On the Mixture and Non-Mixture Cure Fraction Models Based on Fréchet-Weibull Distribution with Application to Cancer Survival Data
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Abstract
Standard survival models do not perform well when clinical data contain a cured fraction of population who will never experience the event. To take care this, we establish mixture and non-mixture cure models based on the Fréchet-Weibull distribution (FWD) and estimate their maximum likelihood estimators. Evaluating these models on clinical data shows that both cure rate models significantly outperform the baseline FWD and Fréchet-Weibull Distribution, Non-Mixture Cure Models. Specifically, the Fréchet-Weibull Distribution, Mixture Cure Model (FWDMCM) yields higher cure estimates, indicating superior suitability for modeling cured proportions. Clinically, Treatment Group I exhibited a higher cured fraction than Group II, a finding validated by Kaplan-Meier survival plots. Mounting cure parameter into the FWD model improves statistical fit and clinical insights for cohorts with long-term survivors. While this study considers a univariate model, extending the proposed framework to bivariate and multivariate contexts presents a key avenue for future research to account for multi-variable influences. For survival data with long-term survivors, implementing mixture cure models is recommended because of the empirical superiority of the Fréchet-Weibull mixture cure model (FWDMCM) over its non-mixture counterpart and standard distribution.
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Copyright (c) 2026 Mohammed Saad, Prof. K. E. Lasisi, Dr. A. Bishir, Dr. U. F. Abbas (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
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