Analyzing RNA-seq data with DESeq2
Michael I. Love, Simon Anders, and Wolfgang Huber
11/14/2024
Abstract
A basic task in the analysis of count data from RNA-seq is the detection of differentially expressed genes. The count data are presented as a table which reports, for each sample, the number of sequence fragments that have been assigned to each gene. Analogous data also arise for other assay types, including comparative ChIP-Seq, HiC, shRNA screening, and mass spectrometry. An important analysis question is the quantification and statistical inference of systematic changes between conditions, as compared to within-condition variability. The package DESeq2 provides methods to test for differential expression by use of negative binomial generalized linear models; the estimates of dispersion and logarithmic fold changes incorporate data-driven prior distributions. This vignette explains the use of the package and demonstrates typical workflows. An RNA-seq workflow on the Bioconductor website covers similar material to this vignette but at a slower pace, including the generation of count matrices from FASTQ files. DESeq2 package version: 1.47.1
- Standard workflow
- Data transformations and visualization
- Variations to the standard
workflow
- Wald test individual steps
- Control features for estimating size factors
- Contrasts
- Interactions
- Time-series experiments
- Likelihood ratio test
- Extended section on shrinkage estimators
- Recommendations for single-cell analysis
- Approach to count outliers
- Dispersion plot and fitting alternatives
- Independent filtering of results
- Tests of log2 fold change above or below a threshold
- Access to all calculated values
- Sample-/gene-dependent normalization factors
- “Model matrix not full rank”
- Theory behind DESeq2
- Frequently asked questions
- How can I get support for DESeq2?
- Why are some p values set to NA?
- How can I get unfiltered DESeq2 results?
- How do I use VST or rlog data for differential testing?
- Why after VST are there still batches in the PCA plot?
- Do normalized counts correct for variables in the design?
- Can I use DESeq2 to analyze paired samples?
- If I have multiple groups, should I run all together or split into pairs of groups?
- Can I run DESeq2 to contrast the levels of many groups?
- Can I use DESeq2 to analyze a dataset without replicates?
- How can I include a continuous covariate in the design formula?
- I ran a likelihood ratio test, but results() only gives me one comparison.
- What are the exact steps performed by DESeq()?
- Is there an official Galaxy tool for DESeq2?
- I want to benchmark DESeq2 comparing to other DE tools.
- I have trouble installing DESeq2 on Ubuntu/Linux…
- Session info
- References
Standard workflow
Note: if you use DESeq2 in published research, please cite:
Love, M.I., Huber, W., Anders, S. (2014) Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2. Genome Biology, 15:550. 10.1186/s13059-014-0550-8
Other Bioconductor packages with similar aims are edgeR, limma, DSS, EBSeq, and baySeq.
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
Why un-normalized counts?
As input, the DESeq2 package expects count data as obtained, e.g., from RNA-seq or another high-throughput sequencing experiment, in the form of a matrix of integer values. The value in the i-th row and the j-th column of the matrix tells how many reads can be assigned to gene i in sample j. Analogously, for other types of assays, the rows of the matrix might correspond e.g. to binding regions (with ChIP-Seq) or peptide sequences (with quantitative mass spectrometry). We will list method for obtaining count matrices in sections below.
The values in the matrix should be un-normalized counts or estimated counts of sequencing reads (for single-end RNA-seq) or fragments (for paired-end RNA-seq). The RNA-seq workflow describes multiple techniques for preparing such count matrices. It is important to provide count matrices as input for DESeq2’s statistical model (Love, Huber, and Anders 2014) to hold, as only the count values allow assessing the measurement precision correctly. The DESeq2 model internally corrects for library size, so transformed or normalized values such as counts scaled by library size should not be used as input.
The DESeqDataSet
The object class used by the DESeq2 package to store the read counts
and the intermediate estimated quantities during statistical analysis is
the DESeqDataSet, which will usually be represented in the code
here as an object dds.
A technical detail is that the DESeqDataSet class extends the RangedSummarizedExperiment class of the SummarizedExperiment package. The “Ranged” part refers to the fact that the rows of the assay data (here, the counts) can be associated with genomic ranges (the exons of genes). This association facilitates downstream exploration of results, making use of other Bioconductor packages’ range-based functionality (e.g. find the closest ChIP-seq peaks to the differentially expressed genes).
A DESeqDataSet object must have an associated design formula. The design formula expresses the variables which will be used in modeling. The formula should be a tilde (~) followed by the variables with plus signs between them (it will be coerced into an formula if it is not already). The design can be changed later, however then all differential analysis steps should be repeated, as the design formula is used to estimate the dispersions and to estimate the log2 fold changes of the model.
Note: In order to benefit from the default settings of the package, you should put the variable of interest at the end of the formula and make sure the control level is the first level.
We will now show 4 ways of constructing a DESeqDataSet, depending on what pipeline was used upstream of DESeq2 to generated counts or estimated counts:
- From transcript abundance files and tximport
- From a count matrix
- From htseq-count files
- From a SummarizedExperiment object
Transcript abundance files and tximport / tximeta
Our recommended pipeline for DESeq2 is to use fast transcript abundance quantifiers upstream of DESeq2, and then to create gene-level count matrices for use with DESeq2 by importing the quantification data using tximport (Soneson, Love, and Robinson 2015). This workflow allows users to import transcript abundance estimates from a variety of external software, including the following methods:
- Salmon (Patro et al. 2017)
- Sailfish (Patro, Mount, and Kingsford 2014)
- kallisto (Bray et al. 2016)
- RSEM (Li and Dewey 2011)
Some advantages of using the above methods for transcript abundance estimation are: (i) this approach corrects for potential changes in gene length across samples (e.g. from differential isoform usage) (Trapnell et al. 2013), (ii) some of these methods (Salmon, Sailfish, kallisto) are substantially faster and require less memory and disk usage compared to alignment-based methods that require creation and storage of BAM files, and (iii) it is possible to avoid discarding those fragments that can align to multiple genes with homologous sequence, thus increasing sensitivity (Robert and Watson 2015).
