In many biomedical cohort studies, recurrent or repeated events for individuals can be terminated by a dependent terminal event like death. In this context, the time of death may be associated with the underlying recurrent process and there often exists the dependence between the occurrences of recurrent events. Moreover, there are some situations in which a portion of patients could be cured. In the present study, the term "cured" means that some patients may neither experience any recurrent events nor death induced by the disease under study. We proposed a joint frailty model in the presence of cure fraction for analysis of the recurrent and terminal events and estimated the effect of covariates on the cure rate and both aforementioned events concurrently. The use of two independent gamma distributed frailties in this model enabled us to consider both the dependence between the recurrences and the survival times and the interrecurrences dependence. The model parameters were estimated employing the maximum likelihood method for a piecewise constant and a parametric baseline hazard function. Our proposed model was evaluated by a simulation study and illustrated using a real data set on patients with breast cancer who had undergone surgery.

中文翻译：

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存在治愈分数时复发事件和死亡的联合虚弱模型：在乳腺癌数据中的应用

在许多生物医学队列研究中，个体的复发或重复事件可以通过死亡等依赖性终末事件终止。在这种情况下，死亡时间可能与潜在的复发过程有关，并且复发事件的发生之间往往存在依赖性。而且，在某些情况下，部分患者是可以治愈的。在本研究中，术语“治愈”意味着一些患者可能既不会经历任何复发事件，也不会因所研究的疾病而导致死亡。我们提出了一个存在治愈率的联合衰弱模型，用于分析复发和终末事件，并同时估计协变量对治愈率和上述两种事件的影响。在该模型中使用两个独立的伽马分布弱点使我们能够同时考虑复发和生存时间之间的依赖性以及复发间的依赖性。使用分段常数和参数基线危险函数的最大似然法估计模型参数。我们提出的模型通过模拟研究进行评估，并使用接受过手术的乳腺癌患者的真实数据集进行说明。