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

Abdullahi, Ibrahim; Phaphan, Wikanda

doi:10.28924/2291-8639-24-2026-185

Research Article

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

Ibrahim Abdullahi*
Wikanda Phaphan

* Corresponding author

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.

How to Cite

I. Abdullahi, W. Phaphan, A Flexible Nakagami–Weibull Mixture Cure Model for Survival Data with Long-Term Survivors, Int. J. Anal. Appl. 24 (2026), 185. https://doi.org/10.28924/2291-8639-24-2026-185

BibTeX

@article{Abdullahi2026,
  author  = {Abdullahi, Ibrahim and Phaphan, Wikanda},
  title   = {A Flexible Nakagami–Weibull Mixture Cure Model for Survival Data with Long-Term Survivors},
  journal = {Int. J. Anal. Appl.},
  volume  = {24},
  year    = {2026},
  pages   = {185},
  doi     = {10.28924/2291-8639-24-2026-185}
}

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