  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 taxa, 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.