Full details on the motivation and methods for importing transcript level abundance and count estimates, summarizing to gene-level count matrices and producing an offset which corrects for potential changes in average transcript length across samples are described in (Soneson, Love, and Robinson 2015). Note that the tximport-to-DESeq2 approach uses estimated gene counts from the transcript abundance quantifiers, but not normalized counts.
A tutorial on how to use the Salmon software for quantifying
transcript abundance can be found here.
We recommend using the --gcBias flag
which estimates a correction factor for systematic biases commonly
present in RNA-seq data (Love, Hogenesch, and
Irizarry 2016; Patro et al. 2017), unless you are certain that
your data do not contain such bias.
Here, we demonstrate how to import transcript abundances and
construct a gene-level DESeqDataSet object from Salmon
quant.sf files, which are stored in the tximportData
package. You do not need the tximportData package for your
analysis, it is only used here for demonstration.
Note that, instead of locating dir using
system.file, a user would typically just provide a path,
e.g. /path/to/quant/files. For a typical use, the
condition information should already be present as a column
of the sample table samples, while here we construct
artificial condition labels for demonstration.
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 BNext we specify the path to the files using the appropriate columns
of samples, and we read in a table that links transcripts
to genes for this dataset.
files <- file.path(dir,"salmon", samples$run, "quant.sf.gz")
names(files) <- samples$run
tx2gene <- read_csv(file.path(dir, "tx2gene.gencode.v27.csv"))We import the necessary quantification data for DESeq2 using the
tximport function. For further details on use of
tximport, including the construction of the
tx2gene table for linking transcripts to genes in your
dataset, please refer to the tximport package
vignette.
Finally, we can construct a DESeqDataSet from the
txi object and sample information in
samples.
The ddsTxi object here can then be used as
dds in the following analysis steps.
Tximeta for import with automatic metadata
Another Bioconductor package, tximeta (Love et al. 2020), extends tximport,
offering the same functionality, plus the additional benefit of
automatic addition of annotation metadata for commonly used
transcriptomes (GENCODE, Ensembl, RefSeq for human and mouse). See the
tximeta package
vignette for more details. tximeta produces a
SummarizedExperiment that can be loaded easily into
DESeq2 using the DESeqDataSet function, with an
example in the tximeta package vignette, and below:
The ddsTxi object here can then be used as
dds in the following analysis steps. If tximeta
recognized the reference transcriptome as one of those with a
pre-computed hashed checksum, the rowRanges of the
dds object will be pre-populated. Again, see the
tximeta vignette for full details.
Count matrix input
Alternatively, the function DESeqDataSetFromMatrix can be used if you already have a matrix of read counts prepared from another source. Another method for quickly producing count matrices from alignment files is the featureCounts function (Liao, Smyth, and Shi 2013) in the Rsubread package. To use DESeqDataSetFromMatrix, the user should provide the counts matrix, the information about the samples (the columns of the count matrix) as a DataFrame or data.frame, and the design formula.
To demonstrate the use of DESeqDataSetFromMatrix, we will
read in count data from the pasilla package. We
read in a count matrix, which we will name cts, and the
sample information table, which we will name coldata.
Further below we describe how to extract these objects from,
e.g. featureCounts output.
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)We examine the count matrix and column data to see if they are consistent in terms of sample order.
## 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## 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-endNote that these are not in the same order with respect to samples!
It is absolutely critical that the columns of the count matrix and the rows of the column data (information about samples) are in the same order. DESeq2 will not make guesses as to which column of the count matrix belongs to which row of the column data, these must be provided to DESeq2 already in consistent order.
As they are not in the correct order as given, we need to re-arrange
one or the other so that they are consistent in terms of sample order
(if we do not, later functions would produce an error). We additionally
need to chop off the "fb" of the row names of
coldata, so the naming is consistent.
## [1] TRUE## [1] FALSE## [1] TRUEIf you have used the featureCounts function (Liao, Smyth, and Shi 2013) in the Rsubread package,
the matrix of read counts can be directly provided from the
"counts" element in the list output. The count matrix and
column data can typically be read into R from flat files using base R
functions such as read.csv or read.delim. For
htseq-count files, see the dedicated input function below.
With the count matrix, cts, and the sample information,
coldata, we can construct a DESeqDataSet:
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 typeIf you have additional feature data, it can be added to the
DESeqDataSet by adding to the metadata columns of a newly
constructed object. (Here we add redundant data just for demonstration,
as the gene names are already the rownames of the dds.)
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 FBgn0261575htseq-count input
You can use the function DESeqDataSetFromHTSeqCount if you have used htseq-count from the HTSeq python package (Anders, Pyl, and Huber 2014). For an example of using the python scripts, see the pasilla data package. First you will want to specify a variable which points to the directory in which the htseq-count output files are located.
However, for demonstration purposes only, the following line of code points to the directory for the demo htseq-count output files packages for the pasilla package.
We specify which files to read in using list.files, and
select those files which contain the string "treated" using
grep. The sub function is used to chop up the sample
filename to obtain the condition status, or you might alternatively read
in a phenotypic table using read.table.
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)Then we build the DESeqDataSet using the following function:
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): conditionSummarizedExperiment input
If one has already created or obtained a
SummarizedExperiment, it can be easily input into DESeq2 as
follows. First we load the package containing the airway
dataset.
The constructor function below shows the generation of a
DESeqDataSet from a RangedSummarizedExperiment
se.
## 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 BioSamplePre-filtering
While it is not necessary to pre-filter low count genes before
running the DESeq2 functions, there are two reasons which make
pre-filtering useful: by removing rows in which there are very few
reads, we reduce the memory size of the dds data object,
and we increase the speed of count modeling within DESeq2. It can also
improve visualizations, as features with no information for differential
expression are not plotted in dispersion plots or MA-plots.
Here we perform pre-filtering to keep only rows that have a count of
at least 10 for a minimal number of samples. The count of 10 is a
reasonable choice for bulk RNA-seq. A recommendation for the minimal
number of samples is to specify the smallest group size, e.g. here there
are 3 treated samples. If there are not discrete groups, one can use the
minimal number of samples where non-zero counts would be considered
interesting. One can also omit this step entirely and just rely on the
independent filtering procedures available in results(),
either IHW or genefilter. See independent filtering section.
