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

**Authors:** Roulan Jiang, Xiang Zhan, Tianying Wang  
**arXiv:** [2207.07796](https://arxiv.org/abs/2207.07796)  
**Date:** 2022-07-16  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2207.07796v2/

## Key points

- Microbiome study involves analyzing microbial communities in various ecosystems
- Estimating population proportion of different taxa within these communities is crucial but challenging due to biases introduced during sampling and preprocessing steps
- Repeated measures and longitudinal study designs can help mitigate the discrepancy between observed and true underlying abundances
- Downstream statistical analyses can still be distorted by zero-inflation and over-dispersion issues
- The Zero-Inflated Poisson Gamma (ZIPG) framework decomposes the mean parameter in Poisson regression into a true abundance level and a multiplicative measurement of sampling variability from the microbial ecosystem
- The ZIPG model provides a flexible way to connect both mean abundance and variability to different covariates while building valid statistical inference procedures for parameter estimation and hypothesis testing
- The proposed method provides significant insights into distinguished differential variability and abundance, offering an innovative approach for addressing common challenges in microbiome studies.

## Summary

The study of microbiomes involves the analysis of microbial communities in various ecosystems, such as the gut microbiota community. Estimating the population proportion of different taxa within these communities is a crucial task, but it can be challenging due to biases introduced during sampling and preprocessing steps. These biases can lead to observed taxa abundances that do not reflect the true abundance patterns in the ecosystem. To address this issue, repeated measures and longitudinal study designs are potential solutions that can help mitigate the discrepancy between observed and true underlying abundances. However, downstream statistical analyses aiming to associate taxa abundances with covariates of interest can still be distorted by widely observed zero-inflation and over-dispersion issues. To overcome these challenges, this study proposes a Zero-Inflated Poisson Gamma (ZIPG) framework that decomposes the mean parameter in Poisson regression into a true abundance level and a multiplicative measurement of sampling variability from the microbial ecosystem. This approach accommodates discrepancies between observations and truths from a perspective of measurement errors. The ZIPG model provides a flexible way to connect both mean abundance and variability to different covariates while building valid statistical inference procedures for parameter estimation and hypothesis testing. Through comprehensive simulation studies and real data applications, this proposed method provides significant insights into distinguished differential variability and abundance. Overall, this study presents an innovative approach for addressing common challenges in microbiome studies related to estimating population proportions of different taxa within microbial communities while accounting for biases introduced during sampling and preprocessing steps. The proposed ZIPG framework offers a flexible solution that can improve downstream statistical analyses aimed at identifying associations between taxa abundances and covariates of interest.