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Keywords: Adaptive LASSO, Causal inference, Confounding, High-dimensional mediators.
Causal mediation analysis has become popular in recent years, in which researchers not only aim to estimate the causal effect of a treatment, but also try to understand how the treatment affects the outcome through intermediate variables, namely mediators. In this paper, 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 confounder (confounders) and the response variable in each model, given that the interest is in estimating the coefficients for the treatment and the mediators in the structural models. The obtained estimators can be interpreted as causal effects without imposing the 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 our proposed method. The proposed method is applied to investigate how DNA methylation plays a role in the regulation of human stress reactivity impacted by childhood trauma.