Testing High-Dimensional Mediation Effect with Arbitrary Exposure-Mediator Coefficients

TL;DR

This paper introduces a novel high-dimensional mediation test that remains valid under all null hypotheses, including complex cases, without structural assumptions on exposure-mediator effects, demonstrated through simulations and real data.

Contribution

It proposes the first high-dimensional mediation test valid under all null cases and without structural assumptions on exposure-mediator coefficients.

Findings

Test is valid under all null cases including strong effects

Test demonstrates consistency and good performance in simulations

Application shows relevance to DNA methylation and lung cancer

Abstract

In response to the unique challenge created by high-dimensional mediators in mediation analysis, this paper presents a novel procedure for testing the nullity of the mediation effect in the presence of high-dimensional mediators. The procedure incorporates two distinct features. Firstly, the test remains valid under all cases of the composite null hypothesis, including the challenging scenario where both exposure-mediator and mediator-outcome coefficients are zero. Secondly, it does not impose structural assumptions on the exposure-mediator coefficients, thereby allowing for an arbitrarily strong exposure-mediator relationship. To the best of our knowledge, the proposed test is the first of its kind to provably possess these two features in high-dimensional mediation analysis. The validity and consistency of the proposed test are established, and its numerical performance is showcased through simulation studies. The application of the proposed test is demonstrated by examining the mediation effect of DNA methylation between smoking status and lung cancer development.