A Brief Review on Compositional Inference of Microbiome Data

The microbiota can be defined as the collection of all microbes, bacteria, viruses, and fungi living in a host. Recent evidence suggests that the bacterial microbiota of the human gut plays an important role in the pathogenesis of many diseases by promoting inflammation. Historically, the first structured model for data analysis of the human gut microbiota was proposed in (Holmes et al., 2012). The central idea of this model is that the microbiota of a given individual represents a sample of a bacterial metacommunity, also called enterotype. An enterotype therefore represents a particular composition of the microbiota in terms of the relative abundances of different bacterial species. A similar specification was recently proposed in the unsupervised setting in (Anderlucci & Viroli, 2020). In both cases, the focus is on classification, and it was proposed to marginalize with respect to probability distributions over enterotypes to obtain a class-conditional likelihood that depends only on the specific parameters of each component of the mixture and the latent indicator variable of the metacommunity (enterotype). We review these two models available in the literature to highlight their similarities and differences, also discussing possible future research.