NON – MIXTURE CURE FRACTION MODEL BASED ON FRÉCHET-WEIBULL DISTRIBUTION WITH APPLICATION TO CANCER SURVIVAL DATA

Abstract

Traditional survival models struggle when clinical data includes a "cured" fraction of the population who will never experience the event in question. To address this, we developed a non-mixture cure models using the Fréchet-Weibull distribution (FWD) and calculated their maximum likelihood estimates. Evaluations using clinical data show that the cure model significantly outperforms the baseline FWD. Specifically, the Fréchet-Weibull Non - Mixture Cure Model (FWDNMCM) provides higher cure estimates, demonstrating its superior ability to model cured proportions. Clinically, Kaplan-Meier survival plots confirmed that Treatment Group I had a higher cured fraction than Group II. Ultimately, integrating cure parameters into the FWD model enhances both the statistical fit and the clinical insights for cohorts featuring long-term survivors. While this study focuses on a univariate model, extending this framework to bivariate and multivariate contexts to account for multiple variables remains a key avenue for future research. For survival data involving long-term survivors, we strongly recommend implementing Non Mixture cure models, as the FWDNMCM empirically outperforms its standard distribution.