Note on factor levels
By default, R will choose a reference level for factors
based on alphabetical order. Then, if you never tell the DESeq2
functions which level you want to compare against (e.g. which level
represents the control group), the comparisons will be based on the
alphabetical order of the levels. There are two solutions: you can
either explicitly tell results which comparison to make using
the contrast argument (this will be shown later), or you
can explicitly set the factors levels. In order to see the change of
reference levels reflected in the results names, you need to either run
DESeq or nbinomWaldTest/nbinomLRT
after the re-leveling operation. Setting the factor levels can be done
in two ways, either using factor:
…or using relevel, just specifying the reference level:
If you need to subset the columns of a DESeqDataSet, i.e., when removing certain samples from the analysis, it is possible that all the samples for one or more levels of a variable in the design formula would be removed. In this case, the droplevels function can be used to remove those levels which do not have samples in the current DESeqDataSet:
Collapsing technical replicates
DESeq2 provides a function collapseReplicates which can assist in combining the counts from technical replicates into single columns of the count matrix. The term technical replicate implies multiple sequencing runs of the same library. You should not collapse biological replicates using this function. See the manual page for an example of the use of collapseReplicates.
About the pasilla dataset
We continue with the pasilla data constructed from the count matrix method above. This data set is from an experiment on Drosophila melanogaster cell cultures and investigated the effect of RNAi knock-down of the splicing factor pasilla (Brooks et al. 2011). The detailed transcript of the production of the pasilla data is provided in the vignette of the data package pasilla.
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).
## 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 0.986726Note 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.
Log fold change shrinkage for visualization and ranking
Shrinkage of effect size (LFC estimates) is useful for visualization
and ranking of genes. To shrink the LFC, we pass the dds
object to the function lfcShrink. Below we specify to use
the apeglm method for effect size shrinkage (Zhu, Ibrahim, and Love 2018), which improves on
the previous estimator.
We provide the dds object and the name or number of the
coefficient we want to shrink, where the number refers to the order of
the coefficient as it appears in resultsNames(dds).
## [1] "Intercept" "condition_treated_vs_untreated"## 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 0.986726Shrinkage estimation is discussed more in a later section.
Speed-up and parallelization thoughts
The above steps should take less than 30 seconds for most analyses.
For experiments with complex designs and many samples (e.g. dozens of
coefficients, ~100s of samples), one may want to have faster computation
than provided by the default run of DESeq. We have two
recommendations:
By using the argument
fitType="glmGamPoi", one can leverage the faster NB GLM engine written by Constantin Ahlmann-Eltze. Note that glmGamPoi’s interface in DESeq2 requires use oftest="LRT"and specification of areduceddesign.One can take advantage of parallelized computation. Parallelizing
DESeq,results, andlfcShrinkcan be easily accomplished by loading the BiocParallel package, and then setting the following arguments:parallel=TRUEandBPPARAM=MulticoreParam(4), for example, splitting the job over 4 cores. However, some words of advice on parallelization: first, it is recommend to filter genes where all samples have low counts, to avoid sending data unnecessarily to child processes, when those genes have low power and will be independently filtered anyway; secondly, there is often diminishing returns for adding more cores due to overhead of sending data to child processes, therefore I recommend first starting with small number of additional cores. Note that obtainingresultsfor coefficients or contrasts listed inresultsNames(dds)is fast and will not need parallelization. As an alternative toBPPARAM, one canregistercores at the beginning of an analysis, and then just specifyparallel=TRUEto the functions when called.
p-values and adjusted p-values
We can order our results table by the smallest p value:
We can summarize some basic tallies using the summary function.
##
## 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 ?resultsHow many adjusted p-values were less than 0.1?
## [1] 1069The results function contains a number of arguments to
customize the results table which is generated. You can read about these
arguments by looking up ?results. Note that the
results function automatically performs independent filtering
based on the mean of normalized counts for each gene, optimizing the
number of genes which will have an adjusted p value below a
given FDR cutoff, alpha. Independent filtering is further
discussed below. By default the argument
alpha is set to \(0.1\).
If the adjusted p value cutoff will be a value other than \(0.1\), alpha should be set to
that value:
##
## 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## [1] 853Independent hypothesis weighting
A generalization of the idea of p value filtering is to weight hypotheses to optimize power. A Bioconductor package, IHW, is available that implements the method of Independent Hypothesis Weighting (Ignatiadis et al. 2016). Here we show the use of IHW for p value adjustment of DESeq2 results. For more details, please see the vignette of the IHW package. The IHW result object is stored in the metadata.
Note: If the results of independent hypothesis weighting are used in published research, please cite:
Ignatiadis, N., Klaus, B., Zaugg, J.B., Huber, W. (2016) Data-driven hypothesis weighting increases detection power in genome-scale multiple testing. Nature Methods, 13:7. 10.1038/nmeth.3885
# (unevaluated code chunk)
library("IHW")
resIHW <- results(dds, filterFun=ihw)
summary(resIHW)
sum(resIHW$padj < 0.1, na.rm=TRUE)
metadata(resIHW)$ihwResultFor advanced users, note that all the values calculated by the DESeq2 package are stored in the DESeqDataSet object or the DESeqResults object, and access to these values is discussed below.
Exploring and exporting results
MA-plot
In DESeq2, the function plotMA shows the log2 fold changes attributable to a given variable over the mean of normalized counts for all the samples in the DESeqDataSet. Points will be colored blue if the adjusted p value is less than 0.1. Points which fall out of the window are plotted as open triangles pointing either up or down.
It is more useful to visualize the MA-plot for the shrunken log2 fold changes, which remove the noise associated with log2 fold changes from low count genes without requiring arbitrary filtering thresholds.
