Subject-specific dirichlet-multinomial regression for multi-district microbiota data analysis

Many environments within the human body host a collection of micro-organisms called microbiota. Recent findings have linked the composition of the microbiota to the development of different human diseases, includ-ing cancer. Motivated by a recent colorectal cancer (CRC) study, we inves-tigate the effect of clinical factors and diet-related covariates on the micro -biota compositions; for the patients enrolled in this study, microbiota abun-dance counts are collected from three different districts, namely, tumor, fe-cal and salivary samples. Building upon the Dirichlet-multinomial regres-sion framework, we develop a high-dimensional Bayesian hierarchical model that exploits subject-specific regression coefficients to simultaneously bor-row strength across districts and include complex interactions between diet and clinical factors if supported by the data. The proposed method identifies relevant associations through model selection priors and thresholding mech-anisms. Posterior inference is performed via a Markov chain Monte Carlo al-gorithm. We use simulation studies to assess the performance of our method, and found our approach to outperform competing methods that do not ac-count for complex interactions. Finally, a thorough analysis of the CRC data illustrates the benefits of the proposed approach.