A semiparametric quantile regression rank score test for zero-inflated data

Zero-inflated data commonly arise in various fields, including economics, healthcare, and environmental sciences, where measurements frequently include an excess of zeros due to structural or sampling mechanisms. Traditional approaches, such as Zero-Inflated Poisson and Zero-Inflated Negative Binomial models, have been widely used to handle excess zeros in count data, but they rely on strong parametric assumptions that may not hold in complex real-world applications. In this paper, we propose a zero-inflated quantile single-index rank-score-based test (ZIQ-SIR) to detect associations between zero-inflated outcomes and covariates, particularly when nonlinear relationships are present. ZIQ-SIR offers a flexible, semi-parametric approach that accounts for the zero-inflated nature of the data and avoids the restrictive assumptions of traditional parametric models. Through simulations, we show that ZIQ-SIR outperforms existing methods by achieving higher power and better Type I error control, owing to its flexibility in modeling zero-inflated and overdispersed data. We apply our method to the real-world dataset: microbiome abundance from the Columbian Gut study. In this application, ZIQ-SIR identifies more significant associations than alternative approaches, while maintaining accurate type I error control.