After calling plotMA, one can use the function identify to interactively detect the row number of individual genes by clicking on the plot. One can then recover the gene identifiers by saving the resulting indices:
Alternative shrinkage estimators
The moderated log fold changes proposed by Love, Huber, and Anders (2014) use a normal
prior distribution, centered on zero and with a scale that is fit to the
data. The shrunken log fold changes are useful for ranking and
visualization, without the need for arbitrary filters on low count
genes. The normal prior can sometimes produce too strong of shrinkage
for certain datasets. In DESeq2 version 1.18, we include two additional
adaptive shrinkage estimators, available via the type
argument of lfcShrink. For more details, see
?lfcShrink
The options for type are:
apeglmis the adaptive t prior shrinkage estimator from the apeglm package (Zhu, Ibrahim, and Love 2018). As of version 1.28.0, it is the default estimator.ashris the adaptive shrinkage estimator from the ashr package (Stephens 2016). Here DESeq2 uses the ashr option to fit a mixture of Normal distributions to form the prior, withmethod="shrinkage".normalis the the original DESeq2 shrinkage estimator, an adaptive Normal distribution as prior.
If the shrinkage estimator apeglm is used in published
research, please cite:
Zhu, A., Ibrahim, J.G., Love, M.I. (2018) Heavy-tailed prior distributions for sequence count data: removing the noise and preserving large differences. Bioinformatics. 10.1093/bioinformatics/bty895
If the shrinkage estimator ashr is used in published
research, please cite:
Stephens, M. (2016) False discovery rates: a new deal. Biostatistics, 18:2. 10.1093/biostatistics/kxw041
In the LFC shrinkage code above, we specified
coef="condition_treated_vs_untreated". We can also just
specify the coefficient by the order that it appears in
resultsNames(dds), in this case coef=2. For
more details explaining how the shrinkage estimators differ, and what
kinds of designs, contrasts and output is provided by each, see the extended section on shrinkage estimators.
## [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")
Note: We have sped up the apeglm method
so it takes roughly about the same amount of time as
normal, e.g. ~5 seconds for the pasilla
dataset of ~10,000 genes and 7 samples. If fast shrinkage estimation of
LFC is needed, but the posterior standard deviation is not
needed, setting apeMethod="nbinomC" will produce a
~10x speedup, but the lfcSE column will be returned with
NA. A variant of this fast method,
apeMethod="nbinomC*" includes random starts.
Note: If there is unwanted variation present in the
data (e.g. batch effects) it is always recommend to correct for this,
which can be accommodated in DESeq2 by including in the design any known
batch variables or by using functions/packages such as
svaseq in sva (Leek 2014) or the RUV functions in
RUVSeq (Risso et al. 2014) to estimate variables that
capture the unwanted variation. In addition, the ashr developers have a
specific method for
accounting for unwanted variation in combination with ashr (Gerard and Stephens 2017).
Plot counts
It can also be useful to examine the counts of reads for a single
gene across the groups. A simple function for making this plot is
plotCounts, which normalizes counts by the estimated size
factors (or normalization factors if these were used) and adds a
pseudocount of 1/2 to allow for log scale plotting. The counts are
grouped by the variables in intgroup, where more than one
variable can be specified. Here we specify the gene which had the
smallest p value from the results table created above. You can
select the gene to plot by rowname or by numeric index.
For customized plotting, an argument returnData
specifies that the function should only return a data.frame for
plotting with ggplot.
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))
More information on results columns
Information about which variables and tests were used can be found by calling the function mcols on the results object.
## [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"For a particular gene, a log2 fold change of -1 for
condition treated vs untreated means that the treatment
induces a multiplicative change in observed gene expression level of
\(2^{-1} = 0.5\) compared to the
untreated condition. If the variable of interest is continuous-valued,
then the reported log2 fold change is per unit of change of that
variable.
Note on p-values set to NA: some values in the
results table can be set to NA for one of the following
reasons:
- If within a row, all samples have zero counts, the
baseMeancolumn will be zero, and the log2 fold change estimates, p value and adjusted p value will all be set toNA. - If a row contains a sample with an extreme count outlier then the
p value and adjusted p value will be set to
NA. These outlier counts are detected by Cook’s distance. Customization of this outlier filtering and description of functionality for replacement of outlier counts and refitting is described below - If a row is filtered by automatic independent filtering, for having
a low mean normalized count, then only the adjusted p value
will be set to
NA. Description and customization of independent filtering is described below
Rich visualization and reporting of results
regionReport An HTML and PDF summary of the results with plots can also be generated using the regionReport package. The DESeq2Report function should be run on a DESeqDataSet that has been processed by the DESeq function. For more details see the manual page for DESeq2Report and an example vignette in the regionReport package.
Glimma Interactive visualization of DESeq2 output, including MA-plots (also called MD-plots) can be generated using the Glimma package. See the manual page for glMDPlot.DESeqResults.
pcaExplorer Interactive visualization of DESeq2 output, including PCA plots, boxplots of counts and other useful summaries can be generated using the pcaExplorer package. See the Launching the application section of the package vignette.
iSEE Provides functions for creating an interactive Shiny-based graphical user interface for exploring data stored in SummarizedExperiment objects, including row- and column-level metadata. Particular attention is given to single-cell data in a SingleCellExperiment object with visualization of dimensionality reduction results. iSEE is on Bioconductor. An example wrapper function for converting a DESeqDataSet to a SingleCellExperiment object for use with iSEE can be found at the following gist, written by Federico Marini:
The iSEEde package provides additional panels that facilitate the interactive visualisation of differential expression results in iSEE applications.
DEvis DEvis is a powerful, integrated solution for the analysis of differential expression data. This package includes an array of tools for manipulating and aggregating data, as well as a wide range of customizable visualizations, and project management functionality that simplify RNA-Seq analysis and provide a variety of ways of exploring and analyzing data. DEvis can be found on CRAN and GitHub.
Exporting results to CSV files
A plain-text file of the results can be exported using the base R functions write.csv or write.delim. We suggest using a descriptive file name indicating the variable and levels which were tested.
Exporting only the results which pass an adjusted p value threshold can be accomplished with the subset function, followed by the write.csv function.
