---
title: "6. RNA-Seq Differential Expression"
author: "Martin Morgan (martin.morgan@roswellpark.org)<br />
    Roswell Park Cancer Institute, Buffalo, NY<br />
    5 - 9 October, 2015"
output:
  BiocStyle::html_document:
    toc: true
    toc_depth: 2
vignette: >
  % \VignetteIndexEntry{6. RNA-Seq Differential Expression}
  % \VignetteEngine{knitr::rmarkdown}
---

```{r style, echo = FALSE, results = 'asis'}
BiocStyle::markdown()
options(width=100, max.print=1000)
knitr::opts_chunk$set(
    eval=as.logical(Sys.getenv("KNITR_EVAL", "TRUE")),
    cache=as.logical(Sys.getenv("KNITR_CACHE", "TRUE")))
```

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

The material in this course requires R version 3.2 and Bioconductor
version 3.2

```{r configure-test}
stopifnot(
    getRversion() >= '3.2' && getRversion() < '3.3',
    BiocInstaller::biocVersion() == "3.2"
)
```

# Background

[Google Doc](https://docs.google.com/document/d/1di3O0mGQwLW80uVXUtdZVEitU-9Gn9hjzHV-Ae6YIcg/edit?usp=sharing)

For Review:

- [Overall Workflow](S1-RNASeq-Workflow.html)
- [Specifying Experimental Design in _R_](S2-RNASeq-Experimental-Design.html)

This lab is derived from:
[RNA-Seq workflow: gene-level exploratory analysis and differential expression](http://bioconductor.org/help/workflows/rnaseqGene/),
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.

# 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 ther 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` calass, called `DESeqDataSet`. It's easy to go
from a `SummarizedExperiment` to `DESeqDataSet`:

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

# Visually exploring the dataset

### The rlog transformation

Many common statistical methods for exploratory analysis of
multidimensional data, especially methods for clustering and
ordination (e.g., principal-component analysis and the like), work
best for (at least approximately) homoskedastic data; this means that
the variance of an observed quantity (here, the expression
strength of a gene) does not depend on the mean. In RNA-Seq data,
however, variance grows with the mean. For example, if one performs
PCA (principal components analysis) directly on a matrix of normalized
read counts, the result typically depends only on the few most
strongly expressed genes because they show the largest absolute
differences between samples. A simple and often used strategy to avoid
this is to take the logarithm of the normalized count values plus a
small pseudocount; however, now the genes with low counts tend to
dominate the results because, due to the strong Poisson noise inherent
to small count values, they show the strongest relative differences
between samples.

As a solution, [DESeq2][] offers the *regularized-logarithm
transformation*, or `rlog()` for short. For genes with high counts,
the rlog transformation differs not much from an ordinary log2
transformation. For genes with lower counts, however, the values are
shrunken towards the genes' averages across all samples. Using an
empirical Bayesian prior on inter-sample differences in the form of a
*ridge penalty*, this is done such that the rlog-transformed data are
approximately homoskedastic. See the help for `?rlog` for more
information and options. Another transformation, the *variance
stabilizing transformation* (`vsn()`), is discussed alongside the
`rlog()` in the [DESeq2][] vignette.

**Note:** the rlog transformation is provided for applications *other*
than differential testing. For differential testing we recommend the
`DESeq()` function applied to raw counts, as described later
in this workflow, which also takes into account the dependence of the
variance of counts on the mean value during the dispersion estimation
step.

