The human microbiome consists of a community of microbes in varying abundances and is shown to be associated with many diseases. An important first step in many microbiome studies is to identify possible distinct microbial communities in a given data set and to identify the important bacterial taxa that characterize these communities. The data from typical microbiome studies are high dimensional count data with excessive zeros due to both absence of species (structural zeros) and low sequencing depth or dropout. Although methods have been developed for identifying the microbial communities based on mixture models of counts, these methods do not account for excessive zeros observed in the data and do not differentiate structural from sampling zeros. In this paper, we introduce a zero-inflated Latent Dirichlet Allocation model (zinLDA) for sparse count data observed in microbiome studies. zinLDA builds on the flexible Latent Dirichlet Allocation model and allows for zero inflation in observed counts. We develop an efficient Markov chain Monte Carlo (MCMC) sampling procedure to fit the model. Results from our simulations show zinLDA provides better fits to the data and is able to separate structural zeros from sampling zeros. We apply zinLDA to the data set from the American Gut Project and identify microbial communities characterized by different bacterial genera.
