- 1 Presentation: RNA-seq work flow
- 2 Lab: Gene-level RNA-seq differential expression
- 2.1 Background
- 2.2 Experimental data
- 2.3 Preparing count matrices
- 2.4 Starting from
`SummarizedExperiment`

- 2.5 From
`SummarizedExperiment`

to`DESeqDataSet`

- 2.6 Differential expression analysis
- 2.7 Diagnostic plots
- 2.8 Independent filtering
- 2.9 Annotation: adding gene names
- 2.10 Exporting results
- 2.11 Session information

- Bioconductor known-gene RNA-seq differential expression work flow, from aligned reads to differential expression of genes. Important statistical issues and their resolution. Placing results of differential expression analysis into biological context. Brief discussion of novel-gene and transcript-level RNAseq differential expression analysis. Primary packages: DESeq2, edgeR.

Resources: Anders, CSAMA, 2015; Love, CSAMA, 2015; Huber, CSAMA, 2015; Pimentel, YouTube, 2015.

Keep it simple

- Classical experimental designs
- Time series
- Without missing values, where possible
- Intended analysis must be feasbile – can the available samples and hypothesis of interest be combined to formulate a testable statistical hypothesis?

Replicate

- Extent of replication determines nuance of biological question.
- No replication (1 sample per treatment): qualitative description with limited statistical options.
- 3-5 replicates per treatment: designed experimental manipulation with cell lines or other well-defined entities; 2-fold (?) change in average expression between groups.
- 10-50 replicates per treatment: population studies, e.g., cancer cell lines.
- 1000’s of replicates: prospective studies, e.g., SNP discovery
- One resource:
*RNASeqPower*

Avoid confounding experimental factors with other factors

- Common problems: samples from one treatment all on the same flow cell; samples from treatment 1 processed first, treatment 2 processed second, etc.

Record co-variates

Be aware of *batch effects*

- Known
- Phenotypic covariates, e.g., age, gender
- Experimental covariates, e.g., lab or date of processing
- Incorporate into linear model, at least approximately

- Unknown
- Or just unexpected / undetected
- Characterize using, e.g.,
*sva*.

- Surrogate variable analysis
- Leek et al., 2010, Nature Reviews Genetics 11 733-739, Leek & Story PLoS Genet 3(9): e161.
- Scientific finding: pervasive batch effects
- Statistical insights: surrogate variable analysis: identify and build surrogate variables; remove known batch effects
- Benefits: reduce dependence, stabilize error rate estimates, and improve reproducibility
*combat*software /*sva**Bioconductor*package

HapMap samples from one facility, ordered by date of processing.

Confounding factors

- Record or avoid

Artifacts of your *particular* protocols

- Sequence contaminants
- Enrichment bias, e.g., non-uniform transcript representation.
- PCR artifacts – adapter contaminants, sequence-specific amplification bias, …

Axes of variation

- Single- versus paired-end
- Length: 50-200nt
- Number of reads per sample

Application-specific, e.g.,

- ChIP-seq: short, single-end reads are usually sufficient
- RNA-seq, known genes: single- or paired-end reads
- RNA-seq, transcripts or novel variants: paired-end reads
- Copy number: single- or paired-end reads
- Structural variants: paired-end reads
- Variants: depth via longer, paired-end reads
- Microbiome: long paired-end reads (overlapping ends)

Alignment strategies

*de novo*- No reference genome; considerable sequencing and computational resources

- Genome
- Established reference genome
- Splice-aware aligners
- Novel transcript discovery

- Transcriptome
- Established reference genome; reliable gene model
- Simple aligners
- Known gene / transcript expression

Splice-aware aligners (and *Bioconductor* wrappers)

- Use known gene model to count aligned reads overlapping regions of interest / gene models
- Gene model can be public (e.g., UCSC, NCBI, ENSEMBL) or
*ad hoc*(gff file) `GenomicAlignments::summarizeOverlaps()`

`Rsubread::featureCount()`

- HTSeq, htseq-count

- tophat uses Bowtie2 to perform basic single- and paired-end alignments, then uses algorithms to place difficult-to-align reads near to their well-aligned mates.
- Cufflinks (doi) takes
*tophat*output and estimate existing and novel transcript abundance. How Cufflinks Works - Cuffdiff assesses statistical significance of estimated abundances between experimental groups
- RSEM includes de novo assembly and quantification

- ‘Next generation’ differential expression tools; transcriptome alignment
- E.g., kallisto takes a radically different approach: from FASTQ to count table without BAM files.
- Very fast, almost as accurate.
- Hints on how it works; arXiv
- Integration with gene-level analyses – Soneson et al.

Unique statistical aspects

- Large data, few samples
- Comparison of each gene, across samples;
*univariate*measures - Each gene is analyzed by the
*same*experimental design, under the*same*null hypothesis

Summarization

Counts

*per se*, rather than a summary (RPKM, FPKM, …), are relevant for analysis- For a given gene, larger counts imply more information; RPKM etc., treat all estimates as equally informative.
- Comparison is across samples at
*each*region of interest; all samples have the same region of interest, so modulo library size there is no need to correct for, e.g., gene length or mapability.

