one might consider further exploration to see if a single sample or a few samples should be removed due to low quality. The automatic outlier filtering/replacement is most useful in situations which the number of outliers is limited. When there are thousands of reported outliers, it might make more sense to turn off the outlier filtering/replacement (DESeq with minReplicatesForReplace=Inf and results with cooksCutoff=FALSE) and perform manual inspection: First it would be advantageous to make a PCA plot as described above to spot individual sample outliers; Second, one can make a boxplot of the Cook’s distances to see if one sample is consistently higher than others (here this is not the case):

par(mar=c(8,5,2,2))
boxplot(log10(assays(dds)[["cooks"]]), range=0, las=2)

Dispersion plot and fitting alternatives

Plotting the dispersion estimates is a useful diagnostic. The dispersion plot below 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 manual page for 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)

ddsCustom <- dds
useForMedian <- mcols(ddsCustom)$dispGeneEst > 1e-7
medianDisp <- median(mcols(ddsCustom)$dispGeneEst[useForMedian],
                     na.rm=TRUE)
dispersionFunction(ddsCustom) <- function(mu) medianDisp
ddsCustom <- estimateDispersionsMAP(ddsCustom)

Independent filtering of results

The results function of the 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 alpha (we use the standard variable name for significance level, though it is unrelated to the dispersion parameter α). The theory behind independent filtering is discussed in greater detail below. The adjusted p values for the genes which do not pass the filter threshold are set to NA.

The default independent filtering is performed using the filtered_p function of the genefilter package, and all of the arguments of filtered_p can be passed to the results function. The filter threshold value and the number of rejections at each quantile of the filter statistic are available as metadata of the object returned by results.

For example, we can visualize the optimization by plotting the filterNumRej attribute of the results object. The results function maximizes the number of rejections (adjusted p value less than a significance level), over the quantiles of a filter statistic (the mean of normalized counts). The threshold chosen (vertical line) is the lowest quantile of the filter for which the number of rejections is within 1 residual standard deviation to the peak of a curve fit to the number of rejections over the filter quantiles:

metadata(res)$alpha

## [1] 0.1

metadata(res)$filterThreshold

##       0% 
## 5.109586

plot(metadata(res)$filterNumRej, 
     type="b", ylab="number of rejections",
     xlab="quantiles of filter")
lines(metadata(res)$lo.fit, col="red")
abline(v=metadata(res)$filterTheta)

Independent filtering can be turned off by setting independentFiltering to FALSE.

resNoFilt <- results(dds, independentFiltering=FALSE)
addmargins(table(filtering=(res$padj < .1),
                 noFiltering=(resNoFilt$padj < .1)))

##          noFiltering
## filtering FALSE TRUE  Sum
##     FALSE  7079    0 7079
##     TRUE      0 1069 1069
##     Sum    7079 1069 8148

Tests of log2 fold change above or below a threshold

It is also possible to provide thresholds for constructing Wald tests of significance. Two arguments to the results function allow for threshold-based Wald tests: lfcThreshold, which takes a numeric of a non-negative threshold value, and altHypothesis, which specifies the kind of test. Note that the alternative hypothesis is specified by the user, i.e. those genes which the user is interested in finding, and the test provides p values for the null hypothesis, the complement of the set defined by the alternative. The altHypothesis argument can take one of the following four values, where β is the log2 fold change specified by the name argument, and x is the lfcThreshold.

• greaterAbs - |β| > x - tests are two-tailed
• lessAbs - |β| < x - p values are the maximum of the upper and lower tests
• greater - β > x
• less - β < −x

The four possible values of altHypothesis are demonstrated in the following code and visually by MA-plots in the following figures.

par(mfrow=c(2,2),mar=c(2,2,1,1))
ylim <- c(-2.5,2.5)
resGA <- results(dds, lfcThreshold=.5, altHypothesis="greaterAbs")
resLA <- results(dds, lfcThreshold=.5, altHypothesis="lessAbs")
resG <- results(dds, lfcThreshold=.5, altHypothesis="greater")
resL <- results(dds, lfcThreshold=.5, altHypothesis="less")
drawLines <- function() abline(h=c(-.5,.5),col="dodgerblue",lwd=2)
plotMA(resGA, ylim=ylim); drawLines()
plotMA(resLA, ylim=ylim); drawLines()
plotMA(resG, ylim=ylim); drawLines()
plotMA(resL, ylim=ylim); drawLines()

