Hi,

our group has been using the function DESeq of the library DESeq2 to perform differential expression analysis. We notice than some features get a p-value much smaller than the machine epsilon. There are two points that we find difficult to understand.

  1.  How are these functions generating the p-values, especially those that are smaller than the epsilon of the machine?

  2.  How meaningful is a comparison of p-values that are negligibly small, say 10^(-250) and 10^(-251)?

We would deeply appreciate any help for the understanding of these questions.

O.F.

I wouldn’t make a big difference between very small pvalues, essentially the data is not consistent with a null model, eg many samples with 0 vs many samples with very high counts will give a very small pvalue. Just consider it a rejectable set of genes at an FDR that you specify. Our work (DESeq2 and now apeglm) focuses a lot on effect size estimation, and LFC thresholds greater than 0. Point null rejection as we argue is sometimes a trivial hurdle to pass over for many genes in well powered gene expression studies.

The machine epsilon point I don’t really see what you’re getting at. We can calculate tail probabilities of a distribution.