You might take a look at Benjamini Hochberg in the paper attached. Best wishes David Booth

Do not compare p-values.

Note that for unregulated genes there is just NO correlation between the p-value and the differential gene expression. Observing a "not very small" p-value can have any reason, and there is no quantifyable (un-)certainty for the conjecture that a gene with such a "not very small" p-value is NOT regulated. In short: "absence of evidence is not evidence of absence" (BMJ 1995;311: 485).

You simply don't have a chance to reliably identify genes that are not regulated.

You can test if the regulation for different genes is different. Use an appropriate statistical model for that (this would include a term for the gene x treatment interaction that would be subject to the test).

Typiclly, "omics" studies are explorative, hypothesis-generating. Adjusting p-values then does not make much sense here. p-values (adjusted or not - that does not matter) can be used to rank the list of genes according to their "statistical signal-to-noise ratio".

If you are in position where you need to do a lot of this sort of thing, then you might find it informative to do a more exhaustive study of the effects of multiple testing. In particular because all the "adjustments" you are trying to make are only approximations and are usually treated separately, not in combination. To do this, you need to formalise the complete set and sequence of tests you might have to make (before seeing the data), and then apply this bank of tests to multiple sets of simulated data for which you know the properties that you are trying to identify. A basic starting point be to use either randomly generated data from some model, or randomised versions of an existing dataset (bootstrapping or permutation): both of these would allow you to see what happens in outcomes from you bank of tests if there are actually no dependencies.

However you might think that this would take you too far from what you are actually trying to achieve, in which case the above response by Jochen Wilhelm is good advice.

It sounds like you have a large number of genes that you are comparing across several groups, and you are interested in identifying genes that show significant differences in certain pairwise comparisons but not in others.

To adjust for multiple comparisons in this situation, you can use a method such as the Benjamini-Hochberg (BH) procedure, which controls the false discovery rate (FDR) at a specified level. The BH procedure works by ranking the p-values obtained from the individual tests and applying a correction factor based on the number of tests being performed.

One approach you could consider is to perform the pairwise comparisons (A vs B and C vs D) separately for each gene, and then use the BH procedure to adjust the p-values for each gene. This would allow you to identify genes that show significant differences in one comparison but not the other, and to correct for the multiple comparisons being performed.

Alternatively, you could perform the pairwise comparisons for all genes simultaneously and then use the BH procedure to adjust the p-values for the comparisons overall. This would allow you to identify genes that show significant differences in either comparison, but may not be as sensitive to differences in specific genes.

It is important to carefully consider the multiple comparisons being performed in your analysis and to use an appropriate method to adjust the p-values to account for these comparisons. This will help to ensure that the results of your analysis are reliable and robust.