Selection of mediators and dependence structure for high-dimensional mediation analysis

Causal mediation analysis examines the potential causal pathways between an exposure variable and outcome through intermediate variables with the goal of estimating direct and indirect effects. In practice, intermediate variables may be high-dimensional, in which case one may first aim to identify the true mediators among them. The dependence structure among mediators may then be studied with the goal of identifying a simple sufficient structure. We propose a two-stage penalized estimation procedure to meet these goals. The first stage involves selecting mediators by identifying non-zero indirect effects via a penalized regression. The second stage aims to simplify the correlation structure among selected mediators enabling the estimation of individual, grouped or joint effects. Through transformation of variables, the correlation selection problem can be reformulated as a standard LASSO problem. The two stages can be performed jointly or sequentially and we study the performance of each implementation through simulation studies. Finally, the proposed approach is applied to a psychiatry study in which the aim is to identify methylation loci that mediate the causal effect of childhood trauma on adult stress level.