Estimating Quantiles and Cure Rate in Survival Data: A Parametric Regression Framework Using the Exponentiated Weibull Distribution

Abstract This paper presents a parametric quantile regression model for survival data that incorporates a cure fraction, addressing limitations of traditional survival models related to clinical interpretability and their limited capacity to account for cured individuals. The proposed model is built upon the exponentiated Weibull distribution and employs a logarithmic link between survival quantiles and covariates, offering a flexible and interpretable framework. Parameter estimation is conducted via an expectation-maximization algorithm within the maximum likelihood framework. Monte Carlo simulation studies assess the model’s performance under varying censoring levels and sample sizes, confirming its ability to yield stable estimates and reliable inference across diverse scenarios. An application to gastric cancer data demonstrates the model’s effectiveness in capturing heterogeneity and uncovering clinically relevant patterns. This methodology advances survival analysis by integrating cure fraction modeling with quantile-based inference in a coherent and robust manner.