## 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 5.13139e-117
## FBgn0029167 3709.741 -2.19491 0.0957474 -22.9240 2.68013e-116
## FBgn0003360 4344.597 -3.17683 0.1416166 -22.4326 1.89322e-111
## FBgn0035085 638.757 -2.55819 0.1359972 -18.8106 6.18406e-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 9.25983e-165
## FBgn0025111 2.09053e-113
## FBgn0029167 7.27922e-113
## FBgn0003360 3.85649e-108
## FBgn0035085 1.00775e-75
## ... ...
## FBgn0003890 0.0991143
## FBgn0010053 0.0991176
## FBgn0034997 0.0993210
## FBgn0004359 0.0993659
## FBgn0027604 0.0993659Multi-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:
## 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 0.750728We create a copy of the DESeqDataSet, so that we can rerun the analysis using a multi-factor design.
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.
## [1] "paired-end" "single-read"## [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:
Again, we access the results using the results function.
## 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 0.691941It 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
## 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 0.969866If 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).
Data transformations and visualization
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:
\[ y = \log_2(n + n_0) \]
where n represents the count values and \(n_0\) is a positive constant.
In this section, we discuss two alternative approaches that offer more theoretical justification and a rational way of choosing parameters equivalent to \(n_0\) 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).
Blind dispersion estimation
The two functions, vst and rlog have an argument
blind, for whether the transformation should be blind to
the sample information specified by the design formula. When
blind equals TRUE (the default), the functions
will re-estimate the dispersions using only an intercept. This setting
should be used in order to compare samples in a manner wholly unbiased
by the information about experimental groups, for example to perform
sample QA (quality assurance) as demonstrated below.
However, blind dispersion estimation is not the appropriate choice if
one expects that many or the majority of genes (rows) will have large
differences in counts which are explainable by the experimental design,
and one wishes to transform the data for downstream analysis. In this
case, using blind dispersion estimation will lead to large estimates of
dispersion, as it attributes differences due to experimental design as
unwanted noise, and will result in overly shrinking the
transformed values towards each other. By setting blind to
FALSE, the dispersions already estimated will be used to
perform transformations, or if not present, they will be estimated using
the current design formula. Note that only the fitted dispersion
estimates from mean-dispersion trend line are used in the transformation
(the global dependence of dispersion on mean for the entire experiment).
So setting blind to FALSE is still for the
most part not using the information about which samples were in which
experimental group in applying the transformation.
Extracting transformed values
These transformation functions return an object of class
DESeqTransform which is a subclass of
RangedSummarizedExperiment. For ~20 samples, running on a newly
created DESeqDataSet, rlog may take 30 seconds,
while vst takes less than 1 second. The running times are
shorter when using blind=FALSE and if the function
DESeq has already been run, because then it is not necessary to
re-estimate the dispersion values. The assay function is used
to extract the matrix of normalized values.
## 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 9.142848Variance stabilizing transformation
Above, we used a parametric fit for the dispersion. In this case, the
closed-form expression for the variance stabilizing transformation is
used by the vst function. If a local fit is used (option
fitType="locfit" to estimateDispersions) a
numerical integration is used instead. The transformed data should be
approximated variance stabilized and also includes correction for size
factors or normalization factors. The transformed data is on the log2
scale for large counts.
Regularized log transformation
The function rlog, stands for regularized log, transforming the original count data to the log2 scale by fitting a model with a term for each sample and a prior distribution on the coefficients which is estimated from the data. This is the same kind of shrinkage (sometimes referred to as regularization, or moderation) of log fold changes used by DESeq and nbinomWaldTest. The resulting data contains elements defined as:
\[ \log_2(q_{ij}) = \beta_{i0} + \beta_{ij} \]
where \(q_{ij}\) is a parameter proportional to the expected true concentration of fragments for gene i and sample j (see formula below), \(\beta_{i0}\) is an intercept which does not undergo shrinkage, and \(\beta_{ij}\) is the sample-specific effect which is shrunk toward zero based on the dispersion-mean trend over the entire dataset. The trend typically captures high dispersions for low counts, and therefore these genes exhibit higher shrinkage from the rlog.
Note that, as \(q_{ij}\) represents the part of the mean value \(\mu_{ij}\) after the size factor \(s_j\) has been divided out, it is clear that the rlog transformation inherently accounts for differences in sequencing depth. Without priors, this design matrix would lead to a non-unique solution, however the addition of a prior on non-intercept betas allows for a unique solution to be found.
Effects of transformations on the variance
The figure below plots the standard deviation of the transformed data, across samples, against the mean, using the shifted logarithm transformation, the regularized log transformation and the variance stabilizing transformation. The shifted logarithm has elevated standard deviation in the lower count range, and the regularized log to a lesser extent, while for the variance stabilized data the standard deviation is roughly constant along the whole dynamic range.
Note that the vertical axis in such plots is the square root of the variance over all samples, so including the variance due to the experimental conditions. While a flat curve of the square root of variance over the mean may seem like the goal of such transformations, this may be unreasonable in the case of datasets with many true differences due to the experimental conditions.
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.
Heatmap of the count matrix
To explore a count matrix, it is often instructive to look at it as a heatmap. Below we show how to produce such a heatmap for various transformations of the data.
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)
Heatmap of the sample-to-sample distances
Another use of the transformed data is sample clustering. Here, we apply the dist function to the transpose of the transformed count matrix to get sample-to-sample distances.
A heatmap of this distance matrix gives us an overview over
similarities and dissimilarities between samples. We have to provide a
hierarchical clustering hc to the heatmap function based on
the sample distances, or else the heatmap function would calculate a
clustering based on the distances between the rows/columns of the
distance matrix.
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)
Principal component plot of the samples
Related to the distance matrix is the PCA plot, which shows the samples in the 2D plane spanned by their first two principal components. This type of plot is useful for visualizing the overall effect of experimental covariates and batch effects.
It is also possible to customize the PCA plot using the ggplot function.
