DMS Statistics and Data Science Seminar

Speaker: Dr. Shuoyang Wang (Assistant Professor, University of Louisville)

Title: Inference on High-dimensional Mediation Analysis with Convoluted Confounding via Deep Neural Networks

Abstract: Traditional linear mediation analysis has inherent limitations when it comes to handling high-dimensional mediators. Particularly, accurately estimating and rigorously inferring mediation effects is challenging, primarily due to the intertwined nature of the mediator selection issue. Despite recent developments, the existing methods are inadequate for addressing the complex relationships introduced by confounders. To tackle these challenges, we propose a novel approach called DP2LM (Deep neural network based Penalized Partially Linear Mediation). DP2LM incorporates deep neural network techniques to account for nonlinear effects in confounders and utilizes the penalized partially linear model to accommodate high dimensionality.  In addition, to address the influence of outliers on mediation effects, we present an enhanced version of DP2LM called QDP2LM (Quantile Deep Neural Network-based Penalized Partially Linear Mediation). QDP2LM builds upon DP2LM and provides a comprehensive assessment of mediation effects across various quantiles. Unlike most existing works that concentrate on mediator selection, our methods prioritize estimation and inference on mediation effects. Specifically, we develop test procedures for testing the direct and indirect mediation effects. Theoretical analysis shows that the proposed procedures control type I error rates for hypothesis testing on mediation effects. Numerical studies show that the proposed methods outperform existing approaches under a variety of settings, demonstrating their versatility and reliability as modeling tools for complex data. Our application of the proposed methods to study DNA methylation's mediation effects of childhood trauma on cortisol stress reactivity reveals previously undiscovered relationships through a comprehensive analysis.