Abstract The current research paper introduces a novel class of mixture cure models, defined by the minimum of Poisson Stable number of independent and identically distributed random variables. This proposed family of mixture cure models generalizes the classical cure model. In this respect, to introduce this family of long-term lifetime models, we explicitly derive the long-term density, survival and hazard functions. We use the Weibull as a common distribution to define the Poisson Stable Weibull mixture cure model. The identifiability property is corroborated and the quantiles of the survival function for the susceptible individuals are computed. The maximum likelihood approach is used to infer the model’s parameters. A simulation study is undertaken to assess its goodness of fit in terms of parameters estimation. We introduce algorithms, which describe the process of maximum likelihood estimation and simulate samples with right-censored survival times. We demonstrate the model’s ability to predict survival times through its application to real-world data from a population-based breast cancer study.
Ammar et al. (Tue,) studied this question.