A Random Activation Framework for Cure Models with Waring-Distributed Latent Causes

This paper introduces a random activation framework for cure rate modeling that provides a novel latent mechanistic interpretation of the standard mixture cure model, utilizing a Waring-distributed number of latent causes. The proposed approach represents unobserved heterogeneity through a discrete latent variable interpreted as the number of potential risk factors, providing a flexible and biologically interpretable characterization of individual susceptibility. In contrast to classical competing risks models based on extremal operators or deterministic activation schemes, the event time is assumed to arise from a stochastic selection among latent causes. This random activation mechanism defines a unified probabilistic framework in which the cure fraction emerges naturally as the probability of having zero latent causes. The Waring distribution is adopted to model the latent count structure due to its hierarchical formulation, which accommodates overdispersion and heavy-tailed behavior strictly within the latent parametrization of individual risk factors. Under this framework, while the population survival function mathematically reduces to the classical mixture cure representation, the model provides an alternative structure where covariates directly impact the expected latent burden. Parameter estimation for the identifiable regression structure is performed via maximum likelihood, and the finite-sample performance of the estimators is assessed through Monte Carlo simulations, showing accurate parameter recovery and stable inferential properties. An application to real survival data illustrates the practical relevance and epidemiological interpretability of the proposed framework. Overall, this work extends the understanding of existing cure rate models by integrating latent count structures and stochastic activation within a coherent setting, providing a powerful interpretation tool for heterogeneous survival data with long-term survivors.