Access to all calculated values

All row-wise calculated values (intermediate dispersion calculations, coefficients, standard errors, etc.) are stored in the DESeqDataSet object, e.g. dds in this vignette. These values are accessible by calling mcols on dds. Descriptions of the columns are accessible by two calls to mcols. Note that the call to substr below is only for display purposes.

mcols(dds,use.names=TRUE)[1:4,1:4]

## DataFrame with 4 rows and 4 columns
##                    gene   baseMean     baseVar   allZero
##             <character>  <numeric>   <numeric> <logical>
## FBgn0000008 FBgn0000008   95.28865 2.29337e+02     FALSE
## FBgn0000017 FBgn0000017 4359.09632 3.71585e+05     FALSE
## FBgn0000018 FBgn0000018  419.06811 2.24013e+03     FALSE
## FBgn0000024 FBgn0000024    6.41105 3.74104e+00     FALSE

substr(names(mcols(dds)),1,10) 

##  [1] "gene"       "baseMean"   "baseVar"    "allZero"    "dispGeneEs"
##  [6] "dispGeneIt" "dispFit"    "dispersion" "dispIter"   "dispOutlie"
## [11] "dispMAP"    "Intercept"  "condition_" "SE_Interce" "SE_conditi"
## [16] "WaldStatis" "WaldStatis" "WaldPvalue" "WaldPvalue" "betaConv"  
## [21] "betaIter"   "deviance"   "maxCooks"

mcols(mcols(dds), use.names=TRUE)[1:4,]

## DataFrame with 4 rows and 2 columns
##                  type            description
##           <character>            <character>
## gene                                        
## baseMean intermediate mean of normalized c..
## baseVar  intermediate variance of normaliz..
## allZero  intermediate all counts for a gen..

The mean values μ_ij = s_jq_ij and the Cook’s distances for each gene and sample are stored as matrices in the assays slot:

head(assays(dds)[["mu"]])

##               treated1    treated2    treated3 untreated1 untreated2
## FBgn0000008  154.18297   72.011890   78.553988  107.92325  169.00095
## FBgn0000017 6441.09688 3008.344869 3281.645427 5333.50912 8351.93629
## FBgn0000018  657.53926  307.106832  335.006715  495.29423  775.59928
## FBgn0000024   11.43421    5.340404    5.825567    6.91794   10.83305
## FBgn0000032 1559.80292  728.513359  794.696964 1164.47564 1823.49484
## FBgn0000037   27.23930   12.722244   13.878028   13.84125   21.67451
##              untreated3  untreated4
## FBgn0000008   60.947217   70.828452
## FBgn0000017 3011.978798 3500.304091
## FBgn0000018  279.706228  325.054365
## FBgn0000024    3.906750    4.540143
## FBgn0000032  657.611313  764.228344
## FBgn0000037    7.816532    9.083808

head(assays(dds)[["cooks"]])

##               treated1    treated2    treated3 untreated1   untreated2
## FBgn0000008 0.08564565 0.297964298 0.077021521 0.10556148 0.0135846197
## FBgn0000017 0.01275474 0.004120273 0.002353591 0.08760807 0.0105562769
## FBgn0000018 0.09813824 0.005595703 0.054059461 0.17277269 0.0021395029
## FBgn0000024 0.06482596 0.129406896 0.030982961 0.26445639 0.0005741831
## FBgn0000032 0.07625620 0.017481712 0.020056352 0.32377428 0.0211262017
## FBgn0000037 0.45819676 0.026766117 0.151000426 0.01530776 0.0859061170
##             untreated3   untreated4
## FBgn0000008 0.19761575 0.0004998745
## FBgn0000017 0.18275047 0.0548693390
## FBgn0000018 0.07090752 0.0104402584
## FBgn0000024 0.02968291 0.0809265572
## FBgn0000032 0.02151283 0.0764805449
## FBgn0000037 0.02257542 0.2489127108

The dispersions α_i can be accessed with the dispersions function.

head(dispersions(dds))

## [1] 0.03082228 0.01305447 0.01518649 0.23983769 0.01654718 0.12963629

head(mcols(dds)$dispersion)

## [1] 0.03082228 0.01305447 0.01518649 0.23983769 0.01654718 0.12963629

The size factors s_j are accessible via sizeFactors:

sizeFactors(dds)