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()
Variations to the standard workflow
Wald test individual steps
The function DESeq runs the following functions in order:
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:
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:
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:
If the full design contained other variables, such as a batch
variable, e.g. ~batch + condition then the likelihood ratio
test would look like:
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):
| method: | apeglm1 |
ashr2 |
normal3 |
|---|---|---|---|
| Good for ranking by LFC | ✓ | ✓ | ✓ |
| Preserves size of large LFC | ✓ | ✓ | |
| Can compute s-values (Stephens 2016) | ✓ | ✓ | |
Allows use of coef |
✓ | ✓ | ✓ |
Allows use of lfcThreshold |
✓ | ✓ | ✓ |
Allows use of contrast |
✓ | ✓ | |
| Can shrink interaction terms | ✓ | ✓ |
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:
## (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
DESeqarguments to these values:useT=TRUE,minmu=1e-6, andminReplicatesForReplace=Inf. The default setting ofminmuwas 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
sizeFactorsfromscran::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):
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.
Local or mean dispersion fit
A local smoothed dispersion fit is automatically substitited in the
case that the parametric curve doesn’t fit the observed dispersion mean
relationship. This can be prespecified by providing the argument
fitType="local" to either DESeq or
estimateDispersions. Additionally, using the mean of gene-wise
disperion estimates as the fitted value can be specified by providing
the argument fitType="mean".
Supply a custom dispersion fit
Any fitted values can be provided during dispersion estimation, using
the lower-level functions described in the manual page for
estimateDispersionsGeneEst. In the code chunk below, we store
the gene-wise estimates which were already calculated and saved in the
metadata column dispGeneEst. Then we calculate the median
value of the dispersion estimates above a threshold, and save these
values as the fitted dispersions, using the replacement function for
dispersionFunction. In the last line, the function
estimateDispersionsMAP, uses the fitted dispersions to generate
maximum a posteriori (MAP) estimates of dispersion.
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 \(\alpha\)). 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:
## [1] 0.1## 0%
## 5.109586plot(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 8148Tests 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 \(\beta\) is the log2 fold change specified
by the name argument, and \(x\) is the lfcThreshold.
greaterAbs- \(|\beta| > x\) - tests are two-tailedlessAbs- \(|\beta| < x\) - p values are the maximum of the upper and lower testsgreater- \(\beta > x\)less- \(\beta < -x\)
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.
## 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## [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"## 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 \(\mu_{ij} = s_j q_{ij}\) and the Cook’s distances for each gene and sample are stored as matrices in the assays slot:
## 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## treated1 treated2 treated3 untreated1 untreated2
## FBgn0000008 0.08564565 0.297964299 0.077021521 0.10556148 0.0135846198
## 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 0.0859061169
## untreated3 untreated4
## FBgn0000008 0.19761575 0.0004998745
## FBgn0000017 0.18275047 0.0548693390
## FBgn0000018 0.07090752 0.0104402584
## FBgn0000024 0.02968291 0.0809265573
## FBgn0000032 0.02151283 0.0764805449
## FBgn0000037 0.02257542 0.2489127110The dispersions \(\alpha_i\) can be accessed with the dispersions function.
## [1] 0.03082228 0.01305447 0.01518649 0.23983770 0.01654718 0.12963629## [1] 0.03082228 0.01305447 0.01518649 0.23983770 0.01654718 0.12963629The size factors \(s_j\) are accessible via sizeFactors:
## treated1 treated2 treated3 untreated1 untreated2 untreated3 untreated4
## 1.6297067 0.7611622 0.8303119 1.1439041 1.7912811 0.6459940 0.7507275For advanced users, we also include a convenience function
coef for extracting the matrix \([\beta_{ir}]\) 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.
## 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 0.46606939The beta prior variance \(\sigma_r^2\) is stored as an attribute of the DESeqDataSet:
## [1] 1e+06 1e+06General 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.
## $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## $type
## [1] "normal"
##
## $package
## [1] "DESeq2"
##
## $version
## [1] '1.47.1'
##
## $betaPriorVar
## Intercept conditiontreated
## 1.000000e+06 1.049206e-01## $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 0.128392406
## [7] 0.000000000 0.452702361 0.057818455 0.000000000 0.176425328 0.000000000
## [13] 0.120967208 0.027145716 0.005428328 0.018807790 0.012312407 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 22The dispersion prior variance \(\sigma_d^2\) is stored as an attribute of the dispersion function:
## function (q)
## coefs[1] + coefs[2]/q
## <bytecode: 0x589d35e1c460>
## <environment: 0x589d35e1cab8>
## attr(,"coefficients")
## asymptDisp extraPois
## 0.01377513 2.88413302
## attr(,"fitType")
## [1] "parametric"
## attr(,"varLogDispEsts")
## [1] 1.025797
## attr(,"dispPriorVar")
## [1] 0.5354389## [1] 0.5354389The version of DESeq2 which was used to construct the DESeqDataSet object, or the version used when DESeq was run, is stored here:
## [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 \(\mu_{ij}\) becomes:
\[ \mu_{ij} = NF_{ij} q_{ij} \]
with normalization factor matrix NF having the same dimensions as the counts matrix K. This matrix can be incorporated as shown below. We recommend providing a matrix with 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) <- normFactorsThese 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:
“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:
Linear combinations
The simplest case is the linear combination, or linear dependency
problem, when two variables contain exactly the same information, such
as in the following sample table. The software cannot fit an effect for
batch and condition, because they produce
identical columns in the model matrix. This is also referred to as
perfect confounding. A unique solution of coefficients (the
\(\beta_i\) in the formula below) is not possible.
## DataFrame with 4 rows and 2 columns
## batch condition
## <factor> <factor>
## 1 1 A
## 2 1 A
## 3 2 B
## 4 2 BAnother situation which will cause problems is when the variables are not identical, but one variable can be formed by the combination of other factor levels. In the following example, the effect of batch 2 vs 1 cannot be fit because it is identical to a column in the model matrix which represents the condition C vs A effect.
## 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 CIn both of these cases above, the batch effect cannot be fit and must be removed from the model formula. There is just no way to tell apart the condition effects and the batch effects. The options are either to assume there is no batch effect (which we know is highly unlikely given the literature on batch effects in sequencing datasets) or to repeat the experiment and properly balance the conditions across batches. A balanced design would look like:
## 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 CGroup-specific condition effects, individuals nested within groups
Finally, there is a case where we can in fact perform inference, but we may need to re-arrange terms to do so. Consider an experiment with grouped individuals, where we seek to test the group-specific effect of a condition or treatment, while controlling for individual effects. The individuals are nested within the groups: an individual can only be in one of the groups, although each individual has one or more observations across condition.
