Little background

I have used edgeR quite some time now and try to teach others to use it as well. Most of them are familiar with hypothesis testing, means, variances etc, but none looked at RNA-seq data before. So the testing part, i.e. comparing the distribution of two treatments is understandable. However the most troublesome part, at least as I experience it, is understanding the different types of dispersion and how these influence hypothesis testing. I think this is much easier to understand when visually shown, but not as the `BCVplot` but more like density plots for several genes when using common dispersion, trended dispersion and tag wise dispersion. 

Question

How could I best explain the concepts of dispersion and the difference among them to people not familiar with dispersion estimates (see little background)? I prefer a visual approach but I'm not sure how this can be done.

Note again that I read the papers and other question, but this seems either too complicated or too focused such that the whole picture gets hard to grasp. 

Hm. The concepts seem pretty obvious to me, but then again I suppose they would be.

• Common dispersion is the mean dispersion across all genes.
• Trended dispersion is the mean dispersion across all genes with similar abundance. In other words, the fitted value of the mean-dispersion trend.

I suppose I should qualify this by saying that we don't literally compute the mean in edgeR, but rather take the dispersion value that maximizes the adjusted profile likelihood. This is unlikely to be helpful for your audience, so you can probably just simplify it by saying that it's the mean.

For the tagwise dispersions, perhaps the simplest way to proceed would be to make a BCV plot from the output of estimateDisp with prior.df=0. This will yield dispersion estimates without any empirical Bayes shrinkage, i.e., "raw" tagwise estimates that do not share information across genes. You can then compare this to the BCV plot with the default prior.df; you should see that the points are squeezed towards the trend (or towards the common value in red, if you set trend="none"). This should demonstrate how empirical Bayes shrinkage works, effectively squeezing values together to reduce the effect of estimation uncertainty when you have low numbers of replicates.

Now, as for how this affects hypothesis testing - there are three main points, in order of obviousness:

1. Larger dispersions = higher variance between replicates, which reduce power to detect DE.
2. The performance of the model (and thus of the DE analysis) depends on the accuracy of the dispersion estimate. If there is a strong mean-dispersion trend, the common dispersion is obviously unsuitable. If the gene-specific dispersions vary around the trend, the trended dispersion is unsuitable. The "raw" tagwise estimates are unbiased estimates of the gene-specific dispersions, and should be the most suitable, except...
3. The performance of the model also depends on the precision with which the dispersions are estimated. Here, the raw estimates are least stable as they use the least amount of information, whereas the trended (and to a greater extent, common) dispersion estimates share information between genes for greater stability. This is why the shrunken tagwise estimates (that you get with default estimateDisp) are so useful, as they provide a compromise between precision and accuracy.

You may already know that we are now recommending the QL framework with glmQLFit and glmQLFTest for routine GLM-based DE analyses. This introduces another set of concepts, namely the distinction between negative binomial dispersions and quasi-likelihood dispersions. Long story short, the NB dispersions aim to model the mean-dispersion relationship across the entire dataset, while the QL dispersions aim to capture the variability and estimation uncertainty of the dispersion for each gene.