Abstract

This paper develops a flexible survival model for data with a cure fraction, where the number of latent risk factors follows a Waring distribution under a minimum activation scheme. The primary objective is to provide a framework that more accurately captures and disentangles the distinct sources of heterogeneity, namely internal (individual susceptibility) and external (unobserved covariates), often confounded in traditional cure rate models. While models based on the Negative Binomial distribution are commonly used, they lack the flexibility to independently characterize these dual sources of variability, thereby limiting their biological interpretability and personalization potential. Motivated by this shortcoming, we propose the Waring frailty model. Its structural properties allow for an explicit decomposition of variance, offering a principled way to distinguish individual-specific risk from contextual or environmental factors. This leads to a personalized cure rate, a critical feature in modern therapeutic areas such as immunotherapy, where patient response is highly heterogeneous. The model’s performance is evaluated through a comprehensive Monte Carlo simulation study and is illustrated with an application to real colon cancer data. The results confirm that the Waring distribution, renowned in accident theory for variance decomposition, provides an effective and interpretable tool for cure rate estimation in survival analysis.

Keywords

frailty model, waring distribution, survival analysis, risk causes, variance decomposition, cure fraction