Normalization

- Libraries differ in size (total counted reads per sample) for un-interesting reasons; we need to account for differences in library size in statistical analysis.
- Total number of counted reads per sample is
*not*a good estimate of library size. It is un-necessarily influenced by regions with large counts, and can introduce bias and correlation across genes. Instead, use a robust measure of library size that takes account of skew in the distribution of counts (simplest: trimmed geometric mean; more advanced / appropriate encountered in the lab). - Library size (total number of counted reads) differs between samples, and should be included
*as a statistical offset*in analysis of differential expression, rather than ‘dividing by’ the library size early in an analysis.

Appropriate error model

- Count data is
*not*distributed normally or as a Poisson process, but rather as negative binomial. - Result of a combination Poisson (`shot’ noise, i.e., within-sample technical and sampling variation in read counts) with variation between biological samples.
- A negative binomial model requires estimation of an additional parameter (‘dispersion’), which is estimated poorly in small samples.
- Basic strategy is to moderate per-gene estimates with more robust local estimates derived from genes with similar expression values (a little more on borrowing information is provided below).

Pre-filtering

- Naively, a statistical test (e.g., t-test) could be applied to each row of a counts table. However, we have relatively few samples (10’s) and very many comparisons (10,000’s) so a naive approach is likely to be very underpowered, resulting in a very high
*false discovery rate* - A simple approach is perform fewer tests by removing regions that could not possibly result in statistical significance, regardless of hypothesis under consideration.
- Example: a region with 0 counts in all samples could not possibly be significant regradless of hypothesis, so exclude from further analysis.
- Basic approaches: ‘K over A’-style filter – require a minimum of A (normalized) read counts in at least K samples. Variance filter, e.g., IQR (inter-quartile range) provides a robust estimate of variability; can be used to rank and discard least-varying regions.
- More nuanced approaches:
*edgeR*vignette; work flow today.

Borrowing information

- Why does low statistical power elevate false discovery rate?
- One way of developing intuition is to recognize a t-test (for example) as a ratio of variances. The numerator is treatment-specific, but the denominator is a measure of overall variability.
- Variances are measured with uncertainty; over- or under-estimating the denominator variance has an asymmetric effect on a t-statistic or similar ratio, with an underestimate
*inflating*the statistic more dramatically than an overestimate deflates the statistic. Hence elevated false discovery rate. - Under the null hypothesis used in microarray or RNA-seq experiments, the expected overall variability of a gene is the same, at least for genes with similar average expression
- The strategy is to estimate the denominator variance as the between-group variance for the gene,
*moderated*by the average between-group variance across all genes. - This strategy exploits the fact that the same experimental design has been applied to all genes assayed, and is effective at moderating false discovery rate.

*DESeq2* `estimateSizeFactors()`

, Anders and Huber, 2010

- For each gene: geometric mean of all samples.
- For each sample: median ratio of the sample gene over the geometric mean of all samples
- Functions other than the median can be used; control genes can be used instead

*DESeq2* `estimateDispersions()`

- Estimate per-gene dispersion
- Fit a smoothed relationship between dispersion and abundance

Placing differentially expressed regions in context

- Gene names associated with genomic ranges
- Gene set enrichment and similar analysis
- Proximity to regulatory marks
- Integrate with other analyses, e.g., methylation, copy number, variants, …

Correlation between genomic copy number and mRNA expression identified 38 mis-labeled samples in the TCGA ovarian cancer Affymetrix microarray dataset.

This lab is derived from: RNA-Seq workflow: gene-level exploratory analysis and differential expression, by Michael Love, Simon Anders, Wolfgang Huber; modified by Martin Morgan, October 2015.

This lab will walk you through an end-to-end RNA-Seq differential expression workflow, using DESeq2 along with other *Bioconductor* packages. The complete work flow starts from the FASTQ files, but we will start after reads have been aligned to a reference genome and reads overlapping known genes have been counted. We will perform exploratory data analysis (EDA), differential gene expression analysis with DESeq2, and visually explore the results.

A number of other *Bioconductor* packages are important in statistical inference of differential expression at the gene level, including Rsubread, edgeR, limma, BaySeq, and others.

The data used in this workflow is an RNA-Seq experiment of airway smooth muscle cells treated with dexamethasone, a synthetic glucocorticoid steroid with anti-inflammatory effects. Glucocorticoids are used, for example, in asthma patients to prevent or reduce inflammation of the airways. In the experiment, four primary human airway smooth muscle cell lines were treated with 1 micromolar dexamethasone for 18 hours. For each of the four cell lines, we have a treated and an untreated sample. The reference for the experiment is:

Himes BE, Jiang X, Wagner P, Hu R, Wang Q, Klanderman B, Whitaker RM, Duan Q, Lasky-Su J, Nikolos C, Jester W, Johnson M, Panettieri R Jr, Tantisira KG, Weiss ST, Lu Q. “RNA-Seq Transcriptome Profiling Identifies CRISPLD2 as a Glucocorticoid Responsive Gene that Modulates Cytokine Function in Airway Smooth Muscle Cells.” PLoS One. 2014 Jun 13;9(6):e99625. PMID: 24926665. GEO: GSE52778.

