MELODY: Mediation Analysis in Logistic Regression for High-Dimensional Mediators and a Binary Outcome

Mediation analysis is a pivotal tool for elucidating the indirect effect of an environmental factor or treatment on disease through potentially high-dimensional omics data, such as gene expression profiles. However, traditional mediation analysis methods tailored for binary outcomes often rely on the rare disease assumption in logistic regression and provide inadequate measures of total mediation effect when multiple mediators have effects in different directions. In this paper, we develop a MEdiation analysis framework in LOgistic regression for high-Dimensional mediators and a binarY outcome (MELODY). It leverages a second-moment-based measure analogous to the $R^2$ for linear models to quantify the total mediation effect. We also develop a variable selection procedure for high-dimensional data to reduce bias introduced by non-mediators. Our comprehensive simulations demonstrate the superior performance of MELODY in scenarios with non-rare disease binary outcomes and high-dimensional mediators. We apply MELODY to the Framingham Heart Study of over 5000 individuals to analyze the mediation effects of metabolomics and transcriptomics data on the pathways from sex to incident coronary heart disease.