A multiple-testing procedure for high-dimensional mediation hypotheses.

Mediation analysis is of rising interest in epidemiology and clinical trials. Among existing methods, the joint significance (JS) test yields an overly conservative type I error rate and low power, particularly for high-dimensional mediation hypotheses. In this article we develop a multiple-testing procedure that accurately controls the family-wise error rate (FWER) and the false discovery rate (FDR) when testing high-dimensional mediation hypotheses. The core of our procedure is based on estimating the proportions of component null hypotheses and the underlying mixture null distribution of p-values. Theoretical developments and simulation experiments prove that the proposed procedure effectively controls FWER and FDR. Two mediation analyses on DNA methylation and cancer research are presented: assessing the mediation role of DNA methylation in genLetic regulation of gene expression in primary prostate cancer samples; exploring the possibility of DNA methylation mediating the effect of exercise on prostate cancer progression. Results of data examples include wellL-behaved quantile-quantile plots and improved power to detect novel mediation relationships. An R package HDMT implementing the proposed procedure is freely accessible in CRAN.