As input, DESeq2 package expects count data as obtained, e.g., from RNA-Seq or another high-throughput sequencing experiment, in the form of a matrix of integer values. The value in the *i*-th row and the *j*-th column of the matrix tells how many reads have been mapped to gene *i* in sample *j*. Analogously, for other types of assays, the rows of the matrix might correspond e.g., to binding regions (with ChIP-Seq) or peptide sequences (with quantitative mass spectrometry).

The count values must be raw counts of sequencing reads. This is important for DESeq2’s statistical model to hold, as only the actual counts allow assessing the measurement precision correctly. Hence, please do not supply other quantities, such as (rounded) normalized counts, or counts of covered base pairs – this will only lead to nonsensical results.

We will discuss how to summarize data from BAM files to a count table later in ther course. Here we’ll ‘jump right in’ and start with a prepared `SummarizedExperiment`

.

`SummarizedExperiment`

We now use R’s `data()`

command to load a prepared `SummarizedExperiment`

that was generated from the publicly available sequencing data files associated with the Himes et al. paper, described above. The steps we used to produce this object were equivalent to those you worked through in the previous sections, except that we used all the reads and all the genes. For more details on the exact steps used to create this object type `vignette("airway")`

into your R session.

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

The information in a `SummarizedExperiment`

object can be accessed with accessor functions. For example, to see the actual data, i.e., here, the read counts, we use the `assay()`

function. (The `head()`

function restricts the output to the first few lines.)

`head(assay(se))`

```
## SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516 SRR1039517 SRR1039520
## ENSG00000000003 679 448 873 408 1138 1047 770
## ENSG00000000005 0 0 0 0 0 0 0
## ENSG00000000419 467 515 621 365 587 799 417
## ENSG00000000457 260 211 263 164 245 331 233
## ENSG00000000460 60 55 40 35 78 63 76
## ENSG00000000938 0 0 2 0 1 0 0
## SRR1039521
## ENSG00000000003 572
## ENSG00000000005 0
## ENSG00000000419 508
## ENSG00000000457 229
## ENSG00000000460 60
## ENSG00000000938 0
```

In this count matrix, each row represents an Ensembl gene, each column a sequenced RNA library, and the values give the raw numbers of sequencing reads that were mapped to the respective gene in each library. We also have metadata on each of the samples (the columns of the count matrix). If you’ve counted reads with some other software, you need to check at this step that the columns of the count matrix correspond to the rows of the column metadata.

We can quickly check the millions of fragments which uniquely aligned to the genes.

`colSums(assay(se))`

```
## SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516 SRR1039517 SRR1039520 SRR1039521
## 20637971 18809481 25348649 15163415 24448408 30818215 19126151 21164133
```

Supposing we have constructed a `SummarizedExperiment`

using one of the methods described in the previous section, we now need to make sure that the object contains all the necessary information about the samples, i.e., a table with metadata on the count matrix’s columns stored in the `colData`

slot:

`colData(se)`

```
## DataFrame with 8 rows and 9 columns
## SampleName cell dex albut Run avgLength Experiment Sample
## <factor> <factor> <factor> <factor> <factor> <integer> <factor> <factor>
## SRR1039508 GSM1275862 N61311 untrt untrt SRR1039508 126 SRX384345 SRS508568
## SRR1039509 GSM1275863 N61311 trt untrt SRR1039509 126 SRX384346 SRS508567
## SRR1039512 GSM1275866 N052611 untrt untrt SRR1039512 126 SRX384349 SRS508571
## SRR1039513 GSM1275867 N052611 trt untrt SRR1039513 87 SRX384350 SRS508572
## SRR1039516 GSM1275870 N080611 untrt untrt SRR1039516 120 SRX384353 SRS508575
## SRR1039517 GSM1275871 N080611 trt untrt SRR1039517 126 SRX384354 SRS508576
## SRR1039520 GSM1275874 N061011 untrt untrt SRR1039520 101 SRX384357 SRS508579
## SRR1039521 GSM1275875 N061011 trt untrt SRR1039521 98 SRX384358 SRS508580
## BioSample
## <factor>
## SRR1039508 SAMN02422669
## SRR1039509 SAMN02422675
## SRR1039512 SAMN02422678
## SRR1039513 SAMN02422670
## SRR1039516 SAMN02422682
## SRR1039517 SAMN02422673
## SRR1039520 SAMN02422683
## SRR1039521 SAMN02422677
```

Here we see that this object already contains an informative `colData`

slot – because we have already prepared it for you, as described in the airway vignette. However, when you work with your own data, you will have to add the pertinent sample / phenotypic information for the experiment at this stage. We highly recommend keeping this information in a comma-separated value (CSV) or tab-separated value (TSV) file, which can be exported from an Excel spreadsheet, and the assign this to the `colData`

slot, making sure that the rows correspond to the columns of the `SummarizedExperiment`

. We made sure of this correspondence by specifying the BAM files using a column of the sample table.

Check out the `rowRanges()`

of the summarized experiment; these are the genomic ranges over which counting occurred.

