Bayesian graphical compositional regression for microbiome data

An important task in microbiome studies is to test the existence of and give characterization to differences in the microbiome composition across groups of samples. Important challenges of this problem include the large within-group heterogeneities among samples and the existence of potential confounding variables that, when ignored, increase the chance of false discoveries and reduce the power for identifying true differences. We propose a probabilistic framework to overcome these issues by combining three ideas: (i) a phylogenetic tree-based decomposition of the cross-group comparison problem into a series of local tests, (ii) a graphical model that links the local tests to allow information sharing across OTUs and taxonomic levels, and (iii) a Bayesian testing strategy that incorporates covariates and integrates out the within-group variation, avoiding potentially unstable point estimates. We derive an efficient inference algorithm based on numerical integration and junction-tree message passing, conduct extensive simulation studies to investigate the performance of our approach, and compare it to state-of-the-art methods in a number of representative settings. We then apply our method to the American Gut data to analyze the association of dietary habits and human's gut microbiome composition in the presence of covariates, and illustrate the importance of incorporating covariates in microbiome cross-group comparison.