A Multiple-Testing Procedure for High-Dimensional Mediation Hypotheses

Abstract

Mediation analysis is of rising interest in epidemiologic studies and clinical trials. Among existing methods, the joint significance 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 genetic 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 well-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. Supplementary materials for this article are available online.

Keywords:

• Composite null hypothesis
• Intersection-union test
• Joint significance
• Mediation analysis

Supplementary Materials

Additional definition of mediation, simulation results and data illustration are provided in online supplementary materials.

Acknowledgments

We thank Li Hsu and Richard Barfield for helpful discussions on mediation hypothesis testing.

Additional information

Funding

The authors gratefully acknowledge funding support from National Institute of Health R01 CA222833, U10CA180819, U01 CA182883, and P50CA097186.