The Beta-pG family of distributions for cure rate regression models

In this paper, we introduce the Beta-pG family of distributions as a flexible framework for modeling long-term survival data. This family extends the traditional Beta-G distribution by incorporating a new parameter p, from which a nonzero long-term survivor fraction is induced through the limiting survival probability. This structure allows the model to capture survival patterns in which a portion of the population remains unaffected by the event of interest over extended follow-up. In particular, we focus on the case where G, the baseline distribution, is specified as the exponential distribution, leading to the Beta-pExponential model. Parameter estimation is performed using maximum likelihood method, allowing likelihood-based inference for the model parameters and the long-term survivor proportions. Monte Carlo simulation studies are conducted to evaluate the finite-sample performance of the estimators across various scenarios. The proposed model is then applied to two melanoma survival datasets, including data from a clinical trial and a population-based cancer registry. In both applications, the fitted model captures the main features of the observed survival curves and provides direct estimates of the long-term survivor proportions. These results illustrate the usefulness of the Beta-pG family as an alternative framework for analyzing survival data with long-term survivors.