Sparse Principal Component based High-Dimensional Mediation Analysis

Abstract: Causal mediation analysis aims to quantify the intermediate effect of a mediator on the causal pathway from treatment to outcome. With multiple mediators, which are potentially causally dependent, the possible decomposition of pathway effects grows exponentially with the number of mediators. Huang and Pan (2016) introduced a principal component analysis (PCA) based approach to address this challenge, in which the transformed mediators are conditionally independent given the orthogonality of the PCs. However, the transformed mediator PCs, which are linear combinations of original mediators, are difficult to interpret. In this study, we propose a sparse high-dimensional mediation analysis approach by adopting the sparse PCA method introduced by Zou and others (2006) to the mediation setting. We apply the approach to a task-based functional magnetic resonance imaging study, and show that our proposed method is able to detect biologically meaningful results related to the identified mediator.