##   treated1   treated2   treated3 untreated1 untreated2 untreated3 untreated4 
##  1.6297067  0.7611622  0.8303119  1.1439041  1.7912811  0.6459940  0.7507275

For advanced users, we also include a convenience function coef for extracting the matrix [β_ir] for all genes i and model coefficients r. This function can also return a matrix of standard errors, see ?coef. The columns of this matrix correspond to the effects returned by resultsNames. Note that the results function is best for building results tables with p values and adjusted p values.

head(coef(dds))

##             Intercept condition_treated_vs_untreated
## FBgn0000008  6.559896                     0.00399148
## FBgn0000017 12.186903                    -0.23842494
## FBgn0000018  8.758176                    -0.10185506
## FBgn0000024  2.596376                     0.21429657
## FBgn0000032  9.991499                    -0.08896298
## FBgn0000037  3.596936                     0.46606939

The beta prior variance σ_r² is stored as an attribute of the DESeqDataSet:

attr(dds, "betaPriorVar")

## [1] 1e+06 1e+06

General information about the prior used for log fold change shrinkage is also stored in a slot of the DESeqResults object. This would also contain information about what other packages were used for log2 fold change shrinkage.

priorInfo(resLFC)

## $type
## [1] "apeglm"
## 
## $package
## [1] "apeglm"
## 
## $version
## [1] '1.29.0'
## 
## $prior.control
## $prior.control$no.shrink
## [1] 1
## 
## $prior.control$prior.mean
## [1] 0
## 
## $prior.control$prior.scale
## [1] 0.2031588
## 
## $prior.control$prior.df
## [1] 1
## 
## $prior.control$prior.no.shrink.mean
## [1] 0
## 
## $prior.control$prior.no.shrink.scale
## [1] 15
## 
## $prior.control$prior.var
## [1] 0.0412735

priorInfo(resNorm)

## $type
## [1] "normal"
## 
## $package
## [1] "DESeq2"
## 
## $version
## [1] '1.47.1'
## 
## $betaPriorVar
##        Intercept conditiontreated 
##     1.000000e+06     1.049206e-01

priorInfo(resAsh)

## $type
## [1] "ashr"
## 
## $package
## [1] "ashr"
## 
## $version
## [1] '2.2.63'
## 
## $fitted_g
## $pi
##  [1] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.128392426
##  [7] 0.000000000 0.452702262 0.057818551 0.000000000 0.176425299 0.000000000
## [13] 0.120967242 0.027145674 0.005428354 0.018807789 0.012312402 0.000000000
## [19] 0.000000000 0.000000000 0.000000000 0.000000000
## 
## $mean
##  [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 
## $sd
##  [1] 0.006752731 0.009549803 0.013505461 0.019099607 0.027010923 0.038199213
##  [7] 0.054021845 0.076398426 0.108043690 0.152796852 0.216087381 0.305593704
## [13] 0.432174761 0.611187408 0.864349522 1.222374817 1.728699044 2.444749633
## [19] 3.457398088 4.889499267 6.914796176 9.778998533
## 
## attr(,"class")
## [1] "normalmix"
## attr(,"row.names")
##  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22

The dispersion prior variance σ_d² is stored as an attribute of the dispersion function:

dispersionFunction(dds)

## function (q) 
## coefs[1] + coefs[2]/q
## <bytecode: 0x556fd805f960>
## <environment: 0x556fd805f308>
## attr(,"coefficients")
## asymptDisp  extraPois 
## 0.01377513 2.88413303 
## attr(,"fitType")
## [1] "parametric"
## attr(,"varLogDispEsts")
## [1] 1.025797
## attr(,"dispPriorVar")
## [1] 0.535439

attr(dispersionFunction(dds), "dispPriorVar")

## [1] 0.535439

The version of DESeq2 which was used to construct the DESeqDataSet object, or the version used when DESeq was run, is stored here:

metadata(dds)[["version"]]

## [1] '1.47.1'

Sample-/gene-dependent normalization factors

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 x sample matrix, and size factors for a single number per sample. Incorporating normalization factors, the mean parameter μ_ij becomes:

μ_ij = NF_ijq_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 row-wise geometric means of 1, so that the mean of normalized counts for a gene is close to the mean of the unnormalized counts. This can be accomplished by dividing out the current row geometric means.

normFactors <- normFactors / exp(rowMeans(log(normFactors)))
normalizationFactors(dds) <- normFactors

These steps then replace estimateSizeFactors which occurs within the DESeq function. The DESeq function will look for pre-existing normalization factors and use these in the place of size factors (and a message will be printed confirming this).

