# Modeling microbial abundances and dysbiosis with beta-binomial regression

## TL;DR

This paper introduces a beta-binomial regression model for microbiome data that accounts for covariate effects on both relative abundance and variability, enabling detection of dysbiosis characterized by increased variability.

## Contribution

The paper presents a novel beta-binomial model that links covariates to both abundance and overdispersion in microbiome counts, facilitating differential abundance and variability testing.

## Key findings

- Model effectively captures overdispersion related to covariates.
- Enables detection of microbiome dysbiosis through variability analysis.
- Demonstrates superior performance in simulations and soil data application.

## Abstract

Using a sample from a population to estimate the proportion of the population with a certain category label is a broadly important problem. In the context of microbiome studies, this problem arises when researchers wish to use a sample from a population of microbes to estimate the population proportion of a particular taxon, known as the taxon's relative abundance. In this paper, we propose a beta-binomial model for this task. Like existing models, our model allows for a taxon's relative abundance to be associated with covariates of interest. However, unlike existing models, our proposal also allows for the overdispersion in the taxon's counts to be associated with covariates of interest. We exploit this model in order to propose tests not only for differential relative abundance, but also for differential variability. The latter is particularly valuable in light of speculation that dysbiosis, the perturbation from a normal microbiome that can occur in certain disease conditions, may manifest as a loss of stability, or increase in variability, of the counts associated with each taxon. We demonstrate the performance of our proposed model using a simulation study and an application to soil microbial data.