Microbiome Data Analysis with Binary Outcome Using Semiparametric Regression Model

In microbiome data analysis, the interest is to infer the relationship among response, covariates and a large number of microbiomes. To model the larger number of microbiomes, we treat them as functional data, and use a semiparametric regression model for their relationship with the response, in which the effects of the covariates are specified as regression coefficients, and that of the microbiome is specified as a functional parameter, via the B-spline, and a logistic link for the outcome. We also infer the correlations among some selected microbiomes. Asymptotic study of model parameters is provided. Simulation study is conducted to evaluate the performance of the method, and the model is applied to analyze real operational taxonomic microbiome data.