Testing latent classes in gut microbiome data using generalized Poisson regression models

Human microbiome research has gained increasing importance due to its critical roles in comprehending human health and disease. Within the realm of microbiome research, the data generated often involves operational taxonomic unit counts, which can frequently present challenges such as over‐dispersion and zero‐inflation. To address dispersion‐related concerns, the generalized Poisson model offers a flexible solution, effectively handling data characterized by over‐dispersion, equi‐dispersion, and under‐dispersion. Furthermore, the realm of zero‐inflated generalized Poisson models provides a strategic avenue to simultaneously tackle both over‐dispersion and zero‐inflation. The phenomenon of zero‐inflation frequently stems from the heterogeneous nature of study populations. It emerges when specific microbial taxa fail to thrive in the microbial community of certain subjects, consequently resulting in a consistent count of zeros for these individuals. This subset of subjects represents a latent class, where their zeros originate from the genuine absence of the microbial taxa. In this paper, we introduce a novel testing methodology designed to uncover such latent classes within generalized Poisson regression models. We establish a closed‐form test statistic and deduce its asymptotic distribution based on estimating equations. To assess its efficacy, we conduct an extensive array of simulation studies, and further apply the test to detect latent classes in human gut microbiome data from the Bogalusa Heart Study.