A Semiparametric Quantile Single-Index Model for Zero-Inflated and Overdispersed Outcomes

We consider the complex data modeling problem motivated by the zero-inflated and overdispersed data from microbiome studies. Analyzing how microbiome abundance is associated with human biological features, such as BMI, is of great importance for host health. Methods based on parametric distributional assumptions, such as zero-inflated Poisson and zero-inflated Negative Binomial regression, have been widely used in modeling such data, yet the parametric assumptions are restricted and hard to verify in real-world applications. We relax the parametric assumptions and propose a semiparametric single-index quantile regression model. It is flexible to include a wide range of possible association functions and adaptable to the various zero proportions across subjects, which relaxes the strong parametric distributional assumptions of most existing zero-inflated data modeling approaches. We establish the asymptotic properties for the index coefficients estimator and quantile regression curve estimation. Through extensive simulation studies, we demonstrate the superior performance of the proposed method regarding model fitting.