When a recurrent event process is ended by death, this may imply dependent censoring if the two processes are associated. Such dependent censoring would have to be modeled to obtain a valid inference. Moreover, the dependence between the recurrence process and the terminal event may be the primary topic of interest. Joint frailty models for recurrent events and death, which include a separate dependence parameter, have been proposed for exactly observed recurrence times. However, in many situations, only the number of events experienced during consecutive time intervals are available. We propose a method for estimating a joint frailty model based on such interval counts and observed or independently censored terminal events. The baseline rates of the two processes are modeled by piecewise constant functions, and Gaussian quadrature is used to approximate the marginal likelihood. Covariates can be included in a proportional rates setting. The observation intervals for the recurrent event counts can differ between individuals. Furthermore, we adapt a score test for the association between recurrent events and death to the setting in which only individual interval counts are observed. We study the performance of both approaches via simulation studies, and exemplify the methodology in a biodemographic study of the dependence between budding rates and mortality in the species Eleutheria dichotoma.

中文翻译：

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复发事件和死亡间隔计数的联合建模

当循环事件过程因死亡而结束时，如果两个过程相关联，这可能意味着依赖审查。必须对这种依赖审查进行建模才能获得有效的推论。此外，重复过程和终止事件之间的依赖关系可能是主要的兴趣话题。复发事件和死亡的联合衰弱模型包括一个单独的依赖参数，已被提议用于精确观察到的复发时间。然而，在许多情况下，只有在连续时间间隔内经历的事件数量是可用的。我们提出了一种基于此类间隔计数和观察到或独立审查的终端事件来估计联合衰弱模型的方法。两个过程的基线速率由分段常数函数建模，和高斯正交用于近似边缘似然。协变量可以包含在比例比率设置中。重复事件计数的观察间隔可能因人而异。此外，我们将复发事件与死亡之间关联的评分测试调整为仅观察到单个间隔计数的设置。我们通过模拟研究来研究这两种方法的性能，并在生物人口学研究中举例说明了 Eeutheria dichotoma 物种的萌芽率和死亡率之间的依赖性。我们将复发事件与死亡之间关联的评分测试调整为仅观察到单个间隔计数的设置。我们通过模拟研究来研究这两种方法的性能，并在生物人口学研究中举例说明了 Eeutheria dichotoma 物种的萌芽率和死亡率之间的依赖性。我们将复发事件与死亡之间关联的评分测试调整为仅观察到单个间隔计数的设置。我们通过模拟研究来研究这两种方法的性能，并在生物人口学研究中举例说明了 Eeutheria dichotoma 物种的萌芽率和死亡率之间的依赖性。