Testing high-dimensional mediation effect with arbitrary exposure–mediator coefficients

2023-10-09

Test (Madrid)

AI Summary

Testing the null hypothesis of no mediation effect in high-dimensional settings—particularly when the exposure–mediator relationship may be arbitrarily strong and no structural assumptions are imposed—remains challenging. Method: We propose a robust, adaptive testing procedure based on debiased estimation, residual projection, and data-driven thresholding, integrating Lasso regularization with cross-validated hyperparameter tuning. Contribution/Results: To our knowledge, this is the first method for high-dimensional mediation analysis that simultaneously achieves adaptivity to arbitrary exposure–mediator signal strength and rigorous control of the composite null hypothesis (i.e., all coefficients along both exposure–mediator and mediator–outcome paths equal zero). We establish its asymptotic validity and consistency. Simulations demonstrate well-controlled Type I error rates and high statistical power under both sparse and dense high-dimensional configurations. Empirical application confirms the significant mediating role of DNA methylation in the smoking–lung cancer association.

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.

Problem

• Testing high-dimensional mediation effect validity
• Handling arbitrary exposure-mediator coefficients
• No structural assumptions on exposure-mediator relationship

Innovation

• Valid under all composite null hypothesis cases
• No structural assumptions on exposure-mediator coefficients
• First test with these features in high-dimensional mediation