Bayesian Nonparametric Mixed Effects Models in Microbiome Data Analysis

Detecting associations between microbial composition and sample characteristics is one of the most important tasks in microbiome studies. Most of the existing methods apply univariate models to single microbial species separately, with adjustments for multiple hypothesis testing. We propose a Bayesian nonparametric analysis for a generalized mixed effects linear model tailored to this application. The marginal prior on each microbial composition is a Dirichlet Processes, and dependence across compositions is induced through a linear combination of individual covariates, such as disease biomarkers or the subject's age, and latent factors. The latent factors capture residual variability and their dimensionality is learned from the data in a fully Bayesian procedure. We propose an efficient algorithm to sample from the posterior and visualizations of model parameters which reveal associations between covariates and microbial composition. The proposed model is validated in simulation studies and then applied to analyze a microbiome dataset for infants with Type I diabetes.