A marginalized two-part Beta regression model for microbiome compositional data

In microbiome studies, an important goal is to detect differential abundance of microbes across clinical conditions and treatment options. However, the microbiome compositional data (quantified by relative abundance) are highly skewed, bounded in [0, 1), and often have many zeros. A two-part model is commonly used to separate zeros and positive values explicitly by two submodels: a logistic model for the probability of a specie being present in Part I, and a Beta regression model for the relative abundance conditional on the presence of the specie in Part II. However, the regression coefficients in Part II cannot provide a marginal (unconditional) interpretation of covariate effects on the microbial abundance, which is of great interest in many applications. In this paper, we propose a marginalized two-part Beta regression model which captures the zero-inflation and skewness of microbiome data and also allows investigators to examine covariate effects on the marginal (unconditional) mean. We demonstrate its practical performance using simulation studies and apply the model to a real metagenomic dataset on mouse skin microbiota. We find that under the proposed marginalized model, without loss in power, the likelihood ratio test performs better in controlling the type I error than those under conventional methods.Author summary: Semi-continuous compositional data are typically analyzed using two-part models which separately describe the probability of zero values and the distribution of positive values. The second part of the model provides a conditional interpretation of covariate effects on the positive response. However, it is of great interest in many applications to assess the covariate effect on the marginal mean of the response. For this purpose, we propose a marginalized two-part model by reparameterizing the marginal mean in Part II. We show that the proposed marginalized two-part model outperforms conventional methods by simulation studies in terms of controlling the Type I error and maximizing the power. We apply our method to a microbiota dataset, and find consistent results with our simulation studies.