Subsampling-based Tests in Mediation Analysis

TL;DR

This paper introduces a subsampling-based testing procedure for mediation analysis that provides accurate size control and higher detection power by addressing the null hypothesis's complexity.

Contribution

It proposes a novel subsampling method with a pivotal null distribution and a Cauchy combination test to improve mediation effect testing accuracy and power.

Findings

More accurate size control compared to classical methods

Higher detection power in numerical studies

Robust to different null cases in mediation analysis

Abstract

Testing for mediation effect poses a challenge since the null hypothesis (i.e., the absence of mediation effects) is composite, making most existing mediation tests quite conservative and often underpowered. In this work, we propose a subsampling-based procedure to construct a test statistic whose asymptotic null distribution is pivotal and remains the same regardless of the three null cases encountered in mediation analysis. The method, when combined with the popular Sobel test, leads to an accurate size control under the null. We further introduce a Cauchy combination test to construct p-values from different subsample splits, which reduces variability in the testing results and increases detection power. Through numerical studies, our approach has demonstrated a more accurate size and higher detection power than the competing classical and contemporary methods.