`rowRanges(se)`

```
## GRangesList object of length 64102:
## $ENSG00000000003
## GRanges object with 17 ranges and 2 metadata columns:
## seqnames ranges strand | exon_id exon_name
## <Rle> <IRanges> <Rle> | <integer> <character>
## [1] X [99883667, 99884983] - | 667145 ENSE00001459322
## [2] X [99885756, 99885863] - | 667146 ENSE00000868868
## [3] X [99887482, 99887565] - | 667147 ENSE00000401072
## [4] X [99887538, 99887565] - | 667148 ENSE00001849132
## [5] X [99888402, 99888536] - | 667149 ENSE00003554016
## ... ... ... ... . ... ...
## [13] X [99890555, 99890743] - | 667156 ENSE00003512331
## [14] X [99891188, 99891686] - | 667158 ENSE00001886883
## [15] X [99891605, 99891803] - | 667159 ENSE00001855382
## [16] X [99891790, 99892101] - | 667160 ENSE00001863395
## [17] X [99894942, 99894988] - | 667161 ENSE00001828996
##
## ...
## <64101 more elements>
## -------
## seqinfo: 722 sequences (1 circular) from an unspecified genome
```

Let’s look at basic properties of the data, especially in relation to the statistical factors known to be important in RNAseq differential expression analysis.

The *library size* is the total number of reads mapped per sample. Use `colSums()`

on the `assay()`

data to summarize library size.

`colSums(assay(airway))`

```
## SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516 SRR1039517 SRR1039520 SRR1039521
## 20637971 18809481 25348649 15163415 24448408 30818215 19126151 21164133
```

- How does library size vary between samples?
- Why will it be important to incorporate library size in assessing differential expression?
- While easy to understand, why is simple scaling by total library size unsatisfactory from a statistical perspective?
- What different approaches might be taken to estimate library size?
- What statistical approaches might be taken to incorporate library size?
- (Answer after completing the DESeq2 workflow) What approach does DESeq2 take to (a) estimate library size; and (b) incorporate library size into differential expression analysis?

Use `rowMeans()`

on the `assay()`

data and either `hist()`

or `plot(density())`

to display the distribution of *average gene expression* across all genes. It may be helpful to transform the data, and to exclude genes with very few counts in all samples.

```
means <- rowMeans(assay(airway))
xlim <- range(log(1 + means))
plot(density(log(1 + means)), xlim=xlim)
```

`plot(density(log(1 + means[means > 1])), xlim=xlim)`

It’s clear that a gene without any expression in any sample cannot possibly be differential expressed, independent of the hypothesis under investigation. How many genes are excluded by this criterion? What is the advantage of excluding these genes

*a priori*, before any hypothesis is evaluated?(Answer after completing the DESeq2 workflow) By extension, it seems intuitive that there is a threshold level of expression below which differential gene expression cannot be detected, independent of the hypothesis under investigation. How does DESeq2 address this?

An MDS plot attempts to represent the distance between N-dimensional points projected to 2 or 3 dimensions.

```
d <- dist(t(log(1 + assay(airway))))
mds <- cmdscale(d)
plot(mds, pch=20, asp=1, cex=2)
```

`plot(mds, pch=20, asp=1, cex=2, col=airway$cell)`

`plot(mds, pch=20, asp=1, cex=2, col=airway$dex)`

- Calculate the (Euclidean) distance between samples and use multi-dimensional scaling to represent these distances in two dimensions.

- In an exploratory fashion, color points based on cell line (
`airway$cell`

) and experimental treatment (`airway$dex`

). - Interpret these plots, and suggest how these might inform subsequent statistical analysis.

If counts were Poisson distributed, there would be a linear relationship between the mean and variance of counts. Can you demonstrate in a straight-forward way that this is not the case?

```
rowVars <- matrixStats::rowVars
plot(rowVars(1 + assay(airway)) ~ rowMeans(1 + assay(airway)), log="xy")
```

`## Warning in xy.coords(x, y, xlabel, ylabel, log): 30633 y values <= 0 omitted from logarithmic plot`

`SummarizedExperiment`

to `DESeqDataSet`

We will use the DESeq2 package for assessing differential expression. The package uses an extended version of the `SummarizedExperiment`

class, called `DESeqDataSet`

. It’s easy to go from a `SummarizedExperiment`

to `DESeqDataSet`

:

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

The ‘design’ argument is a formula which expresses how the counts for each gene depend on the variables in `colData`

. Remember you can always get information on method arguments with `?`

, e.g `?DESeqDataSet`

.

It will be convenient to make sure that `untrt`

is the first level in the `dex`

factor, so that the default log2 fold changes are calculated as treated over untreated (by default R will chose the first alphabetical level, remember: computers don’t know what to do unless you tell them). The function `relevel()`

achieves this:

`dds$dex <- relevel(dds$dex, "untrt")`

In addition, if you have at any point subset the columns of the `DESeqDataSet`

you should similarly call `droplevels()`

on the factors if the subsetting has resulted in some levels having 0 samples.