An example of such an experiment is below:
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 BNote that individual (ind) is a factor not a
numeric. This is very important.
To make R display all the rows, we can do:
## 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 BWe have two groups of samples X and Y, each with three distinct individuals (labeled here 1-6). For each individual, we have conditions A and B (for example, this could be control and treated).
This design can be analyzed by DESeq2 but requires a bit of
refactoring in order to fit the model terms. Here we will use a trick
described in the edgeR user guide, from
the section Comparisons Both Between and Within Subjects. If we
try to analyze with a formula such as, ~ ind + grp*cnd, we
will obtain an error, because the effect for group is a linear
combination of the individuals.
However, the following steps allow for an analysis of group-specific
condition effects, while controlling for differences in individual. For
object construction, you can use a simple design, such as
~ ind + cnd, as long as you remember to replace it before
running DESeq. Then add a column ind.n which
distinguishes the individuals nested within a group. Here, we add this
column to coldata, but in practice you would add this column to
dds.
## 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 3Now we can reassign our DESeqDataSet a design of
~ grp + grp:ind.n + grp:cnd, before we call DESeq.
This new design will result in the following model matrix:
## (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"Note that, if you have unbalanced numbers of individuals in the two
groups, you will have zeros for some of the interactions between
grp and ind.n. You can remove these columns
manually from the model matrix and pass the corrected model matrix to
the full argument of the DESeq function. See
example code in the next section. Note that, in this case, you will not
be able to create the DESeqDataSet with the design that leads
to less than full rank model matrix. You can either use
design=~1 when creating the dataset object, or you can
provide the corrected model matrix to the design slot of
the dataset from the start.
Above, the terms grpX.cndB and grpY.cndB
give the group-specific condition effects, in other words, the condition
B vs A effect for group X samples, and likewise for group Y samples.
These terms control for all of the six individual effects. These
group-specific condition effects can be extracted using results
with the name argument.
Furthermore, grpX.cndB and grpY.cndB can be
contrasted using the contrast argument, in order to test if
the condition effect is different across group:
Levels without samples
The base R function for creating model matrices will produce a column of zeros if a level is missing from a factor or a combination of levels is missing from an interaction of factors. The solution to the first case is to call droplevels on the column, which will remove levels without samples. This was shown in the beginning of this vignette.
The second case is also solvable, by manually editing the model matrix, and then providing this to DESeq. Here we construct an example dataset to illustrate:
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 BNote that if we try to estimate all interaction terms, we introduce a column with all zeros, as there are no condition C samples for group 3. (Here, unname is used to display the matrix concisely.)
## [1] "(Intercept)" "conditionB" "conditionC"
## [4] "group2" "group3" "conditionB:group2"
## [7] "conditionC:group2" "conditionB:group3" "conditionC:group3"## [,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"## (Intercept) conditionB conditionC group2
## FALSE FALSE FALSE FALSE
## group3 conditionB:group2 conditionC:group2 conditionB:group3
## FALSE FALSE FALSE FALSE
## conditionC:group3
## TRUEWe can remove this column like so:
## [,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 1Now this matrix m1 can be provided to the
full argument of DESeq. For a likelihood ratio
test of interactions, a model matrix using a reduced design such as
~ condition + group can be given to the
reduced argument. Wald tests can also be generated instead
of the likelihood ratio test, but for user-supplied model matrices, the
argument betaPrior must be set to FALSE.
Theory behind DESeq2
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:
\[ K_{ij} \sim \textrm{NB}(\mu_{ij}, \alpha_i) \]
\[ \mu_{ij} = s_j q_{ij} \]
\[ \log_2(q_{ij}) = x_{j.} \beta_i \]
where counts \(K_{ij}\) for gene i, sample j are modeled using a negative binomial distribution with fitted mean \(\mu_{ij}\) and a gene-specific dispersion parameter \(\alpha_i\). The fitted mean is composed of a sample-specific size factor \(s_j\) and a parameter \(q_{ij}\) proportional to the expected true concentration of fragments for sample j. The coefficients \(\beta_i\) 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 \(\alpha_i\) 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.
\[ \textrm{Var}(K_{ij}) = E[ (K_{ij} - \mu_{ij})^2 ] = \mu_{ij} + \alpha_i \mu_{ij}^2 \]
An option in DESeq2 is to provide maximum a posteriori
estimates of the log2 fold changes in \(\beta_i\) 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:
- estimation of size factors \(s_j\) by estimateSizeFactors
- estimation of dispersion \(\alpha_i\) by estimateDispersions
- negative binomial GLM fitting for \(\beta_i\) 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
sharingModeoptionsfit-onlyormaximumof 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 functionlfcShrinkallows 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 \(\beta\) is left multiplied by the contrast
vector \(c\) to form the numerator of
the test statistic. The denominator is formed by multiplying the
covariance matrix \(\Sigma\) for the
coefficients on either side by the contrast vector \(c\). The square root of this product is an
estimate of the standard error for the contrast. The contrast statistic
is then compared to a Normal distribution as are the Wald statistics for
the 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
Filtering criteria
The goal of independent filtering is to filter out those tests from the procedure that have no, or little chance of showing significant evidence, without even looking at their test statistic. Typically, this results in increased detection power at the same experiment-wide type I error. Here, we measure experiment-wide type I error in terms of the false discovery rate.
A good choice for a filtering criterion is one that
- is statistically independent from the test statistic under the null hypothesis,
- is correlated with the test statistic under the alternative, and
- does not notably change the dependence structure – if there is any – between the tests that pass the filter, compared to the dependence structure between the tests before filtering.
The benefit from filtering relies on property (2), and we will explore it further below. Its statistical validity relies on property (1) – which is simple to formally prove for many combinations of filter criteria with test statistics – and (3), which is less easy to theoretically imply from first principles, but rarely a problem in practice. We refer to (Bourgon, Gentleman, and Huber 2010) for further discussion of this topic.
