Is that necessary to do multiple test correction on mediation analysis

Question

I'm doing a mediation analysis to find the 'significant' mediator between variables X and Y. I have 4 potential mediators (M1,M2,M3,M4) and I conducted 4 univariate mediation analysis. More specifically, I conducted mediation analysis in path X->M1->Y, X->M2->Y, X->M3->Y, X->M4->Y respectively.

Should I do a Bonferroni correction on the p-value of the mediation results? And based on the number of tests, does that mean the adjusted p-value equal to the p-value of indirect effect divided by 4? I'd be very grateful for any suggestions.

Answer 1

Since you are applying multiple univariate analyses, you are testing multiple hypotheses and you should correct for multiple testing. However, Bonferroni is just one way to correct, which controls the family-wise error rate, FWER. The FWER is the probability of at least one false positive. Even among FWER controlling procedures, it is conservative. (Applying the Bonferroni correction, your adjusted p-value would be min{4p, 1}, where p is your nominal p value.)

A less conservative error rate would be to correct the p-values with the false discovery rate (FDR). The false discovery rate is the expected proportion of false positives out of those mediators you call significant.

If you use R, you can get information with references on different correction methods with

?p.adjust

This documentation is also available online.

Incidentally, it so happens that I actually just posted a freely available article on more involved methods for this exact topic, but these approaches probably aren't worth it with only 4 hypotheses.