Zero-Inflated gaussian mixed models for analyzing longitudinal microbiome data

Abstract

Motivation The human microbiome is variable and dynamic in nature. Longitudinal studies could explain the mechanisms in maintaining the microbiome in health or causing dysbiosis in disease. However, it remains challenging to properly analyze the longitudinal microbiome data from either 16S rRNA or metagenome shotgun sequencing studies, output as proportions or counts. Most microbiome data are sparse, requiring statistical models to handle zero-inflation. Moreover, longitudinal design induces correlation among the samples and thus further complicates the analysis and interpretation of the microbiome data. Results In this article, we propose zero-inflated Gaussian mixed models (ZIGMMs) to analyze longitudinal microbiome data. ZIGMMs is a robust and flexible method which can be applicable for longitudinal microbiome proportion data or count data generated with either 16S rRNA or shotgun sequencing technologies. It can include various types of fixed effects and random effects and account for various within-subject correlation structures, and can effectively handle zero-inflation. We developed an efficient Expectation-Maximization (EM) algorithm to fit the ZIGMMs by taking advantage of the standard procedure for fitting linear mixed models. We demonstrate the computational efficiency of our EM algorithm by comparing with two other zero-inflated methods. We show that ZIGMMs outperform the previously used linear mixed models (LMMs), negative binomial mixed models (NBMMs) and zero-inflated Beta regression mixed model (ZIBR) in detecting associated effects in longitudinal microbiome data through extensive simulations. We also apply our method to two public longitudinal microbiome datasets and compare with LMMs and NBMMs in detecting dynamic effects of associated taxa.

Statistical challenges in longitudinal microbiome data analysis

“…Ignoring the ordering of data points and the continuity of changes across time in the statistical analysis can lead to erroneous conclusions [ 21 ]. To model trends in longitudinal microbiome studies, spline models [ 69 ] or linear mixed models (LMMs) that regress the observations as a function of time [ 86 , 88 ] can be used. These models can easily account for missing values observed across time through interpolation.…”

“…However, as samples are collected from the same subject for multiple times, we also need to consider auto-correlation among within-subject samples [ 36 ], where the independent error assumption in standard LMMs is no longer applicable. Dependent within-subjects errors in LMMs [ 86 , 88 ] in the form of auto-regressive of order 1 (AR(1)) or continuous-time auto-regressive of order 1 can be used. A generalized Dirichlet-Multinomial distribution model [ 81 ] has also been proposed as an alternative approach to account for within-subject correlations [ 36 ].…”

“…The model does not account for within-subject correlation structure (i.e. auto-regressive correlation structure) explicitly in the model [ 86 ]. The authors suggested that individual-specific random intercepts were often adequate in practice to capture these correlations.…”

“…Zero-inflated Gaussian mixed models (ZIGMM) was developed to account for within-subject correlations and other properties of microbiome data [ 86 ]. Similar to all methods presented above, ZIGMM is also univariate.…”

Benchmarking Differential Abundance Analysis Methods for Correlated Microbiome Sequencing Data

“…Given the rising popularity of complex study designs involving temporal 55 , spatial 56 , and repeated sampling 4 of the microbiome, statistical tools that could properly address the correlation structure in microbiome data are much needed. Although there are several tools for differential abundance analysis of correlated microbiome data (DAA-c) [26][27][28][29][36][37][38] , their performance has not been evaluated independently by a large-scale benchmarking study. It is unclear whether these methods can control for false positives while retaining sufficient power for real microbiome datasets under diverse settings.…”