Finally, we are ready to run the differential expression pipeline. With the data object prepared, the DESeq2 analysis can now be run with a single call to the function `DESeq()`

:

`dds <- DESeq(dds)`

`## estimating size factors`

`## estimating dispersions`

`## gene-wise dispersion estimates`

`## mean-dispersion relationship`

`## final dispersion estimates`

`## fitting model and testing`

This function will print out a message for the various steps it performs. These are described in more detail in the manual page `?DESeq`

. Briefly these are: the estimation of size factors (which control for differences in the library size of the sequencing experiments), the estimation of dispersion for each gene, and fitting a generalized linear model.

A `DESeqDataSet`

is returned which contains all the fitted information within it, and the following section describes how to extract out result tables of interest from this object.

Calling `results()`

without any arguments will extract the estimated log2 fold changes and *p* values for the last variable in the design formula. If there are more than 2 levels for this variable, `results()`

will extract the results table for a comparison of the last level over the first level.

`(res <- results(dds))`

```
## log2 fold change (MAP): dex trt vs untrt
## Wald test p-value: dex trt vs untrt
## DataFrame with 64102 rows and 6 columns
## baseMean log2FoldChange lfcSE stat pvalue padj
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
## ENSG00000000003 708.60217 -0.37415246 0.09884435 -3.7852692 0.0001535422 0.001289269
## ENSG00000000005 0.00000 NA NA NA NA NA
## ENSG00000000419 520.29790 0.20206175 0.10974241 1.8412367 0.0655868755 0.197066699
## ENSG00000000457 237.16304 0.03616686 0.13834540 0.2614244 0.7937652378 0.913855995
## ENSG00000000460 57.93263 -0.08445399 0.24990710 -0.3379415 0.7354072485 0.884141561
## ... ... ... ... ... ... ...
## LRG_94 0 NA NA NA NA NA
## LRG_96 0 NA NA NA NA NA
## LRG_97 0 NA NA NA NA NA
## LRG_98 0 NA NA NA NA NA
## LRG_99 0 NA NA NA NA NA
```

As `res`

is a `DataFrame`

object, it carries metadata with information on the meaning of the columns:

`mcols(res, use.names=TRUE)`

```
## DataFrame with 6 rows and 2 columns
## type description
## <character> <character>
## baseMean intermediate mean of normalized counts for all samples
## log2FoldChange results log2 fold change (MAP): dex trt vs untrt
## lfcSE results standard error: dex trt vs untrt
## stat results Wald statistic: dex trt vs untrt
## pvalue results Wald test p-value: dex trt vs untrt
## padj results BH adjusted p-values
```

The first column, `baseMean`

, is a just the average of the normalized count values, dividing by size factors, taken over all samples. The remaining four columns refer to a specific contrast, namely the comparison of the `trt`

level over the `untrt`

level for the factor variable `dex`

. See the help page for `results()`

(by typing `?results`

) for information on how to obtain other contrasts.

The column `log2FoldChange`

is the effect size estimate. It tells us how much the gene’s expression seems to have changed due to treatment with dexamethasone in comparison to untreated samples. This value is reported on a logarithmic scale to base 2: for example, a log2 fold change of 1.5 means that the gene’s expression is increased by a multiplicative factor of \(2^{1.5} \approx 2.82\).

Of course, this estimate has an uncertainty associated with it, which is available in the column `lfcSE`

, the standard error estimate for the log2 fold change estimate. We can also express the uncertainty of a particular effect size estimate as the result of a statistical test. The purpose of a test for differential expression is to test whether the data provides sufficient evidence to conclude that this value is really different from zero. DESeq2 performs for each gene a *hypothesis test* to see whether evidence is sufficient to decide against the *null hypothesis* that there is no effect of the treatment on the gene and that the observed difference between treatment and control was merely caused by experimental variability (i.e., the type of variability that you can just as well expect between different samples in the same treatment group). As usual in statistics, the result of this test is reported as a *p* value, and it is found in the column `pvalue`

. (Remember that a *p* value indicates the probability that a fold change as strong as the observed one, or even stronger, would be seen under the situation described by the null hypothesis.)

We can also summarize the results with the following line of code, which reports some additional information.

`summary(res)`

```
##
## out of 33469 with nonzero total read count
## adjusted p-value < 0.1
## LFC > 0 (up) : 2617, 7.8%
## LFC < 0 (down) : 2203, 6.6%
## outliers [1] : 0, 0%
## low counts [2] : 15441, 46%
## (mean count < 5)
## [1] see 'cooksCutoff' argument of ?results
## [2] see 'independentFiltering' argument of ?results
```

Note that there are many genes with differential expression due to dexamethasone treatment at the FDR level of 10%. This makes sense, as the smooth muscle cells of the airway are known to react to glucocorticoid steroids. However, there are two ways to be more strict about which set of genes are considered significant:

- lower the false discovery rate threshold (the threshold on
`padj`

in the results table) - raise the log2 fold change threshold from 0 using the
`lfcThreshold`

argument of`results()`

. See the DESeq2 vignette for a demonstration of the use of this argument.

Sometimes a subset of the *p* values in `res`

will be `NA`

(“not available”). This is `DESeq()`

’s way of reporting that all counts for this gene were zero, and hence not test was applied. In addition, *p* values can be assigned `NA`

if the gene was excluded from analysis because it contained an extreme count outlier. For more information, see the outlier detection section of the vignette.

