Abstract

Human microbiome data is crucial for understanding the mechanism of diseases and treatment effectiveness. Researchers often aim to describe how counts of taxa differ among discrete groups (such as control versus treatment) or according to other factors. Most existing models analyze each taxon separately, assuming no correlation between taxa within an individual. In reality, counts of taxa within subjects are correlated. Treating these counts as independent ignores the underlying biological structure in the data and may make it harder to accurately estimate changes in abundances of particular taxa. We developed a model that jointly models all taxa, accounting for the correlations between them. Typical microbiome datasets contain hundreds or thousands of taxa and require thousands or even millions of parameter estimates for the variance-covariance matrix, making it computationally impractical. To address this, we applied rank reduction to the variance-covariance matrix, reducing the number of parameter to be estimated. We conducted simulation studies and real data analysis, comparing our reduced-rank model with three existing models: the negative binomial model in the DESeq R package, and the the negative binomial mixed and zero-inflated negative binomial mixed models in the NBZIMM R package. Our results show that modeling all taxa together and accounting for correlations between taxa improves accuracy in effect estimates, reduces bias, narrows confidence intervals, and increases statistical power compared to modeling taxa independently.

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