Heterogeneous Mediation Analysis for Causal Inference
AbstractMediation analysis is widely used to understand mediating mechanisms of variables in causal inference. However, existing approaches do not consider heterogeneity in mediation effects. Mediators in different sub-populations could have opposite effects on the outcome, and could be difficult to identify under the homogeneous model framework. In this paper, we propose a new mediator selection method, which can identify sub-populations and select mediators in each sub-population for heterogeneous data simultaneously. We perform a multi-directional clustering analysis to determine sub-group mediators and the corresponding subjects. Specifically, to select mediators, we propose a new joint penalty which penalizes the effect of independent variable on a mediator and the effect of a mediator on the response jointly. The proposed algorithm is implemented through the convex-smooth gradient descent. Our numerical studies show that the proposed method outperforms the existing methods for heterogeneous data. We also apply the proposed mediation method to estimate mediation effects of DNA methylation variations in glucocorticoid receptor regulatory network genes for post-traumatic stress disorder (PTSD) among African-Americans. Based on data from the Detroit Neighborhood Health Study, we have found heterogeneous mediators, which are indeed associated with PTSD or traumatic experiences according to literature but were not selected by existing homogeneous mediation selection methods.