Scalable Bayesian Semiparametric Additive Regression Models For Microbiome Studies

Statistical analysis of microbiome data is challenging. Bayesian multinomial logistic-normal (MLN) models have gained popularity due to their ability to account for the count compositional nature of these data, but existing approaches are either computationally intractable or restricted to purely parametric or non-parametric methods, which limit their flexibility and scalability. In this work, we introduce \textit{MultiAddGPs}, a novel semi-parametric framework that integrates additive Gaussian Process (GP) regression within a Bayesian MLN model to disentangle linear and non-linear covariate effects, including non-stationary dynamics. Our approach builds on the computationally efficient Collapse-Uncollapse (CU) sampler and additive GP regression, introducing a novel back-sampling algorithm and marginal likelihood approximation for efficient inference and hyperparameter estimation. Our models are over 240,000 times faster than alternatives while simultaneously producing more accurate posterior estimates. Additionally, we incorporate non-stationary kernel functions designed to model treatment interventions and disease effects. We demonstrate our approach using simulated and real data studies and produce novel biological insights from a previously published human gut microbiome study. Our methods are publicly available as part of the \textit{fido} software package on CRAN \footnotemark.