Power Enhancement in High-Dimensional Heterogeneous Mediation Analysis

Mediation models are widely used in many scientific areas to understand how an exposure variable impacts an outcome variable through an intermediate variable. In this article, we develop powerful inferential methods to analyze mediation effects in high-dimensional contexts with intercorrelated potential mediators in models with linear and generalized linear outcomes. We draw attention to heterogeneous mediation, and show that existing testing approaches based on the total indirect effect are often underpowered when the mediation effects are not homogeneous. To overcome this limitation, we investigate the root cause and propose new solutions. The proposed tests are equipped with expanded capability to handle heterogeneous and even contrasting mediation effects, and have substantial increases in statistical power compared to existing methods, importantly, without compromising the Type I error rate. We demonstrate robust test performance under different mediation patterns by providing rigorous theoretical justifications and comprehensive numerical studies. The practicality is further demonstrated using a real-data application investigating the mediating role of healthcare expenditures in the relationship between economic growth and public health outcomes. An R package POEM is developed to facilitate practical implementation.