Microbiome subcommunity learning with logistic-tree normal latent Dirichlet allocation

Mixed-membership (MM) models such as Latent Dirichlet Allocation (LDA) have been applied to microbiome compositional data to identify latent subcommunities of microbial species. These subcommunities are informative for understanding the biological interplay of microbes and for predicting health outcomes. However, microbiome compositions typically display substantial cross-sample heterogeneities in subcommunity compositions -- that is, the variability in the proportions of microbes in shared subcommunities across samples -- which is not accounted for in prior analyses. To address this limitation, we incorporate the logistic-tree normal (LTN) model into LDA to form a new MM model. This model allows cross-sample variation in the composition of each subcommunity around some "centroid" composition that defines the subcommunity. Incorporation of auxiliary P\'olya-Gamma variables enables a computationally efficient collapsed blocked Gibbs sampler to carry out Bayesian inference under this model. We compare the LDA and the new model and show that in the presence of large cross-sample heterogeneity, LDA can produce inference which is sensitive to the specification of the number of subcommunities. As such, the popular strategy of overspecifying the number of subcommunities and hoping that some meaningful subcommunities will emerge alongside artificial ones can lead to misleading conclusions. In contrast, by accounting for such heterogeneity, our new model restores the robustness of the inference in the specification of the number of subcommunities and allows meaningful subcommunities to be identified.