The function `rlog()` returns a `SummarizedExperiment`
object which contains the rlog-transformed values in its `assay()` slot:

```{r}
rld <- rlog(dds)
head(assay(rld))
```

To show the effect of the transformation, we plot the first sample
against the second, first simply using the `log2()` function (after
adding 1, to avoid taking the log of zero), and then using the
rlog-transformed values. For the `log2()` method, we need estimate size
factors to account for sequencing depth (this is done automatically
for the `rlog()` method).

```{r rldplot, fig.width=10, fig.height=5}
opar <- par( mfrow = c( 1, 2 ) )
dds <- estimateSizeFactors(dds)
plot( log2( 1 + counts(dds, normalized=TRUE)[ , 1:2] ),
     col=rgb(0,0,0,.2), pch=16, cex=0.3 )
plot( assay(rld)[ , 1:2],
     col=rgb(0,0,0,.2), pch=16, cex=0.3 )
par(opar)
```

Note that, in order to make it easier to see where several points are
plotted on top of each other, we set the plotting color to a
semi-transparent black and changed the points to solid circles
(`pch=16`) with reduced size (`cex=0.3`).

We can see how genes with low counts seem to be excessively variable
on the ordinary logarithmic scale, while the rlog transform compresses
differences for genes for which the data cannot provide good information anyway.

### Sample distances

A useful first step in an RNA-Seq analysis is often to assess overall
similarity between samples: Which samples are similar to each other,
which are different? Does this fit to the expectation from the
experiment's design?

We use the R function `dist()` to calculate the Euclidean distance
between samples. To avoid that the distance measure is dominated by a
few highly variable genes, and have a roughly equal contribution from
all genes, we use it on the rlog-transformed data:

```{r}
sampleDists <- dist( t( assay(rld) ) )
sampleDists
```

Note the use of the function `t()` to transpose the data matrix. We
need this because `dist()` calculates distances between data *rows* and
our samples constitute the columns.

We visualize the distances in a heatmap, using the function
`heatmap.2()` from the [gplots][] package.

```{r}
library("gplots")
library("RColorBrewer")
```

We have to provide a hierarchical clustering `hc` to the `heatmap.2()`
function based on the sample distances, or else the `heatmap.2()`
function would calculate a clustering based on the distances between
the rows/columns of the distance matrix.

```{r distheatmap, fig.width=8}
sampleDistMatrix <- as.matrix( sampleDists )
rownames(sampleDistMatrix) <- paste( rld$dex, rld$cell, sep="-" )
colors <- colorRampPalette( rev(brewer.pal(9, "Blues")) )(255)
hc <- hclust(sampleDists)
heatmap.2( sampleDistMatrix, Rowv=as.dendrogram(hc),
          symm=TRUE, trace="none", col=colors,
          margins=c(2,10), labCol=FALSE )
```

Note that we have changed the row names of the distance matrix to
contain treatment type and patient number instead of sample ID, so
that we have all this information in view when looking at the heatmap.

### PCA plot

Another way to visualize sample-to-sample distances is a
principal-components analysis (PCA). In this ordination method, the
data points (i.e., here, the samples) are projected onto the 2D plane
such that they spread out in the two directions which explain most of
the differences in the data. The x-axis is the direction (or principal
component) which separates the data points the most. The amount of the
total variance which is contained in the direction is printed in the
axis label.

```{r plotpca, fig.width=6, fig.height=4.5}
plotPCA(rld, intgroup = c("dex", "cell"))
```

Here, we have used the function `plotPCA()` which comes with [DESeq2][].
The two terms specified by `intgroup` are the interesting groups for
labelling the samples; they tell the function to use them to choose
colors. We can also build the PCA plot from scratch using
`r CRANpkg("ggplot2")`. This is done by asking the `plotPCA()` function
to return the data used for plotting rather than building the plot.
See the [ggplot2][] [documentation](http://docs.ggplot2.org/current/)
for more details.

```{r}
(data <- plotPCA(rld, intgroup = c( "dex", "cell"), returnData=TRUE))
percentVar <- round(100 * attr(data, "percentVar"))
```

We can then use this data to build up the plot, specifying that the
color of the points should reflect dexamethasone treatment and the
shape should reflect the cell line.

```{r}
library("ggplot2")
```

```{r ggplotpca, fig.width=6, fig.height=4.5}
qplot(PC1, PC2, color=dex, shape=cell, data=data) +
  xlab(paste0("PC1: ", percentVar[1], "% variance")) +
  ylab(paste0("PC2: ", percentVar[2], "% variance"))
```

From both visualizations, we see that the differences between cells are
considerable, though not stronger than the differences due to
treatment with dexamethasone. This shows why it will be important to
account for this in differential testing by using a paired design
("paired", because each dex treated sample is paired with one
untreated sample from the *same* cell line). We are already set up for
this by using the design formula `~ cell + dex` when setting up the
data object in the beginning.