The methods provided by the cqn or 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 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)

“Model matrix not full rank”

While most experimental designs run easily using design formula, some design formulas can cause problems and result in the DESeq function returning an error with the text: “the model matrix is not full rank, so the model cannot be fit as specified.” There are two main reasons for this problem: either one or more columns in the model matrix are linear combinations of other columns, or there are levels of factors or combinations of levels of multiple factors which are missing samples. We address these two problems below and discuss possible solutions:

## DataFrame with 4 rows and 2 columns
##      batch condition
##   <factor>  <factor>
## 1        1         A
## 2        1         A
## 3        2         B
## 4        2         B

## DataFrame with 6 rows and 2 columns
##      batch condition
##   <factor>  <factor>
## 1        1         A
## 2        1         A
## 3        1         B
## 4        1         B
## 5        2         C
## 6        2         C

## DataFrame with 6 rows and 2 columns
##      batch condition
##   <factor>  <factor>
## 1        1         A
## 2        1         B
## 3        1         C
## 4        2         A
## 5        2         B
## 6        2         C

coldata <- DataFrame(grp=factor(rep(c("X","Y"),each=6)),
                     ind=factor(rep(1:6,each=2)),
                     cnd=factor(rep(c("A","B"),6)))
coldata

## DataFrame with 12 rows and 3 columns
##          grp      ind      cnd
##     <factor> <factor> <factor>
## 1          X        1        A
## 2          X        1        B
## 3          X        2        A
## 4          X        2        B
## 5          X        3        A
## ...      ...      ...      ...
## 8          Y        4        B
## 9          Y        5        A
## 10         Y        5        B
## 11         Y        6        A
## 12         Y        6        B

as.data.frame(coldata)

##    grp ind cnd
## 1    X   1   A
## 2    X   1   B
## 3    X   2   A
## 4    X   2   B
## 5    X   3   A
## 6    X   3   B
## 7    Y   4   A
## 8    Y   4   B
## 9    Y   5   A
## 10   Y   5   B
## 11   Y   6   A
## 12   Y   6   B

coldata$ind.n <- factor(rep(rep(1:3,each=2),2))
as.data.frame(coldata)

##    grp ind cnd ind.n
## 1    X   1   A     1
## 2    X   1   B     1
## 3    X   2   A     2
## 4    X   2   B     2
## 5    X   3   A     3
## 6    X   3   B     3
## 7    Y   4   A     1
## 8    Y   4   B     1
## 9    Y   5   A     2
## 10   Y   5   B     2
## 11   Y   6   A     3
## 12   Y   6   B     3

model.matrix(~ grp + grp:ind.n + grp:cnd, coldata)

##    (Intercept) grpY grpX:ind.n2 grpY:ind.n2 grpX:ind.n3 grpY:ind.n3 grpX:cndB
## 1            1    0           0           0           0           0         0
## 2            1    0           0           0           0           0         1
## 3            1    0           1           0           0           0         0
## 4            1    0           1           0           0           0         1
## 5            1    0           0           0           1           0         0
## 6            1    0           0           0           1           0         1
## 7            1    1           0           0           0           0         0
## 8            1    1           0           0           0           0         0
## 9            1    1           0           1           0           0         0
## 10           1    1           0           1           0           0         0
## 11           1    1           0           0           0           1         0
## 12           1    1           0           0           0           1         0
##    grpY:cndB
## 1          0
## 2          0
## 3          0
## 4          0
## 5          0
## 6          0
## 7          0
## 8          1
## 9          0
## 10         1
## 11         0
## 12         1
## attr(,"assign")
## [1] 0 1 2 2 2 2 3 3
## attr(,"contrasts")
## attr(,"contrasts")$grp
## [1] "contr.treatment"
## 
## attr(,"contrasts")$ind.n
## [1] "contr.treatment"
## 
## attr(,"contrasts")$cnd
## [1] "contr.treatment"

results(dds, contrast=list("grpY.cndB","grpX.cndB"))

group <- factor(rep(1:3,each=6))
condition <- factor(rep(rep(c("A","B","C"),each=2),3))
d <- DataFrame(group, condition)[-c(17,18),]
as.data.frame(d)

