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.

翻译：治愈率模型处理的是生存数据中部分个体永远不会经历感兴趣事件的情况。现有参数化方法主要基于有限混合模型，这对治愈机制和易感事件时间分布都施加了限制性假设。本文引入基于相位型分布的治愈模型，利用其潜在马尔可夫跳跃过程表示，允许免疫在基线或随访期间动态发生。该结构产生了灵活且可解释的长期生存表述形式，同时将经典混合治愈模型作为特例包含其中。建立了统一的回归框架用于协变量对治愈率和易感生存分布的影响分析，所提出的模型类具有稠密性，降低了参数设定错误的影响。通过期望最大化算法进行参数估计，并辅以自动模型选择策略。模拟研究和实际数据示例验证了该方法的实践优势。