12 months ago by

EMBL European Molecular Biology Laboratory

There's another reason to support Gordon's view. There is a fundamental difference between p-values and FDR: p-values are per-hypothesis (i.e., per-gene) properties, whereas FDR is an average across all rejected hypotheses. I.e., if you have a set of hypotheses (genes) rejected at a certain FDR $\alpha$, then the local fdr for some of these is less than $\alpha$, and for some, more than $\alpha$. The only thing you know is that the FDR overall is $\alpha$.

In general, there is no 1:1 relation between p-value and FDR. In the special case of the Benjamini-Hochberg method, such a 1:1 relation can be constructed (what's called the 'adjusted p-value'), but this assumes that the Benjamini-Hochberg method is used, with no modifications such as filtering, weighting, etc.

This assumption has seemed so natural that often it has not even been questioned (hence the popularity of the 'adjusted p-value' terminology), but in fact is not natural if there is heterogeneity between the tests, e.g., if we know that some tests have more power than others, or some have a higher prior probability of being null than others.

For these reasons, the p-value and not the adjusted p-value is the preferable quantity to use in a volcano plot.