##    group condition
## 1      1         A
## 2      1         A
## 3      1         B
## 4      1         B
## 5      1         C
## 6      1         C
## 7      2         A
## 8      2         A
## 9      2         B
## 10     2         B
## 11     2         C
## 12     2         C
## 13     3         A
## 14     3         A
## 15     3         B
## 16     3         B

m1 <- model.matrix(~ condition*group, d)
colnames(m1)

## [1] "(Intercept)"       "conditionB"        "conditionC"       
## [4] "group2"            "group3"            "conditionB:group2"
## [7] "conditionC:group2" "conditionB:group3" "conditionC:group3"

unname(m1)

##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
##  [1,]    1    0    0    0    0    0    0    0    0
##  [2,]    1    0    0    0    0    0    0    0    0
##  [3,]    1    1    0    0    0    0    0    0    0
##  [4,]    1    1    0    0    0    0    0    0    0
##  [5,]    1    0    1    0    0    0    0    0    0
##  [6,]    1    0    1    0    0    0    0    0    0
##  [7,]    1    0    0    1    0    0    0    0    0
##  [8,]    1    0    0    1    0    0    0    0    0
##  [9,]    1    1    0    1    0    1    0    0    0
## [10,]    1    1    0    1    0    1    0    0    0
## [11,]    1    0    1    1    0    0    1    0    0
## [12,]    1    0    1    1    0    0    1    0    0
## [13,]    1    0    0    0    1    0    0    0    0
## [14,]    1    0    0    0    1    0    0    0    0
## [15,]    1    1    0    0    1    0    0    1    0
## [16,]    1    1    0    0    1    0    0    1    0
## attr(,"assign")
## [1] 0 1 1 2 2 3 3 3 3
## attr(,"contrasts")
## attr(,"contrasts")$condition
## [1] "contr.treatment"
## 
## attr(,"contrasts")$group
## [1] "contr.treatment"

all.zero <- apply(m1, 2, function(x) all(x==0))
all.zero

##       (Intercept)        conditionB        conditionC            group2 
##             FALSE             FALSE             FALSE             FALSE 
##            group3 conditionB:group2 conditionC:group2 conditionB:group3 
##             FALSE             FALSE             FALSE             FALSE 
## conditionC:group3 
##              TRUE

idx <- which(all.zero)
m1 <- m1[,-idx]
unname(m1)

##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
##  [1,]    1    0    0    0    0    0    0    0
##  [2,]    1    0    0    0    0    0    0    0
##  [3,]    1    1    0    0    0    0    0    0
##  [4,]    1    1    0    0    0    0    0    0
##  [5,]    1    0    1    0    0    0    0    0
##  [6,]    1    0    1    0    0    0    0    0
##  [7,]    1    0    0    1    0    0    0    0
##  [8,]    1    0    0    1    0    0    0    0
##  [9,]    1    1    0    1    0    1    0    0
## [10,]    1    1    0    1    0    1    0    0
## [11,]    1    0    1    1    0    0    1    0
## [12,]    1    0    1    1    0    0    1    0
## [13,]    1    0    0    0    1    0    0    0
## [14,]    1    0    0    0    1    0    0    0
## [15,]    1    1    0    0    1    0    0    1
## [16,]    1    1    0    0    1    0    0    1

The DESeq2 model

The DESeq2 model and all the steps taken in the software are described in detail in our publication (Love, Huber, and Anders 2014), and we include the formula and descriptions in this section as well. The differential expression analysis in DESeq2 uses a generalized linear model of the form:

K_ij ∼ NB(μ_ij, α_i)

μ_ij = s_jq_ij

log₂(q_ij) = x_j.β_i

where counts K_ij for gene i, sample j are modeled using a negative binomial distribution with fitted mean μ_ij and a gene-specific dispersion parameter α_i. The fitted mean is composed of a sample-specific size factor s_j and a parameter q_ij proportional to the expected true concentration of fragments for sample j. The coefficients β_i give the log2 fold changes for gene i for each column of the model matrix X. Note that the model can be generalized to use sample- and gene-dependent normalization factors s_ij.

The dispersion parameter α_i defines the relationship between the variance of the observed count and its mean value. In other words, how far do we expected the observed count will be from the mean value, which depends both on the size factor s_j and the covariate-dependent part q_ij as defined above.

