Tag Archives: rnaseq

Beyond Benjamini-Hochberg: Independent Hypothesis Weighting (IHW) for multiple test correction

Multiple hypothesis testing is a critical part of modern bioinformatic analysis.  When testing for significant changes between conditions on many thousands of genes, for instance in an RNA-Seq experiment, the goal is maximize the number of discoveries while controlling the false discoveries.

Typically, this is done by using the Benjamini-Hochberg (BH) procedure, which aims to adjust p-values so that no more than a set fraction (usually 5%) of discoveries are false positives (FDR = 0.05). The BH method is better powered and less stringent than the more strict family-wise error rate (FWER) control, and therefore more appropriate to modern genomics experiments that make thousands of simultaneous comparisons.  However, the BH method is still limited by the fact that it uses only p-values to control the FDR, while treating each test as equally powered.

A new method, Independent Hypothesis Weighting (IHW), aims to take advantage of the fact that individual tests may differ in their statistical properties, such as sample size, true effect size, signal-to-noise ratio, or prior probability of being false.  For example, in an RNA-Seq experiment, highly-expressed genes may have better signal-to-noise than low-expressed genes.

The IHW method applies weights (a non-negative number between zero and one) to each test in a data-driven way.  The input to the method is a vector of p-values (just like BH/FDR) and a vector of continuous or categorical covariates (i.e., any data about each test that is assumed to be independent of the test p-value under the null hypothesis).

From the paper linked above, Table 1 lists possible covariates:

Application Covariate

Differential expression analysis Sum of read counts per gene across all samples [12]
Genome-wide association study (GWAS) Minor allele frequency
Expression-QTL analysis Distance between the genetic variant and genomic location of the phenotype
ChIP-QTL analysis Comembership in a topologically associated domain [16]
t-test Overall variance [9]
Two-sided tests Sign of the effect
Various applications Signal quality, sample size

In simplified form, the IHW method takes the tests and groups them based on the supplied covariate.  It then calculates the number of discoveries (rejections of the null hypothesis) using a set of weights. The weights are iterated until the method converges on the optimal weights for each covariate-based group that maximize the overall discoveries.  Additional procedures are employed to prevent over-fitting of the data and to make the procedure scale easily to millions of comparisons.

The authors of the method claim that IHW is better powered than BH for making empirical discoveries when working with genomic data.  It can be accessed from within Bioconductor.


Beware of biological variability in your *-Seq experiments

From this excellent paper on biological variability in RNA-Seq experiments (bold highlights are mine):

“Biological variability has important implications for the design, analysis and interpretation of RNA-sequencing experiments. […] If only a few biological replicates are available, it will be impossible to estimate the level of biological variability in expression for each gene in a study. Supplementary Table 1 summarizes a large number of published RNA-sequencing studies over the past three years. In every case, except for the two studies we analyzed here, conclusions were based on a small number (n ≤ 2) of biological replicates. One goal of RNA-sequencing studies may be simply to identify and catalog expression of new or alternative transcripts. However, all of these studies make broader biological statements on the basis of a very small set of biological replicates.

Our analysis has two important implications for studies performed with a small number of biological replicates. First, significant results in these studies may be due to biological variation and may not be reproducible; and second, it is impossible to know whether expression patterns are specific to the individuals in the study or are a characteristic of the study populations. These ideas are now widely accepted for DNA microarray experiments, where a large number of biological replicates are now required to justify scientific conclusions. Our analysis suggests that as biological variability is a fundamental characteristic of gene expression, sequencing experiments should be subject to similar requirements.”

If you are doing RNA-Seq, be very vigilant in your experimental design and find a way to incorporate more replicates, even at the expense of testing fewer comparisons.   It’s better to test one comparison (tissue X vs. Y, for example) with 5 or more replicates than to test three comparisons (Tissue X vs. Y, Y vs. Z, and X vx Z) with only 2 replicates for each tissue type.


Create a volcano plot on EBSeq output

The differential expression analysis program EBSeq produces a number of data objects as part of the workflow, but there aren’t many options for visualization of the data.

The authors suggest the use of heatmap.2 in R:

heatmap.2(NormalizedMatrix[GenesOfInterest,], scale=”row”, trace=”none”, Colv=F)

However, this depends on knowing ahead of time your genes of interest.  It is not practical to generate a heatmap with hundreds or thousands of DE genes.

I wanted to produce something approximating a volcano plot for EBSeq results.  What I came up with initially was the following:

A pseudo-volcano plot for EBSeq results.  The y-axis is posterior probability of differential expression (PPDE).
A pseudo-volcano plot for EBSeq results. The y-axis is posterior probability of differential expression (PPDE).

To make this plot, I had to grab some data arrays from the large object “EBOut” that is produced by calling the “EBTest” method and from the “GeneFC” object as below:

plot(GeneFC$PostFC, EBOut$PPDE, 
xlim =c(0,5), ylim=c(0,1), 
main="Control/Experimental FC vs. PPDE",
sub=GeneFC$Direction, xlab="EBSeq Posterior Fold Change", ylab="EBSeq posterior prob of DE")


The “abline” command places a horizontal line where the PPDE is equal to or greater than 95%.  This would be equivalent to an FDR of 0.05.

If you want to inspect the plot interactively in R to identify gene names above the threshold and/or with large posterior fold changes you would use:

identify(GeneFC$PostFC, EBOut$PPDE, labels=names(GeneFC$PostFC))

To make it look more like a canonical volcano plot, I then tried:

plot(log2(GeneFC$RealFC), EBOut$PPDE, 
xlim =c(-5,5), 
main="Log2FoldChange vs. PPDE", 
xlab="EBSeq Log2 Fold Change", ylab="EBSeq PPDE")

Creating the following plot:

Fig 2.  Log(2) Fold Change on the X-axis.
Fig 2. Log(2) Fold Change on the X-axis.

This is good, except I want to subset the data and add colors. To do this I need to create a new dataframe from the EBOut$PPDE and GeneFC$PostFC objects:

volc_df = data.frame(EBOut$PPDE, GeneFC$PostFC)

With everything in one dataframe, plotting and subsetting the data is easier. Inspired by this post at Stephen Turner’s “Getting Genetics Done” blog, I prepared my final colored volcano plot as follows:

with(volc_df, plot(log2(PostFC), PPDE, pch=20, main="Volcano Plot EBSeq", xlim=c(-5,5)))


with(subset(volc_df, PPDE > 0.95 & abs(log2(PostFC)) < 2), points(log2(PostFC), PPDE, pch=20, col="orange")) 

with(subset(volc_df, PPDE > 0.95 & abs(log2(PostFC)) < 2), points(log2(PostFC), PPDE, pch=20, col="red"))

The final plot looks like this:

Fig 3.  The final plot, with colored points for the DE genes, and higher fold change indicated with red.
Fig 3. The final plot, with colored points for the DE genes, and higher fold change indicated with red.