Survival models incorporating cure fractions, commonly known as cure fraction models or long-term survival models, are widely employed in epidemiological studies to account for both immune and susceptible patients in relation to the failure event of interest under investigation. In such studies, there is also a need to estimate the unobservable heterogeneity caused by prognostic factors that cannot be observed. Moreover, the hazard function may exhibit a non-monotonic form, specifically, an unimodal hazard function. In this article, we propose a long-term survival model based on the defective version of the Dagum distribution, with a power variance function (PVF) frailty term introduced in the hazard function to control for unobservable heterogeneity in patient populations, which is useful for accommodating survival data in the presence of a cure fraction and with a non-monotone hazard function. The distribution is conveniently reparameterized in terms of the cure fraction, and then associated with the covariates via a logit link function, enabling direct interpretation of the covariate effects on the cure fraction, which is not usual in the defective approach. It is also proven a result that generates defective models induced by PVF frailty distribution. We discuss maximum likelihood estimation for model parameters and evaluate its performance through Monte Carlo simulation studies. Finally, the practicality and benefits of our model are demonstrated through two health-related datasets, focusing on severe cases of COVID-19 in pregnant and postpartum women and on patients with malignant skin neoplasms.

翻译：包含治愈分数的生存模型，通常称为治愈分数模型或长期生存模型，广泛应用于流行病学研究，以解释与所研究关注失败事件相关的免疫患者和易感患者。在此类研究中，还需要估计由无法观测的预后因素引起的不可观测异质性。此外，风险函数可能呈现非单调形式，具体为单峰风险函数。本文提出一种基于Dagum分布缺陷版本的长期生存模型，在风险函数中引入幂方差函数（PVF）脆弱项以控制患者群体的不可观测异质性，该模型适用于存在治愈分数且风险函数非单调的生存数据。通过以治愈分数进行方便的重新参数化，并借助logit链接函数与协变量关联，可直接解释协变量对治愈分数的影响，这在缺陷方法中并不常见。本文还证明了一个由PVF脆弱分布诱导生成缺陷模型的结果。我们讨论了模型参数的最大似然估计，并通过蒙特卡洛模拟研究评估其性能。最后，通过两个健康相关数据集（重点关注COVID-19重症的孕产妇和恶性皮肤肿瘤患者）展示了我们模型的实用性和优势。