---
title: "B.3 -- An RNA-seq Work Flow"
author:
  Martin Morgan <Martin.Morgan@RoswellPark.org><br/>
  Lori Shepherd <Lori.Shepherd@RoswellPark.org><br/>
date: "July 26-28, 2017"
output:
  BiocStyle::html_document2:
    toc: true
    toc_depth: 2
vignette: >
  % \VignetteIndexEntry{B.3 -- An RNA-seq Work Flow}
  % \VignetteEngine{knitr::rmarkdown}
---

```{r style, echo = FALSE, results = 'asis'}
knitr::opts_chunk$set(
    eval=as.logical(Sys.getenv("KNITR_EVAL", "TRUE")),
    cache=as.logical(Sys.getenv("KNITR_CACHE", "TRUE")))
```

```{r setup, echo=FALSE}
suppressPackageStartupMessages({
    library(DESeq2)
    library(gplots)
    library(ggplot2)
    library(RColorBrewer)
    library(org.Hs.eg.db)
})
```

- _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][].


# Presentation: RNA-seq work flow

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

[Anders, CSAMA, 2015]: https://bioconductor.org/help/course-materials/2015/CSAMA2015/lect/L05-deseq2-anders.pdf
[Pimentel, YouTube, 2015]: https://www.youtube.com/watch?v=ztyjiCCt_lM
[Love, CSAMA, 2015]: https://bioconductor.org/help/course-materials/2015/CSAMA2015/lect/L06-rna-stats-love.pdf
[Huber, CSAMA, 2015]: https://bioconductor.org/help/course-materials/2015/CSAMA2015/lect/L03-testing-huber.pdf

## Experimental design

### Keep it simple

- Classical experimental designs
- Time series
- Without missing values, where possible
- Intended analysis must be feasible -- 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](http://www.nature.com/nrg/journal/v11/n10/abs/nrg2825.html),
      Leek & Story PLoS Genet 3(9):
      [e161](http://dx.doi.org/10.1371/journal.pgen.0030161).
    - 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 
    
  ![](our_figures/nrg2825-f2.jpg) 
  HapMap samples from one facility, ordered by date of processing.

### Wet-lab

- 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, ...

### Sequencing

- 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

### 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)

- [Bowtie2](http://bowtie-bio.sourceforge.net/bowtie2) [Rbowtie][])
- [STAR](http://bowtie-bio.sourceforge.net/bowtie2)
  ([doi](http://dx.doi.org/10.1093/bioinformatics/bts635))
- [subread](http://dx.doi.org/10.1093/nar/gkt214) ([Rsubread][])
- Systematic evaluation (Engstrom et al., 2013,
  [doi](http://dx.doi.org/10.1038/nmeth.2722))

## Reduction to 'count tables'

- 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](http://www-huber.embl.de/users/anders/HTSeq/doc/overview.html),
  [htseq-count](http://www-huber.embl.de/users/anders/HTSeq/doc/count.html)

### (Bowtie2 / tophat / Cufflinks / Cuffdiff / etc)

- [tophat](http://ccb.jhu.edu/software/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](http://cole-trapnell-lab.github.io/cufflinks/)
  ([doi](http://dx.doi.org/10.1038/nprot.2012.016)) takes _tophat_
  output and estimate existing and novel transcript abundance.
  [How Cufflinks Works](http://cole-trapnell-lab.github.io/cufflinks/papers)
- [Cuffdiff](http://cole-trapnell-lab.github.io/cufflinks/cuffdiff/)
  assesses statistical significance of estimated abundances between
  experimental groups
- [RSEM](http://www.biomedcentral.com/1471-2105/12/323) includes de
  novo assembly and quantification

### (kallisto / sailfish)

- 'Next generation' differential expression tools; transcriptome
  alignment
- E.g., [kallisto](http://pachterlab.github.io/kallisto) takes a
  radically different approach: from FASTQ to count table without BAM
  files.
- Very fast, almost as accurate.
- Hints on
  [how it works](https://liorpachter.wordpress.com/2015/05/10/near-optimal-rna-seq-quantification-with-kallisto/);
  [arXiv](http://arxiv.org/abs/1505.02710)
- Integration with gene-level analyses --   [Soneson et al][].

[Soneson et al]: http://f1000research.com/articles/4-1521/v1

## Analysis

### 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 regardless 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.

## Statistical Issues In-depth: Normalization and Dispersion

### Normalization

[DESeq2][] `estimateSizeFactors()`, Anders and Huber,
[2010](http://genomebiology.com/2010/11/10/r106)

- 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

### Dispersion

- [DESeq2][] `estimateDispersions()`
- Estimate per-gene dispersion
- Fit a smoothed relationship between dispersion and abundance

## Comprehension: 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, ...
  
  ![Copy number / expression QC](our_figures/copy_number_QC_2.png)
  Correlation between genomic copy number and mRNA expression
  identified 38 mis-labeled samples in the TCGA ovarian cancer
  Affymetrix microarray dataset.