Novices in high-throughput biology often assume that thresholding these *p* values at a low value, say 0.05, as is often done in other settings, would be appropriate – but it is not. We briefly explain why:

There are 5648 genes with a *p* value below 0.05 among the 33469 genes, for which the test succeeded in reporting a *p* value:

`sum(res$pvalue < 0.05, na.rm=TRUE)`

`## [1] 5648`

`sum(!is.na(res$pvalue))`

`## [1] 33469`

Now, assume for a moment that the null hypothesis is true for all genes, i.e., no gene is affected by the treatment with dexamethasone. Then, by the definition of *p* value, we expect up to 5% of the genes to have a *p* value below 0.05. This amounts to 1673 genes. If we just considered the list of genes with a *p* value below 0.05 as differentially expressed, this list should therefore be expected to contain up to 1673 / 5648 = 30% false positives.

DESeq2 uses the Benjamini-Hochberg (BH) adjustment as described in the base R *p.adjust* function; in brief, this method calculates for each gene an adjusted *p* value which answers the following question: if one called significant all genes with a *p* value less than or equal to this gene’s *p* value threshold, what would be the fraction of false positives (the *false discovery rate*, FDR) among them (in the sense of the calculation outlined above)? These values, called the BH-adjusted *p* values, are given in the column `padj`

of the `res`

object.

Hence, if we consider a fraction of 10% false positives acceptable, we can consider all genes with an adjusted *p* value below \(10% = 0.1\) as significant. How many such genes are there?

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

`## [1] 4820`

We subset the results table to these genes and then sort it by the log2 fold change estimate to get the significant genes with the strongest down-regulation.

```
resSig <- subset(res, padj < 0.1)
head(resSig[ order( resSig$log2FoldChange ), ])
```

```
## log2 fold change (MAP): dex trt vs untrt
## Wald test p-value: dex trt vs untrt
## DataFrame with 6 rows and 6 columns
## baseMean log2FoldChange lfcSE stat pvalue padj
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
## ENSG00000162692 508.17023 -3.449475 0.1767138 -19.520120 7.406383e-85 9.537305e-82
## ENSG00000105989 333.21469 -2.847364 0.1763098 -16.149771 1.139834e-58 5.871121e-56
## ENSG00000146006 46.80760 -2.828093 0.3377003 -8.374564 5.542861e-17 2.708041e-15
## ENSG00000214814 243.27698 -2.753559 0.2235537 -12.317215 7.317772e-35 1.232942e-32
## ENSG00000267339 26.23357 -2.704476 0.3519722 -7.683776 1.544666e-14 5.924944e-13
## ENSG00000013293 244.49733 -2.641050 0.1992872 -13.252481 4.365309e-40 8.842448e-38
```

…and with the strongest upregulation. The `order()`

function gives the indices in increasing order, so a simple way to ask for decreasing order is to add a `-`

sign. Alternatively, you can use the argument `decreasing=TRUE`

.

`head(resSig[ order( -resSig$log2FoldChange ), ])`

```
## log2 fold change (MAP): dex trt vs untrt
## Wald test p-value: dex trt vs untrt
## DataFrame with 6 rows and 6 columns
## baseMean log2FoldChange lfcSE stat pvalue padj
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
## ENSG00000109906 385.07103 4.847164 0.3313657 14.62784 1.866158e-48 5.902298e-46
## ENSG00000179593 67.24305 4.830815 0.3314192 14.57615 3.983670e-48 1.196960e-45
## ENSG00000152583 997.43977 4.313961 0.1721375 25.06114 1.320082e-138 2.379844e-134
## ENSG00000163884 561.10717 4.074297 0.2104708 19.35802 1.744626e-83 1.965757e-80
## ENSG00000250978 56.31819 4.054731 0.3294746 12.30666 8.340703e-35 1.392280e-32
## ENSG00000168309 159.52692 3.977191 0.2558532 15.54481 1.725211e-54 7.775524e-52
```

A quick way to visualize the counts for a particular gene is to use the `plotCounts()`

function, which takes as arguments the `DESeqDataSet`

, a gene name, and the group over which to plot the counts.

```
topGene <- rownames(res)[which.min(res$padj)]
data <- plotCounts(dds, gene=topGene, intgroup=c("dex"), returnData=TRUE)
```

We can also make more customizable plots using the `ggplot()`

function from the ggplot2 package:

```
library(ggplot2)
ggplot(data, aes(x=dex, y=count, fill=dex)) +
scale_y_log10() +
geom_dotplot(binaxis="y", stackdir="center")
```

`## `stat_bindot()` using `bins = 30`. Pick better value with `binwidth`.`

An “MA-plot” provides a useful overview for an experiment with a two-group comparison. The log2 fold change for a particular comparison is plotted on the y-axis and the average of the counts normalized by size factor is shown on the x-axis (“M” for minus, because a log ratio is equal to log minus log, and “A” for average).

