Adaptive Bootstrap Tests for Composite Null Hypotheses in the Mediation Pathway Analysis

TL;DR

This paper introduces an adaptive bootstrap testing framework for mediation analysis that effectively handles the composite null hypothesis, improving power and maintaining error control in scientific studies.

Contribution

The paper develops a novel adaptive bootstrap method for mediation tests that better manages the composite null hypothesis, enhancing test power over existing approaches.

Findings

Improved statistical power compared to traditional tests.

Type I error is well-controlled under the composite null.

The method is supported by theoretical analysis and numerical simulations.

Abstract

Mediation analysis aims to assess if, and how, a certain exposure influences an outcome of interest through intermediate variables. This problem has recently gained a surge of attention due to the tremendous need for such analyses in scientific fields. Testing for the mediation effect is greatly challenged by the fact that the underlying null hypothesis (i.e. the absence of mediation effects) is composite. Most existing mediation tests are overly conservative and thus underpowered. To overcome this significant methodological hurdle, we develop an adaptive bootstrap testing framework that can accommodate different types of composite null hypotheses in the mediation pathway analysis. Applied to the product of coefficients (PoC) test and the joint significance (JS) test, our adaptive testing procedures provide type I error control under the composite null, resulting in much improved statistical power compared to existing tests. Both theoretical properties and numerical examples of the proposed methodology are discussed.