A Flexible Nakagami–Weibull Mixture Cure Model for Survival Data with Long-Term Survivors

Abstract

Standard parametric survival models typically assume that all individuals will eventually experience the event of interest, an assumption that may be unrealistic in the presence of long-term survivors. To address this limitation, we propose a new parametric cure rate model called the Nakagami–Weibull Mixture Cure Model (NWMCM). The proposed model incorporates the Nakagami–Weibull distribution as the baseline distribution for susceptible individuals within a classical mixture cure framework, providing greater flexibility for modeling survival data with a cure fraction. Parameter estimation is performed using the maximum likelihood method under right-censored data through numerical optimization, while an EM-type algorithm is outlined to facilitate potential computational implementation. The finitesample performance of the estimators is evaluated through a Monte Carlo simulation study, which demonstrates satisfactory performance in terms of bias and mean squared error. The practical applicability of the proposed model is illustrated using a melanoma survival dataset. The results show that the NWMCM provides an improved goodness-offit compared with several existing mixture cure models based on likelihood and information criteria measures. Overall, the proposed model offers a flexible and useful framework for analyzing survival data with long-term survivors.