Dirichlet-tree multinomial mixtures for clustering microbiome compositions

Studying the human microbiome has gained substantial interest in recent years, and a common task in the analysis of these data is to cluster microbiome compositions into subtypes. This subdivision of samples into subgroups serves as an intermediary step in achieving personalized diagnosis and treatment. In applying existing clustering methods to modern microbiome studies including the American Gut Project (AGP) data, we found that this seemingly standard task, however, is very challenging in the microbiome composition context due to several key features of such data. Standard distance-based clustering algorithms generally do not produce reliable results as they do not take into account the heterogeneity of the cross-sample variability among the bacterial taxa, while existing model-based approaches do not allow sufficient flexibility for the identification of complex within-cluster variation from cross-cluster variation. Direct applications of such methods generally lead to overly dispersed clusters in the AGP data and such phenomenon is common for other microbiome data. To overcome these challenges, we introduce Dirichlet-tree multinomial mixtures (DTMM) as a Bayesian generative model for clustering amplicon sequencing data in microbiome studies. DTMM models the microbiome population with a mixture of Dirichlet-tree kernels that utilizes the phylogenetic tree to offer a more flexible covariance structure in characterizing within-cluster variation, and it provides a means for identifying a subset of signature taxa that distinguish the clusters. We perform extensive simulation studies to evaluate the performance of DTMM and compare it to state-of-the-art model-based and distance-based clustering methods in the microbiome context. Finally, we report a case study on the fecal data from the AGP to identify compositional clusters among individuals with inflammatory bowel disease and diabetes.