Var(K_ij) = E[(K_ij − μ_ij)²] = μ_ij + α_iμ_ij²

An option in DESeq2 is to provide maximum a posteriori estimates of the log2 fold changes in β_i after incorporating a zero-centered Normal prior (betaPrior). While previously, these moderated, or shrunken, estimates were generated by DESeq or nbinomWaldTest functions, they are now produced by the lfcShrink function. Dispersions are estimated using expected mean values from the maximum likelihood estimate of log2 fold changes, and optimizing the Cox-Reid adjusted profile likelihood, as first implemented for RNA-seq data in edgeR (Cox and Reid 1987,edgeR_GLM). The steps performed by the DESeq function are documented in its manual page ?DESeq; briefly, they are:

1. estimation of size factors s_j by estimateSizeFactors
2. estimation of dispersion α_i by estimateDispersions
3. negative binomial GLM fitting for β_i and Wald statistics by nbinomWaldTest

For access to all the values calculated during these steps, see the section above.

Changes compared to DESeq

The main changes in the package DESeq2, compared to the (older) version DESeq, are as follows:

• RangedSummarizedExperiment is used as the superclass for storage of input data, intermediate calculations and results.
• Optional, maximum a posteriori estimation of GLM coefficients incorporating a zero-centered 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 variance in log2 fold change estimates for genes with low counts or highly variable counts. These estimates are now provided by the lfcShrink function.
• Maximum a posteriori estimation of dispersion replaces the sharingMode options fit-only or maximum of the previous version of the package. This is similar to the dispersion estimation methods of DSS (Wu, Wang, and Wu 2012).
• All estimation and inference is based on the generalized linear model, which includes the two condition case (previously the exact test was used).
• 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.
• It is possible to provide a matrix of sample-/gene-dependent normalization factors.
• Automatic independent filtering on the mean of normalized counts.
• Automatic outlier detection and handling.

Methods changes since the 2014 DESeq2 paper

• In version 1.18 (November 2017), we add two alternative shrinkage estimators, which can be used via lfcShrink: an estimator using a t prior from the apeglm packages, and an estimator with a fitted mixture of normals prior from the ashr package.
• In version 1.16 (November 2016), the log2 fold change shrinkage is no longer default for the DESeq and nbinomWaldTest functions, by setting the defaults of these to betaPrior=FALSE, and by introducing a separate function lfcShrink, which performs log2 fold change shrinkage for visualization and ranking of genes. While for the majority of bulk RNA-seq experiments, the LFC shrinkage did not affect statistical testing, DESeq2 has become used as an inference engine by a wider community, and certain sequencing datasets show better performance with the testing separated from the use of the LFC prior. Also, the separation of LFC shrinkage to a separate function lfcShrink allows for easier methods development of alternative effect size estimators.
• A small change to the independent filtering routine: instead of taking the quantile of the filter (the mean of normalized counts) which directly maximizes the number of rejections, the threshold chosen is the lowest quantile of the filter for which the number of rejections is close to the peak of a curve fit to the number of rejections over the filter quantiles. ``Close to’’ is defined as within 1 residual standard deviation. This change was introduced in version 1.10 (October 2015).
• For the calculation of the beta prior variance, instead of matching the empirical quantile to the quantile of a Normal distribution, DESeq2 now uses the weighted quantile function of the Hmisc package. The weighting is described in the manual page for nbinomWaldTest. The weights are the inverse of the expected variance of log counts (as used in the diagonals of the matrix W in the GLM). The effect of the change is that the estimated prior variance is robust against noisy estimates of log fold change from genes with very small counts. This change was introduced in version 1.6 (October 2014).

For a list of all changes since version 1.0.0, see the NEWS file included in the package.

Count outlier detection

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 (Cook 1977). For more on the implementation of Cook’s distance see the manual page for the 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 <- res$stat
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))

Contrasts

Contrasts can be calculated for a DESeqDataSet object for which the GLM coefficients have already been fit using the Wald test steps (DESeq with test="Wald" or using nbinomWaldTest). The vector of coefficients β 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 Σ 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 DESeq2 package.

$$ W = \frac{c^t \beta}{\sqrt{c^t \Sigma c}} $$

Expanded model matrices

For the specific combination of lfcShrink with the type normal and using contrast, DESeq2 uses expanded model matrices to produce shrunken log2 fold change estimates where the shrinkage is independent of the choice of reference level. In all other cases, DESeq2 uses standard model matrices, as produced by model.matrix. The expanded model matrices differ from the standard model matrices, in that they have an indicator column (and therefore a coefficient) for each level of factors in the design formula in addition to an intercept. This is described in the DESeq2 paper. Using type normal with coef uses standard model matrices, as does the apeglm shrinkage estimator.