`plotMA(res, ylim=c(-5,5))`

Each gene is represented with a dot. Genes with an adjusted \(p\) value below a threshold (here 0.1, the default) are shown in red. The DESeq2 package incorporates a prior on log2 fold changes, resulting in moderated log2 fold changes from genes with low counts and highly variable counts, as can be seen by the narrowing of spread of points on the left side of the plot. This plot demonstrates that only genes with a large average normalized count contain sufficient information to yield a significant call.

We can label individual points on the MA plot as well. Here we use the `with()`

R function to plot a circle and text for a selected row of the results object. Within the `with()`

function, only the `baseMean`

and `log2FoldChange`

values for the selected rows of `res`

are used.

```
plotMA(res, ylim=c(-5,5))
with(res[topGene, ], {
points(baseMean, log2FoldChange, col="dodgerblue", cex=2, lwd=2)
text(baseMean, log2FoldChange, topGene, pos=2, col="dodgerblue")
})
```

Whether a gene is called significant depends not only on its LFC but also on its within-group variability, which DESeq2 quantifies as the *dispersion*. For strongly expressed genes, the dispersion can be understood as a squared coefficient of variation: a dispersion value of 0.01 means that the gene’s expression tends to differ by typically \(\sqrt{0.01} = 10\%\) between samples of the same treatment group. For weak genes, the Poisson noise is an additional source of noise.

The function `plotDispEsts()`

visualizes DESeq2’s dispersion estimates:

`plotDispEsts(dds)`

The black points are the dispersion estimates for each gene as obtained by considering the information from each gene separately. Unless one has many samples, these values fluctuate strongly around their true values. Therefore, we fit the red trend line, which shows the dispersions’ dependence on the mean, and then shrink each gene’s estimate towards the red line to obtain the final estimates (blue points) that are then used in the hypothesis test. The blue circles above the main “cloud” of points are genes which have high gene-wise dispersion estimates which are labelled as dispersion outliers. These estimates are therefore not shrunk toward the fitted trend line.

Another useful diagnostic plot is the histogram of the *p* values.

`hist(res$pvalue, breaks=20, col="grey50", border="white")`

This plot becomes a bit smoother by excluding genes with very small counts:

`hist(res$pvalue[res$baseMean > 1], breaks=20, col="grey50", border="white")`

The MA plot highlights an important property of RNA-Seq data. For weakly expressed genes, we have no chance of seeing differential expression, because the low read counts suffer from so high Poisson noise that any biological effect is drowned in the uncertainties from the read counting. We can also show this by examining the ratio of small *p* values (say, less than, 0.01) for genes binned by mean normalized count:

```
# create bins using the quantile function
qs <- c(0, quantile(res$baseMean[res$baseMean > 0], 0:7/7))
# cut the genes into the bins
bins <- cut(res$baseMean, qs)
# rename the levels of the bins using the middle point
levels(bins) <- paste0("~",round(.5*qs[-1] + .5*qs[-length(qs)]))
# calculate the ratio of $p$ values less than .01 for each bin
ratios <- tapply(res$pvalue, bins, function(p) mean(p < .01, na.rm=TRUE))
# plot these ratios
barplot(ratios, xlab="mean normalized count", ylab="ratio of small p values")
```

At first sight, there may seem to be little benefit in filtering out these genes. After all, the test found them to be non-significant anyway. However, these genes have an influence on the multiple testing adjustment, whose performance improves if such genes are removed. By removing the weakly-expressed genes from the input to the FDR procedure, we can find more genes to be significant among those which we keep, and so improved the power of our test. This approach is known as *independent filtering*.

The term *independent* highlights an important caveat. Such filtering is permissible only if the filter criterion is independent of the actual test statistic. Otherwise, the filtering would invalidate the test and consequently the assumptions of the BH procedure. This is why we filtered on the average over *all* samples: this filter is blind to the assignment of samples to the treatment and control group and hence independent. The independent filtering software used inside DESeq2 comes from the *genefilter* package, which contains a reference to a paper describing the statistical foundation for independent filtering.

Our result table only uses Ensembl gene IDs, but gene names may be more informative. *Bioconductor*’s annotation packages help with mapping various ID schemes to each other.

We load the *AnnotationDbi* package and the annotation package *org.Hs.eg.db*:

`library(org.Hs.eg.db)`

This is the organism annotation package (“org”) for *Homo sapiens* (“Hs”), organized as an AnnotationDbi database package (“db”), using Entrez Gene IDs (“eg”) as primary key. To get a list of all available key types, use:

`columns(org.Hs.eg.db)`

```
## [1] "ACCNUM" "ALIAS" "ENSEMBL" "ENSEMBLPROT" "ENSEMBLTRANS" "ENTREZID"
## [7] "ENZYME" "EVIDENCE" "EVIDENCEALL" "GENENAME" "GO" "GOALL"
## [13] "IPI" "MAP" "OMIM" "ONTOLOGY" "ONTOLOGYALL" "PATH"
## [19] "PFAM" "PMID" "PROSITE" "REFSEQ" "SYMBOL" "UCSCKG"
## [25] "UNIGENE" "UNIPROT"
```

```
res$hgnc_symbol <-
unname(mapIds(org.Hs.eg.db, rownames(res), "SYMBOL", "ENSEMBL"))
```

