Testing High-Dimensional Mediation Effect with Arbitrary Exposure-Mediator Coefficients
Yinan Lin, Zijian Guo, Baoluo Sun, Zhenhua Lin
TL;DR
This paper tackles testing the mediation effect in high-dimensional settings where mediators are numerous. It develops a debiased estimator for the mediation effect $\gamma = \beta_A^{\top}\theta_M$ using a variance-enhanced projection direction (VePD) to both correct bias and stabilize variance, yielding a robust test for $\gamma=0$ that remains valid under the composite null and imposes no structural constraints on $\beta_A$. A ridge-augmented covariance is used to prevent super-efficiency issues when $\beta_A$ may be zero, and the test employs a Bonferroni-corrected $\infty$-norm statistic with asymptotic normality under mild high-dimensional assumptions. Theoretical results establish asymptotic validity under $\mathcal{H}_0$ and nontrivial power under local alternatives, with simulations showing robust size control and competitive power, and a LUAD data analysis demonstrating multiple significant mediation pathways through DNA methylation. Overall, the approach provides a principled, assumption-light toolkit for high-dimensional mediation inference with practical applicability to genomics and epidemiology.
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.