A marginal regression model for longitudinal compositional count with application to microbiome data

Music City Center 

Microbiome data from sequencing experiments contain compositional counts of various microbial taxa that exhibit varying levels of zero inflation and overdispersion. We first propose a distribution named adaptively zero-inflated generalized Dirichlet multinomial (AIGDM) that uses GDM to model the relative abundance of the present taxa and the zero-inflation part to model taxa absence when needed. We introduce a likelihood-ratio test to determine the necessity of having the zero-inflation part for each taxon. We then develop an AIGDM-based marginal regression model for longitudinal microbiome compositional counts. The model combines the ability of AIGDM to flexibly model microbial compositions and the ability of the generalized estimating equation method (GEE) to handle correlations between the repeated measures. Under the model, we propose association tests for mean, dispersion, and absence-presence proportion parameters to characterize what aspect of the microbial composition distribution is disrupted by the exposure in a longitudinal study. We also propose an omnibus test by combining these tests to achieve overall power and robustness.

Association test

Compositional data

Generalized Dirichlet multinomial

Sequence count data

Zero inflation 

Section on Statistics in Epidemiology