# Lab: Gene-level RNA-seq differential expression

## Background

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.

[RNA-Seq workflow]: https://bioconductor.org/help/workflows/rnaseqGene/

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.

## Experimental data

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](http://www.ncbi.nlm.nih.gov/pubmed/24926665).
GEO: [GSE52778](http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE52778).

## Preparing count matrices

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 the course. Here we'll 'jump right in' and start with a
prepared `SummarizedExperiment`.

## Starting from `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.

```{r}
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.)

```{r}
head(assay(se))
```

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.

```{r}
colSums(assay(se))
```

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:

```{r}
colData(se)
```

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.

<!-- FIXME rowRanges -->

Check out the `rowRanges()` of the summarized experiment; these are
the genomic ranges over which counting occurred.

```{r rowRanges}
rowRanges(se)
```

## From `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`:

```{r}
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`.

## Differential expression analysis

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:

```{r}
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.

### Running the pipeline

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()`:

```{r}
dds <- DESeq(dds)
```

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.

### Building the results table

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.

```{r}
(res <- results(dds))
```

As `res` is a `DataFrame` object, it carries metadata
with information on the meaning of the columns:

```{r}
mcols(res, use.names=TRUE)
```

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.

```{r}
summary(res)
```

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.

### Multiple testing

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 `r sum(res$pvalue < .05, na.rm=TRUE)` genes with a *p* value
below 0.05 among the `r sum(!is.na(res$pvalue))` genes, for which the
test succeeded in reporting a *p* value:

```{r}
sum(res$pvalue < 0.05, na.rm=TRUE)
sum(!is.na(res$pvalue))
```

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
`r round(sum(!is.na(res$pvalue)) * .05 )` genes.
If we just considered the list of genes with a *p* value below 0.05 as
differentially expressed, this list should therefore be expected to
contain up to
`r round(sum(!is.na(res$pvalue)) * .05)` /
`r sum(res$pvalue < .05, na.rm=TRUE)` =
`r round(sum(!is.na(res$pvalue))*.05 / sum(res$pvalue < .05, na.rm=TRUE) * 100)`%
 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?

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

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.

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

...and with the strongest up-regulation. 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`.


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

## Diagnostic plots

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. 

```{r plotcounts, fig.width=5, fig.height=5}
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:

```{r ggplotcountsdot, fig.height=5}
library(ggplot2)
ggplot(data, aes(x=dex, y=count, fill=dex)) +
  scale_y_log10() + 
  geom_dotplot(binaxis="y", stackdir="center")
```

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).

```{r plotma, eval=FALSE}
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.

```{r plotma2, eval=FALSE}
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: 

```{r plotdispests}
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 labeled 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.

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

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

```{r histpvalue2}
hist(res$pvalue[res$baseMean > 1], breaks=20, col="grey50", border="white")
```



## Independent filtering

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:

```{r sensitivityovermean, fig.height=4}
# 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.

## Annotation: adding gene names

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][]:

```{r}
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:

```{r}
columns(org.Hs.eg.db)
res$hgnc_symbol <- 
    unname(mapIds(org.Hs.eg.db, rownames(res), "SYMBOL", "ENSEMBL"))
res$entrezgene <- 
    unname(mapIds(org.Hs.eg.db, rownames(res), "ENTREZID", "ENSEMBL"))
```

Now the results have the desired external gene ids:
```{r}
resOrdered <- res[order(res$pvalue),]
head(resOrdered)
```

## Exporting results

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*.

```{r eval=FALSE}
write.csv(as.data.frame(resOrdered), file="results.csv")
```

## Session information

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.

```{r}
sessionInfo()
```

[AnnotationDbi]: https://bioconductor.org/packages/AnnotationDbi
[BaySeq]: https://bioconductor.org/packages/BaySeq
[DESeq2]: https://bioconductor.org/packages/DESeq2
[IRanges]: https://bioconductor.org/packages/IRanges
[RNASeqPower]: https://bioconductor.org/packages/RNASeqPower
[Rbowtie]: https://bioconductor.org/packages/Rbowtie
[Rsubread]: https://bioconductor.org/packages/Rsubread
[airway]: https://bioconductor.org/packages/airway
[edgeR]: https://bioconductor.org/packages/edgeR
[genefilter]: https://bioconductor.org/packages/genefilter
[ggplot2]:https://cran.r-project.org/package=ggplot2 
[gplots]: https://cran.r-project.org/package=gplots
[limma]: https://bioconductor.org/packages/limma
[sva]: https://bioconductor.org/packages/sva
[org.Hs.eg.db]: https://bioconductor.org/packages/org.Hs.eg.db

[Bioconductor support site]: https://support.bioconductor.org
