Inference of Microbial Interactions Using Copula Models with Mixture Margins

TL;DR

This paper introduces a copula-based statistical method with mixed zero-beta margins to accurately infer microbial interactions from sparse relative abundance data, improving network analysis in microbiome studies.

Contribution

It develops a novel two-stage maximum likelihood approach with a likelihood-ratio test for dependence, tailored for microbial data with zero-inflation and compositional constraints.

Findings

The method accurately estimates microbial interactions in simulations.

The likelihood-ratio test outperforms traditional correlation tests.

Application to the American Gut Project data reveals meaningful microbial networks.

Abstract

Quantification of microbial interactions from 16S rRNA and meta-genomic sequencing data is difficult due to their sparse nature, as well as the fact that the data only provides measures of relative abundance. In this paper, we propose using copula models with mixed zero-beta margins for estimation of taxon-taxon interactions using the normalized microbial relative abundances. Copulas allow for separate modeling of the dependence structure from the margins, marginal covariate adjustment, and uncertainty measurement. Our method shows that a two-stage maximum likelihood approach provides accurate estimation of the model parameters. A corresponding two-stage likelihood-ratio test for the dependence parameter is derived. Simulation studies show that the test is valid and more powerful than tests based upon Pearson's and rank correlations. Furthermore, we demonstrate that our method can be used to build biologically meaningful microbial networks based on the data set of the American Gut Project.