A simple and powerful method for large-scale composite null hypothesis testing with applications in mediation analysis.

The article focuses on developing a simple and powerful method for large-scale composite null hypothesis testing, particularly applied to mediation analysis in genome-wide epigenetic studies. It addresses the challenge of testing the composite null hypothesis that at least one of two causal effects (exposure-to-mediator and mediator-to-outcome) is zero, a problem complicated by large-scale multiple testing and the conservativeness of classical tests like Sobel's and joint significance tests. The proposed method directly estimates the type I error by counting observed test statistics in a defined region, providing non-asymptotic theoretical guarantees of type I error control under weak assumptions and demonstrating strong power through extensive simulations. Applied to DNA methylation data from the Normative Aging Study, the method efficiently identifies significant mediators with controlled error rates and substantially faster computation compared to existing approaches.