Cure models: from mixture to matrix distributions

2026-01-27

AI Summary

This study addresses the limitations of traditional cure rate models, which rely on fixed mixture structures and struggle to capture the dynamic emergence of immune states. To overcome this, we propose a cure rate model based on phase-type distributions, leveraging their representation as latent Markov jump processes to allow individuals to enter an immune state dynamically—either at baseline or during follow-up. The framework unifies regression modeling for both the probability of being cured and the survival distribution of the susceptible subgroup, accommodating covariate effects on both components. The proposed model generalizes classical mixture cure models as a special case, benefits from the denseness property of phase-type distributions to mitigate parametric misspecification, and integrates an expectation–maximization algorithm with an automated model selection strategy. Simulation studies and real-data analyses demonstrate that our approach substantially outperforms existing methods in flexibility, interpretability, and goodness-of-fit.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• cure models
• survival data
• mixture models
• phase-type distributions
• parametric misspecification

Innovation

• cure rate models
• phase-type distributions
• Markov jump process
• mixture models
• EM algorithm