Independent filtering and multiple testing

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))

use <- res$baseMean > metadata(res)$filterThreshold
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)))

How can I get support for DESeq2?

We welcome 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:

• all questions should take place on the Bioconductor support site: https://support.bioconductor.org, which serves as a repository of questions and answers. This helps to save the developers’ time in responding to similar questions. Make sure to tag your post with deseq2. It is often very helpful in addition to describe the aim of your experiment.
• before posting, first search the Bioconductor support site mentioned above for past threads which might have answered your question.
• 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. ?results. We spend a lot of time documenting individual functions and the exact steps that the software is performing.
• include all of your R code, especially the creation of the DESeqDataSet and the design formula. Include complete warning or error messages, and conclude your message with the full output of sessionInfo().
• if possible, include the output of 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 levels().

Why are some p values set to NA?

See the details above.

How can I get unfiltered DESeq2 results?

Users can obtain unfiltered GLM results, i.e. without outlier removal or independent filtering with the following call:

dds <- DESeq(dds, minReplicatesForReplace=Inf)
res <- results(dds, cooksCutoff=FALSE, independentFiltering=FALSE)

In this case, the only p values set to NA are those from genes with all counts equal to zero.

How do I use VST or rlog 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 DESeq function applied to raw counts as outlined above.

Why after VST are there still batches in the PCA plot?

The transformations implemented in DESeq2, vst and rlog, compute a variance stabilizing transformation which is roughly similar to putting the data on the log2 scale, while also dealing with the sampling variability of low counts. It uses the design formula to calculate the within-group variability (if blind=FALSE) or the across-all-samples variability (if blind=TRUE). It does not use the design to remove variation in the data. It therefore does not remove variation that can be associated with batch or other covariates (nor does DESeq2 have a way to specify which covariates are nuisance and which are of interest).

It is possible to visualize the transformed data with batch variation removed, using the removeBatchEffect function from limma. This simply removes any shifts in the log2-scale expression data that can be explained by batch. The paradigm for this operation for designs with balanced batches would be:

mat <- assay(vsd)
mm <- model.matrix(~condition, colData(vsd))
mat <- limma::removeBatchEffect(mat, batch=vsd$batch, design=mm)
assay(vsd) <- mat
plotPCA(vsd)

The design argument is necessary to avoiding removing variation associated with the treatment conditions. See ?removeBatchEffect in the limma package for details.

Do normalized counts correct for variables in the design?

No. The design variables are not used when estimating the size factors, and counts(dds, normalized=TRUE) is providing counts scaled by size or normalization factors. The design is only used when estimating dispersion and log2 fold changes.

The only case in which there is more than size factor scaling on the counts is when either normalization factors have been provided (e.g. from cqn or EDASeq), or if tximport is used and the upstream software corrected for various technical biases (e.g. Salmon quantification with GC bias correction). In this case, the average transcript length is taken into account when scaling the counts with counts(dds, normalized=TRUE). For details, see the tximport package vignette and citation (Soneson, Love, and Robinson 2015).

Can I use DESeq2 to analyze paired samples?

Yes, you should use a multi-factor design which includes the sample information as a term in the design formula. This will account for differences between the samples while estimating the effect due to the condition. The condition of interest should go at the end of the design formula, e.g. ~ subject + condition.

If I have multiple groups, should I run all together or split into pairs of groups?

Typically, we recommend users to run samples from all groups together, and then use the contrast argument of the results function to extract comparisons of interest after fitting the model using DESeq.

The model fit by DESeq estimates a single dispersion parameter for each gene, which defines how far we expect the observed count for a sample will be from the mean value from the model given its size factor and its condition group. See the section above and the DESeq2 paper for full details. Having a single dispersion parameter for each gene is usually sufficient for analyzing multi-group data, as the final dispersion value will incorporate the within-group variability across all groups.

