High Dimensional Mediation Analysis with Applications to Causal Gene Identification

Abstract

Mediation analysis has been a popular framework for elucidating the mediating mechanism of the exposure effect on the outcome. Previous literature in causal mediation primarily focused on the classical settings with univariate exposure and univariate mediator, with recent growing interests in high dimensional mediator. In this paper, we study the mediation model with high dimensional exposure and high dimensional mediator, and introduce two procedures for mediator selection, MedFix and MedMix. MedFix is our new application of adaptive lasso with one additional tuning parameter. MedMix is a novel mediation model based on high dimensional linear mixed model, for which we also develop a new variable selection algorithm. Our study is motivated by the causal gene identification problem, where causal genes are defined as the genes that mediate the genetic effect. For this problem, the genetic variants are the high dimensional exposure, the gene expressions the high dimensional mediator, and the phenotype of interest the outcome. We evaluate the proposed methods using a mouse f2 dataset for diabetes study, and extensive real data driven simulations. We show that the mixed model based approach leads to higher accuracy in mediator selection and mediation effect size estimation, and is more reproducible across independent measurements of the response and more robust against model misspecification. The source R code will be made available on Github https://github.com/QiZhangStat/highMed upon the publication of this paper.