A Bayesian zero‐inflated Dirichlet‐multinomial regression model for multivariate compositional count data

The Dirichlet‐multinomial (DM) distribution plays a fundamental role in modern statistical methodology development and application. Recently, the DM distribution and its variants have been used extensively to model multivariate count data generated by high‐throughput sequencing technology in omics research due to its ability to accommodate the compositional structure of the data as well as overdispersion. A major limitation of the DM distribution is that it is unable to handle excess zeros typically found in practice which may bias inference. To fill this gap, we propose a novel Bayesian zero‐inflated DM model for multivariate compositional count data with excess zeros. We then extend our approach to regression settings and embed sparsity‐inducing priors to perform variable selection for high‐dimensional covariate spaces. Throughout, modeling decisions are made to boost scalability without sacrificing interpretability or imposing limiting assumptions. Extensive simulations and an application to a human gut microbiome dataset are presented to compare the performance of the proposed method to existing approaches. We provide an accompanying R package with a user‐friendly vignette to apply our method to other datasets.