However, for some datasets, exploratory data analysis (EDA) plots could reveal that one or more groups has much higher within-group variability than the others. A simulated example of such a set of samples is shown below. This is case where, by comparing groups A and B separately – subsetting a DESeqDataSet to only samples from those two groups and then running DESeq on this subset – will be more sensitive than a model including all samples together. It should be noted that such an extreme range of within-group variability is not common, although it could arise if certain treatments produce an extreme reaction (e.g. cell death). Again, this can be easily detected from the EDA plots such as PCA described in this vignette.

Here we diagram an extreme range of within-group variability with a simulated dataset. Typically, it is recommended to run DESeq across samples from all groups, for datasets with multiple groups. However, this simulated dataset shows a case where it would be preferable to compare groups A and B by creating a smaller dataset without the C samples. Group C has much higher within-group variability, which would inflate the per-gene dispersion estimate for groups A and B as well:

Can I run DESeq2 to contrast the levels of many groups?

DESeq2 will work with any kind of design specified using the R formula. We enourage users to consider exploratory data analysis such as principal components analysis rather than performing statistical testing of all pairs of many groups of samples. Statistical testing is one of many ways of describing differences between samples.

As a speed concern with fitting very large models, note that each additional level of a factor in the design formula adds another parameter to the GLM which is fit by DESeq2. Users might consider first removing genes with very few reads, as this will speed up the fitting procedure.

Can I use DESeq2 to analyze a dataset without replicates?

No. This analysis is not possible in DESeq2.

How can I include a continuous covariate in the design formula?

Continuous covariates can be included in the design formula in exactly the same manner as factorial covariates, and then results for the continuous covariate can be extracted by specifying name. Continuous covariates might make sense in certain experiments, where a constant fold change might be expected for each unit of the covariate. However, in some cases, more meaningful results may be obtained by cutting continuous covariates into a factor defined over a small number of bins (e.g. 3-5). In this way, the average effect of each group is controlled for, regardless of the trend over the continuous covariates. In R, numeric vectors can be converted into factors using the function cut.

I ran a likelihood ratio test, but results() only gives me one comparison.

“… How do I get the p values for all of the variables/levels that were removed in the reduced design?”

This is explained in the help page for ?results in the section about likelihood ratio test p-values, but we will restate the answer here. When one performs a likelihood ratio test, the p values and the test statistic (the stat column) are values for the test that removes all of the variables which are present in the full design and not in the reduced design. This tests the null hypothesis that all the coefficients from these variables and levels of these factors are equal to zero.

The likelihood ratio test p values therefore represent a test of all the variables and all the levels of factors which are among these variables. However, the results table only has space for one column of log fold change, so a single variable and a single comparison is shown (among the potentially multiple log fold changes which were tested in the likelihood ratio test). This is indicated at the top of the results table with the text, e.g., log2 fold change (MLE): condition C vs A, followed by, LRT p-value: ‘~ batch + condition’ vs ‘~ batch’. This indicates that the p value is for the likelihood ratio test of all the variables and all the levels, while the log fold change is a single comparison from among those variables and levels. See the help page for results for more details.

What are the exact steps performed by DESeq()?

See the manual page for DESeq, which links to the subfunctions which are called in order, where complete details are listed. Also you can read the three steps listed in the DESeq2 model in this document.

Is there an official Galaxy tool for DESeq2?

Yes. The repository for the DESeq2 tool is

https://github.com/galaxyproject/tools-iuc/tree/master/tools/deseq2

and a link to its location in the Tool Shed is

https://toolshed.g2.bx.psu.edu/view/iuc/deseq2/d983d19fbbab.

I want to benchmark DESeq2 comparing to other DE tools.

One aspect which can cause problems for comparison is that, by default, DESeq2 outputs NA values for adjusted p values based on independent filtering of genes which have low counts. This is a way for the DESeq2 to give extra information on why the adjusted p value for this gene is not small. Additionally, p values can be set to NA based on extreme count outlier detection. These NA values should be considered negatives for purposes of estimating sensitivity and specificity. The easiest way to work with the adjusted p values in a benchmarking context is probably to convert these NA values to 1:

res$padj <- ifelse(is.na(res$padj), 1, res$padj)

I have trouble installing DESeq2 on Ubuntu/Linux…

“I try to install DESeq2, but I get an error trying to install the R packages XML and/or RCurl:”

ERROR: configuration failed for package XML

ERROR: configuration failed for package RCurl

You need to install the following devel versions of packages using your standard package manager, e.g. sudo apt-get install or sudo apt install

• libxml2-dev
• libcurl4-openssl-dev