# 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 results 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.

## Other comparisons

In general, the results for a comparison of any two levels of a
variable can be extracted using the `contrast` argument to
`results()`. The user should specify three values: the name of the
variable, the name of the level in the numerator, and the name of the
level in the denominator.  Here we extract results for the log2 of the
fold change of one cell line over another:

```{r}
results(dds, contrast=c("cell", "N061011", "N61311"))
```

If results for an interaction term are desired, the `name`
argument of `results()` should be used. Please see the 
help for the `results()` function for more details.

## 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 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`.


```{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}
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 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.

```{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")
```

# Gene clustering

In the sample distance heatmap made previously, the dendrogram at the
side shows us a hierarchical clustering of the samples. Such a
clustering can also be performed for the genes.  Since the clustering
is only relevant for genes that actually carry signal, one usually
carries it out only for a subset of most highly variable genes. Here,
for demonstration, let us select the 35 genes with the highest
variance across samples. We will work with the `rlog()` transformed
counts:

```{r}
library("genefilter")
topVarGenes <- head(order(-rowVars(assay(rld))),35)
```

The heatmap becomes more interesting if we do not look at absolute
expression strength but rather at the amount by which each gene
deviates in a specific sample from the gene's average across all
samples. Hence, we center each genes' values across samples,
and plot a heatmap. We provide the column side colors to help identify
the treated samples (in blue) from the untreated samples (in grey).

```{r genescluster, fig.height=9}
colors <- colorRampPalette( rev(brewer.pal(9, "PuOr")) )(255)
sidecols <- c("grey","dodgerblue")[ rld$dex ]
mat <- assay(rld)[ topVarGenes, ]
mat <- mat - rowMeans(mat)
colnames(mat) <- paste0(rld$dex,"-",rld$cell)
heatmap.2(mat, trace="none", col=colors, ColSideColors=sidecols,
          labRow=FALSE, mar=c(10,2), scale="row")
```

We can now see blocks of genes which covary across patients. Note that
a set of genes at the top of the heatmap are separating the N061011
cell line from the others. At the bottom of the heatmap, we see a set
of genes for which the treated samples have higher gene expression.

# 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 `r Biocpkg("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 `r Biocpkg("AnnotationDbi")` package and the annotation package
`r Biocannopkg("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
(`r Biocpkg("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](https://support.bioconductor.org) along
with all code used in the analysis.

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

# Resources

Acknowledgements

- Core (Seattle): Sonali Arora, Marc Carlson, Nate Hayden, Jim Hester,
  Valerie Obenchain, Herv&eacute; Pag&egrave;s, Paul Shannon, Dan
  Tenenbaum.

- The research reported in this presentation was supported by the
  National Cancer Institute and the National Human Genome Research
  Institute of the National Institutes of Health under Award numbers
  U24CA180996 and U41HG004059, and the National Science Foundation
  under Award number 1247813. The content is solely the responsibility
  of the authors and does not necessarily represent the official views
  of the National Institutes of Health or the National Science
  Foundation.

[airway]: https://bioconductor.org/packages/airway
[gplots]: https://cran.r-project.org/package=gplots
[ggplot2]:https://cran.r-project.org/package=ggplot2 
[AnnotationDbi]: https://bioconductor.org/packages/AnnotationDbi
[Rsubread]: https://bioconductor.org/packages/Rsubread
[edgeR]: https://bioconductor.org/packages/edgeR
[limma]: https://bioconductor.org/packages/limma
[BaySeq]: https://bioconductor.org/packages/BaySeq
[DESeq2]: https://bioconductor.org/packages/DESeq2