Bayesian Balance-Regression in Microbiome Studies Using Stochastic Search

In microbiome studies, 16S rRNA sequencing is commonly used to quantify the taxonomic abundance of a microbial community. The resulting data are counts of amplicons. However, the total count is not informative because of the sampling, sample preparation, and sequencing processes. These counts are used to obtain estimates of the relative abundance of the taxa, which is compositional with a unit sum constraint. Analysis of compositional data requires special statistical treatment to account for the intrinsic dependence of the components due to this constraint. Balance, defined as the normalized log-ratio of the geometric mean of the values for the two groups of components, provides an interesting way of studying microbial community structure, where the two groups represent the beneficial and detrimental taxa, respectively. Such a balance can be used to quantify dysbiosis of the microbial community that is associated with a clinical outcome. However, identification of the outcome-associated balance is challenging. In this paper, we introduce a Bayesian balance-regression and a Markov Chain Monte Carlo (MCMC) stochastic search algorithm to identify the compositional balance that is associated with the outcome. Specifically, we propose a random walk strategy in MCMC that explores the very large space of all possible balance defined from high-dimensional compositional vector. Simulation studies suggest that the algorithm can identify the bacterial taxa that define the outcome-associated balance with a high probability. The effect of the balance on the outcome can be easily inferred from their predictive posterior distribution. We apply the proposed methods to two human microbiome studies and identify the balance of gut microbiome composition associated with body mass index and risk of inflammatory bowel disease, respectively.