Does it make sense to average q-values?

Question

I have 3 lists of significant hits (p-value < 0.05). I also adjusted for multiple comparison problem and added q-values to each list. These 3 lists (hits) also partially overlap. For the hits that overlap I was wondering if it makes sense to average the q-value? So, for instance,

Hit X (List1): pval=0.004, qval=0.0045

Hit X (List2): pval=0.0006, qval=0.0006

Hit X (List3): pval=0.02, qval=0.04

Therefore, to summarize my findings I would add to "Hit X" an average q-val of (0.0045+0.0006+0.04)/3 = 0.0150.

Not sure if that makes sense though?

Answer 1

I'll begin with a question: how are calculating the false discovery rate (FDR)? In a standard Benjamini Hochberg adjustment, you assume independence between tests. Therefore, your assertion that they partially overlap would suggest that you should avoid using the standard Benjamini Hochberg adjustment. Instead you need to adjust without the assumption of independence between tests. To do this you would you use the general case of the FDR:

$FDR \le \frac{{{m_0}}}{m}q\left( {1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{m}} \right) \approx \frac{{{m_0}}}{m}q\log \left( m \right)$

From there, there is now no need to take an average of p-values or of q-values. The whole idea of the multiple testing correction is that you do the correction and then rank your significant hits. I don't see why you would want to average them.