An association test based on the mixture of zero-inflated Poisson regression models for detecting differential microbial abundance in case-control studies

Motivation: The human microbial communities play an important role in human health and disease because human metabolism, nutrient intake and energy generation fall under the influence of these communities. Association analysis concerning relative abundances among these communities with status-related outcomes can provide essential information, which can help us to understand the impact that changes in the relative abundances profile can have on disease status. Proper testing of overdispersion and zero-inflated microbiome data is challenging. Existing methods fail to pinpoint the degree of association. Results: In this thesis, we propose a likelihood ratio test for testing the association between the relative abundance of bacteria and disease covariate for microbiome data while using a generalized zero-inflated Poisson regression mixture model. Simulation studies have shown that the likelihood ratio statistic, which examines the null hypothesis that the distribution of the bacterial count arises from healthy individuals and individuals with disease is the same versus the alternative hypothesis that the distribution of the bacterial count arises from healthy individuals and individuals with disease are different, converges to a chi-square distribution. The power of the likelihood ratio test is also evaluated by our simulation study. The application of our proposed method on the real microbiome data has shown that the associated bacteria at the genus level has different distributions of the bacteria counts between the healthy individuals and individuals with carcinoma. Our proposed method provides a useful tool for identifying differentiate taxonomic abundances underlying different disease status.