Two-stage Adaptive Testing of Large-scale Mediation Hypotheses

In testing large-scale mediation hypotheses, the exposure-mediator and mediator-outcome path-specific p-values obtained for each hypothesis from the same sample can be combined into a pair of asymptotically independent p-values, which can then be used to test a global null hypothesis and a composite mediation null hypothesis, respectively.

A first-stage screening procedure targeting the more stringent global null can effectively reduce the number of mediation hypotheses to be tested in the second stage, which in turn reduces the conservativeness of multiple comparison.

The framework can incorporate any data-adaptive choice of screening threshold in Stage 1, and any step-up false discovery rate control method in Stage 2.

The proposed procedure controls the false discovery rate asymptotically while being consistently well powered across a wide range of scenarios.