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In microbiome studies, it is of interest to use a sample from a population ofmicrobes, such as the gut microbiota community, to estimate the populationproportion of these taxa. However, due to biases introduced in sampling andpreprocessing steps, these observed taxa abundances may not reflect true taxaabundance patterns in the ecosystem. Repeated measures, including longitudinalstudy designs, may be potential solutions to mitigate the discrepancy betweenobserved abundances and true underlying abundances. Yet, widely observedzero-inflation and over-dispersion issues can distort downstream statisticalanalyses aiming to associate taxa abundances with covariates of interest. Tothis end, we propose a Zero-Inflated Poisson Gamma (ZIPG) framework to addressthe aforementioned challenges. From a perspective of measurement errors, weaccommodate the discrepancy between observations and truths by decomposing themean parameter in Poisson regression into a true abundance level and amultiplicative measurement of sampling variability from the microbialecosystem. Then, we provide a flexible model by connecting both mean abundanceand the variability to different covariates, and build valid statisticalinference procedures for both parameter estimation and hypothesis testing.Through comprehensive simulation studies and real data applications, theproposed ZIPG method provides significant insights into distinguisheddifferential variability and abundance.

A Flexible Zero-Inflated Poisson-Gamma model with application to microbiome read counts