Mediation Analysis with Compositional Exposures.

Understanding the causal pathways linking the gut microbiome to downstream biomarkers and clinical outcomes is central to microbiome research. When the microbiome acts as the exposure, the high dimensionality and compositional structure of the data introduce unique methodological challenges for mediation analysis. To address these challenges, we propose a latent variable mediation framework that captures variation in microbial composition through a microbial balance, defined as the log-ratio between two unknown subsets of taxa. This balance serves as a latent scalar exposure and simplifies the estimation of the overall indirect effect at the community level, while simultaneously identifying specific taxa that contribute to the overall direct and indirect effects. We describe the model's estimation and inference, and illustrate the method using data from the Multiethnic Cohort-Adiposity Phenotype Study, where we examine the mediation pathway from the gut microbiome through lipopolysaccharide-binding protein, a marker of metabolic endotoxemia, to percent liver fat.