Abstract
Causal mediation analysis has become popular in recent years. The goal of mediation analyses is to learn the direct effects of exposure on outcome as well as mediated effects on the pathway from exposure to outcome. A set of generalized structural equations to estimate the direct and indirect effects for mediation analysis is proposed when the number of mediators is of high-dimensionality. Specifically, a two-step procedure is considered where the penalization framework can be adopted to perform variable selection. A partial linear model is used to account for a nonlinear relationship among pre-treatment confounders and the response variable in each model. Procedures for estimating the coefficients for the treatment and the mediators in the structural models are developed. The obtained estimators can be interpreted as causal effects without imposing a linear assumption on the model structure. The performance of Sobel's method in obtaining the standard error and confidence interval for the estimated joint indirect effect is also evaluated in simulation studies. Simulation results show a superior performance of the proposed method. It is applied to an epidemiologic study in which the goal is to understand how DNA methylation mediates the effect of childhood trauma on regulation of human stress reactivity.
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