  In microbiome studies, it is of interest to use a sample from a population of
microbes, such as the gut microbiota community, to estimate the population
proportion of these taxa. However, due to biases introduced in sampling and
preprocessing steps, these observed taxa abundances may not reflect true taxa
abundance patterns in the ecosystem. Repeated measures, including longitudinal
study designs, may be potential solutions to mitigate the discrepancy between
observed abundances and true underlying abundances. Yet, widely observed
zero-inflation and over-dispersion issues can distort downstream statistical
analyses aiming to associate taxa abundances with covariates of interest. To
this end, we propose a Zero-Inflated Poisson Gamma (ZIPG) framework to address
the aforementioned challenges. From a perspective of measurement errors, we
accommodate the discrepancy between observations and truths by decomposing the
mean parameter in Poisson regression into a true abundance level and a
multiplicative measurement of sampling variability from the microbial
ecosystem. Then, we provide a flexible model by connecting both mean abundance
and the variability to different covariates, and build valid statistical
inference procedures for both parameter estimation and hypothesis testing.
Through comprehensive simulation studies and real data applications, the
proposed ZIPG method provides significant insights into distinguished
differential variability and abundance.
