Regularized estimation for right-censored zero-inflated poisson regression: methods and applications to health data

In biomedical and epidemiological studies, count data frequently exhibit excess zeros, right-censoring, and multicollinearity among covariates features that challenge standard modeling approaches and may compromise inferential validity. To address these complexities, we develop a regularized estimation framework for the right-censored zero-inflated Poisson (RCZIP) regression model. Specifically, we introduce and compare three penalized estimators Ridge, Liu, and a novel Modified Ridge-Type (MRT) estimator each tailored to address multicollinearity while accommodating zero inflation and censoring mechanisms. We assess the performance of the proposed methods via extensive Monte Carlo simulations under varying degrees of censoring and collinearity, using error-based metrics such as mean squared error (MSE), mean absolute error (MAE), and mean squared deviation error (MSDE). Simulation results demonstrate that the MRT estimator consistently outperforms both the maximum likelihood estimator and existing penalized approaches, especially in high-censoring and high-collinearity settings. To illustrate practical relevance, we apply the proposed framework to two real-world health datasets: one on healthcare utilization from the National Health and Nutrition Examination Survey (NHANES), and another on social contact patterns in Mayotte. These applications underscore the utility of regularized RCZIP models in improving estimation accuracy and interpretability in complex biomedical data settings.