`## 'select()' returned 1:many mapping between keys and columns`

```
res$entrezgene <-
unname(mapIds(org.Hs.eg.db, rownames(res), "ENTREZID", "ENSEMBL"))
```

`## 'select()' returned 1:many mapping between keys and columns`

Now the results have the desired external gene ids:

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

```
## log2 fold change (MAP): dex trt vs untrt
## Wald test p-value: dex trt vs untrt
## DataFrame with 6 rows and 8 columns
## baseMean log2FoldChange lfcSE stat pvalue padj
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
## ENSG00000152583 997.4398 4.313961 0.1721375 25.06114 1.320082e-138 2.379844e-134
## ENSG00000165995 495.0929 3.186823 0.1281565 24.86665 1.708459e-136 1.540005e-132
## ENSG00000101347 12703.3871 3.618735 0.1489428 24.29613 2.153705e-130 1.294233e-126
## ENSG00000120129 3409.0294 2.871488 0.1182491 24.28337 2.937761e-130 1.324049e-126
## ENSG00000189221 2341.7673 3.230395 0.1366746 23.63567 1.657244e-123 5.975359e-120
## ENSG00000211445 12285.6151 3.553360 0.1579821 22.49216 4.952520e-112 1.488067e-108
## hgnc_symbol entrezgene
## <character> <character>
## ENSG00000152583 SPARCL1 8404
## ENSG00000165995 CACNB2 783
## ENSG00000101347 SAMHD1 25939
## ENSG00000120129 DUSP1 1843
## ENSG00000189221 MAOA 4128
## ENSG00000211445 GPX3 2878
```

You can easily save the results table in a CSV file, which you can then load with a spreadsheet program such as Excel. The call to *as.data.frame* is necessary to convert the *DataFrame* object (*IRanges* package) to a *data.frame* object which can be processed by *write.csv*.

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

As last part of this document, we call the function *sessionInfo*, which reports the version numbers of R and all the packages used in this session. It is good practice to always keep such a record as it will help to trace down what has happened in case that an R script ceases to work because the functions have been changed in a newer version of a package. The session information should also **always** be included in any emails to the Bioconductor support site along with all code used in the analysis.

`sessionInfo()`

```
## R version 3.3.1 Patched (2016-10-12 r71512)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 16.04.1 LTS
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=en_US.UTF-8
## [4] LC_COLLATE=C LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C LC_ADDRESS=C
## [10] LC_TELEPHONE=C LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] stats4 parallel stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] org.Hs.eg.db_3.4.0 AnnotationDbi_1.36.0
## [3] RColorBrewer_1.1-2 ggplot2_2.2.0
## [5] gplots_3.0.1 DESeq2_1.14.0
## [7] VariantAnnotation_1.20.1 RNAseqData.HNRNPC.bam.chr14_0.12.0
## [9] ShortRead_1.32.0 GenomicAlignments_1.10.0
## [11] Rsamtools_1.26.1 BiocParallel_1.8.1
## [13] rtracklayer_1.34.1 airway_0.108.0
## [15] SummarizedExperiment_1.4.0 Biobase_2.34.0
## [17] GenomicRanges_1.26.1 GenomeInfoDb_1.10.1
## [19] Biostrings_2.42.0 XVector_0.14.0
## [21] IRanges_2.8.1 S4Vectors_0.12.0
## [23] BiocGenerics_0.20.0 BiocStyle_2.2.0
##
## loaded via a namespace (and not attached):
## [1] splines_3.3.1 gtools_3.5.0 Formula_1.2-1 assertthat_0.1
## [5] latticeExtra_0.6-28 BSgenome_1.42.0 yaml_2.1.14 RSQLite_1.0.0
## [9] lattice_0.20-34 chron_2.3-47 digest_0.6.10 colorspace_1.3-0
## [13] htmltools_0.3.5 Matrix_1.2-7.1 plyr_1.8.4 XML_3.98-1.5
## [17] biomaRt_2.30.0 genefilter_1.56.0 zlibbioc_1.20.0 xtable_1.8-2
## [21] scales_0.4.1 gdata_2.17.0 htmlTable_1.7 tibble_1.2
## [25] annotate_1.52.0 GenomicFeatures_1.26.0 nnet_7.3-12 lazyeval_0.2.0
## [29] survival_2.40-1 magrittr_1.5 evaluate_0.10 hwriter_1.3.2
## [33] foreign_0.8-67 tools_3.3.1 data.table_1.9.6 matrixStats_0.51.0
## [37] stringr_1.1.0 munsell_0.4.3 locfit_1.5-9.1 cluster_2.0.5
## [41] caTools_1.17.1 grid_3.3.1 RCurl_1.95-4.8 bitops_1.0-6
## [45] rmarkdown_1.1 gtable_0.2.0 codetools_0.2-15 DBI_0.5-1
## [49] gridExtra_2.2.1 knitr_1.15 Hmisc_4.0-0 KernSmooth_2.23-15
## [53] stringi_1.1.2 Rcpp_0.12.7 geneplotter_1.52.0 rpart_4.1-10
## [57] acepack_1.4.1
```