A New Nakagami–Weibull Non-Mixture Cure Model with Applications to Right-Censored Survival Data

Cure fraction models provide a useful framework for analysing survival data in which some individuals may never experience the event of interest. This paper introduces a flexible Nakagami–Weibull Non-Mixture Cure (NWNMC) model for right-censored survival data with a long-term surviving fraction, constructed by embedding the Nakagami–Weibull baseline distribution within the promotion-time cure framework. This provides additional flexibility for capturing complex survival and hazard rate behaviours. Several key mathematical properties of the model are established, and parameter estimation is carried out using maximum likelihood under right censoring, with inferential procedures developed based on the observed information matrix. A Monte Carlo simulation study examines the finite-sample performance of the maximum likelihood estimators under different parameter values and sample sizes, showing that the estimators are reliable, with decreasing bias and root mean square error as the sample size increases. The practical usefulness of the proposed model is demonstrated through two real-data applications involving business customer churn and colon cancer survival data. The NWNMC model provides the best fit for the customer churn data and remains competitive for the colon cancer data. These results confirm that the proposed model offers a flexible and effective alternative for modelling heterogeneous survival data with a cure fraction.