Mixture Margin Random-effects Copula Models for Inferring Temporally Conserved Microbial Co-variation Networks from Longitudinal Data

Longitudinal microbiome studies, in which data on a single subject is collected repeatedly over time, are becoming increasingly common in biomedical research. Such studies provide an opportunity to study the inherently dynamic nature of a microbiome in a way that cannot be done using cross-sectional studies. In this paper, we develop random-effects copula models with mixed zero-beta margins to identify biologically meaningful temporally conserved co-variation between two bacterial taxa, while accounting for the excessive zeros seen in 16S rRNA and metagenomic sequencing data. The model assumes a random-effects model for the dependence parameter in the copulas, which captures the conserved microbial co-variation while allowing for a time-specific dependence parameters. We develop a Monte Carlo EM algorithm for efficient estimation of model parameters and a corresponding Monte Carlo likelihood ratio test for the mean dependence parameter. Simulation studies show that our test controls the Type I error rate and provides an unbiased estimate of the mean dependence parameter. Additionally, we apply our method to a longitudinal pediatric cohort and identify changes in both local and global patterns of microbial co-variation networks in infants treated with antibiotics. Our analysis shows that the no antibiotics network is less dependent on individual taxon, thus making it more stable than the antibiotics network and more robust to both targeted and random attacks. Author summaryIdentification of co-variation between two microbes in microbial communities provides important insights into the community structure and stability. The commonly used measures of co-variation do not handle excessive zeros observed in the data and cannot be applied to longitudinal microbiome data directly. In this paper, we develop random-effects copula models with mixed zero-beta margins to identify biologically meaningful temporally conserved co-variation between two bacterial taxa, while accounting for the excessive zeros seen in 16S rRNA and metagenomic sequencing data. The model captures the conserved microbial co-variations while allowing for a time-specific dependence parameters. We develop an efficient Monte Carlo-based algorithm for parameter estimation and statistical inference. We analyze the data from a pediatric longitudinal cohort and identify changes in both local and global patterns of microbial co-variation networks in infants treated with antibiotics.