Cure models: from mixture to matrix distributions

TL;DR

This paper introduces a flexible cure model based on phase-type distributions that captures long-term survival and cure mechanisms more accurately than traditional mixture models, with a unified regression framework and EM estimation.

Contribution

It proposes a novel cure model using phase-type distributions, extending classical mixture models, with a unified regression approach and automatic model selection.

Findings

Flexible modeling of long-term survival and cure mechanisms.

Improved estimation accuracy demonstrated through simulations.

Real-data application shows practical advantages.

Abstract

Cure rate models address survival data in which a proportion of individuals will never experience the event of interest. Existing parametric approaches are predominantly based on finite mixtures, which impose restrictive assumptions on both the cure mechanism and the distribution of susceptible event times. A cure model based on phase-type distributions is introduced, leveraging their latent Markov jump process representation to allow immunity to occur either at baseline or dynamically during follow-up. This structure yields a flexible and interpretable formulation of long-term survival while encompassing classical mixture cure models as special cases. A unified regression framework is developed for covariate effects on both the cure rate and the susceptible survival distribution, and the proposed model class is dense, reducing the impact of parametric misspecification. Estimation is performed via expectation-maximization algorithms, accompanied by an automatic model selection strategy. Simulation studies and a real-data example demonstrate the practical advantages of the approach.