Negative Binomial Mixed Models for Analyzing Longitudinal Microbiome Data

Xinyan Zhang, Yu-Fang Pei, Lei Zhang, Boyi Guo, Amanda H. Pendegraft, Wenzhuo Zhuang, Nengjun Yi

The metagenomics sequencing data provide valuable resources for investigating the associations between the microbiome and host environmental/clinical factors and the dynamic changes of microbial abundance over time. The distinct properties of microbiome measurements include varied total sequence reads across samples, over-dispersion and zero-inflation. Additionally, microbiome studies usually collect samples longitudinally, which introduces time-dependent and correlation structures among the samples and thus further complicates the analysis and interpretation of microbiome count data. In this article, we propose negative binomial mixed models (NBMMs) for longitudinal microbiome studies. The proposed NBMMs can efficiently handle over-dispersion and varying total reads, and can account for the dynamic trend and correlation among longitudinal samples. We develop an efficient and stable algorithm to fit the NBMMs. We evaluate and demonstrate the NBMMs method via extensive simulation studies and application to a longitudinal microbiome data. The results show that the proposed method has desirable properties and outperform the previously used methods in terms of flexible framework for modeling correlation structures and detecting dynamic effects. We have developed an R package NBZIMM to implement the proposed method, which is freely available from the public GitHub repository http://github.com//nyiuab//NBZIMM and provides a useful tool for analyzing longitudinal microbiome data.