A simple filtering criterion readily available in the results object is the mean of normalized counts irrespective of biological condition, and so this is the criterion which is used automatically by the results function to perform independent filtering. Genes with very low counts are not likely to see significant differences typically due to high dispersion. For example, we can plot the \(-\log_{10}\) p values from all genes over the normalized mean counts:
plot(res$baseMean+1, -log10(res$pvalue),
log="x", xlab="mean of normalized counts",
ylab=expression(-log[10](pvalue)),
ylim=c(0,30),
cex=.4, col=rgb(0,0,0,.3))
Why does it work?
Consider the p value histogram below It shows how the filtering ameliorates the multiple testing problem – and thus the severity of a multiple testing adjustment – by removing a background set of hypotheses whose p values are distributed more or less uniformly in [0,1].
use <- res$baseMean > metadata(res)$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")Histogram of p values for all tests. The area shaded in blue indicates the subset of those that pass the filtering, the area in khaki those that do not pass:
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)))
Frequently asked questions
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:
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
Session info
## R Under development (unstable) (2024-10-21 r87258)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.1 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.21-bioc/R/lib/libRblas.so
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB LC_COLLATE=C
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## time zone: America/New_York
## tzcode source: system (glibc)
##
## attached base packages:
## [1] stats4 stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] pheatmap_1.0.12 vsn_3.75.0
## [3] ggplot2_3.5.1 airway_1.27.0
## [5] pasilla_1.35.0 DEXSeq_1.53.0
## [7] RColorBrewer_1.1-3 AnnotationDbi_1.69.0
## [9] BiocParallel_1.41.0 tximeta_1.25.0
## [11] DESeq2_1.47.1 SummarizedExperiment_1.37.0
## [13] Biobase_2.67.0 MatrixGenerics_1.19.0
## [15] matrixStats_1.4.1 GenomicRanges_1.59.0
## [17] GenomeInfoDb_1.43.0 IRanges_2.41.0
## [19] S4Vectors_0.45.1 BiocGenerics_0.53.3
## [21] generics_0.1.3 tximportData_1.35.0
## [23] readr_2.1.5 tximport_1.35.0
##
## loaded via a namespace (and not attached):
## [1] jsonlite_1.8.9 magrittr_2.0.3 GenomicFeatures_1.59.1
## [4] farver_2.1.2 rmarkdown_2.29 BiocIO_1.17.0
## [7] zlibbioc_1.53.0 vctrs_0.6.5 memoise_2.0.1
## [10] Rsamtools_2.23.0 RCurl_1.98-1.16 SQUAREM_2021.1
## [13] mixsqp_0.3-54 htmltools_0.5.8.1 S4Arrays_1.7.1
## [16] progress_1.2.3 AnnotationHub_3.15.0 curl_6.0.1
## [19] truncnorm_1.0-9 SparseArray_1.7.2 sass_0.4.9
## [22] bslib_0.8.0 plyr_1.8.9 httr2_1.0.6
## [25] cachem_1.1.0 GenomicAlignments_1.43.0 lifecycle_1.0.4
## [28] pkgconfig_2.0.3 Matrix_1.7-1 R6_2.5.1
## [31] fastmap_1.2.0 GenomeInfoDbData_1.2.13 numDeriv_2016.8-1.1
## [34] digest_0.6.37 colorspace_2.1-1 irlba_2.3.5.1
## [37] geneplotter_1.85.0 RSQLite_2.3.7 hwriter_1.3.2.1
## [40] labeling_0.4.3 invgamma_1.1 filelock_1.0.3
## [43] fansi_1.0.6 httr_1.4.7 abind_1.4-8
## [46] compiler_4.5.0 withr_3.0.2 bit64_4.5.2
## [49] DBI_1.2.3 hexbin_1.28.5 biomaRt_2.63.0
## [52] MASS_7.3-61 rappdirs_0.3.3 DelayedArray_0.33.1
## [55] rjson_0.2.23 tools_4.5.0 glue_1.8.0
## [58] restfulr_0.0.15 grid_4.5.0 gtable_0.3.6
## [61] tzdb_0.4.0 preprocessCore_1.69.0 ensembldb_2.31.0
## [64] hms_1.1.3 xml2_1.3.6 utf8_1.2.4
## [67] XVector_0.47.0 BiocVersion_3.21.1 pillar_1.9.0
## [70] stringr_1.5.1 limma_3.63.2 emdbook_1.3.13
## [73] vroom_1.6.5 genefilter_1.89.0 splines_4.5.0
## [76] dplyr_1.1.4 BiocFileCache_2.15.0 lattice_0.22-6
## [79] survival_3.7-0 rtracklayer_1.67.0 bit_4.5.0
## [82] annotate_1.85.0 tidyselect_1.2.1 locfit_1.5-9.10
## [85] Biostrings_2.75.1 knitr_1.49 ProtGenerics_1.39.0
## [88] xfun_0.49 statmod_1.5.0 stringi_1.8.4
## [91] UCSC.utils_1.3.0 lazyeval_0.2.2 yaml_2.3.10
## [94] evaluate_1.0.1 codetools_0.2-20 bbmle_1.0.25.1
## [97] archive_1.1.10 tibble_3.2.1 BiocManager_1.30.25
## [100] affyio_1.77.0 cli_3.6.3 xtable_1.8-4
## [103] munsell_0.5.1 jquerylib_0.1.4 Rcpp_1.0.13-1
## [106] dbplyr_2.5.0 coda_0.19-4.1 png_0.1-8
## [109] bdsmatrix_1.3-7 XML_3.99-0.17 parallel_4.5.0
## [112] blob_1.2.4 prettyunits_1.2.0 AnnotationFilter_1.31.0
## [115] bitops_1.0-9 txdbmaker_1.3.0 mvtnorm_1.3-2
## [118] apeglm_1.29.0 affy_1.85.0 scales_1.3.0
## [121] crayon_1.5.3 rlang_1.1.4 ashr_2.2-63
## [124] KEGGREST_1.47.0