将延迟进入纳入复发事件与终点事件的联合脆弱模型
Incorporating delayed entry into the joint frailty model for recurrent events and a terminal event
AI总结：
针对复发事件与死亡联合建模中的延迟进入和左截断问题，提出基于脆弱分布积分比的边际似然估计方法，并通过模拟及老年尿路感染数据验证。
摘要：
在复发事件研究中，通常需要采用联合建模方法，以考虑由死亡等终点事件导致的潜在相依删失。针对个体从事件过程开始即被观察的情形，已有研究探讨了用于复发事件与死亡、并带有额外相依参数的联合脆弱模型。然而，样本往往是在更晚的时间点被选取，从而产生延迟进入。因此，只有尚未经历终点事件的个体才会被纳入研究。我们提出了一种从此类左截断数据估计联合脆弱模型的方法。如果复发过程与终点事件相关，那么被选存活者中的脆弱分布将不同于潜在总体中的脆弱分布。经过正确校正的边际似然可表示为脆弱分布上两个积分之比，并可使用 Gauss 求积法进行近似。基线率被设定为分段常数函数，并假定协变量对事件率具有乘性效应。我们在模拟研究中评估了该估计程序的性能，并将该方法应用于估计老年人群中复发性尿路感染和死亡的年龄别率。
英文摘要：
In studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events and death with an additional dependence parameter have been studied for cases in which individuals are observed from the start of the event processes. However, the samples are often selected at a later time, which results in delayed entry. Thus, only individuals who have not yet experienced the terminal event will be included in the study. We propose a method for estimating the joint frailty model from such left-truncated data. The frailty distribution among the selected survivors differs from the frailty distribution in the underlying population if the recurrence process and the terminal event are associated. The correctly adjusted marginal likelihood can be expressed as a ratio of two integrals over the frailty distribution, which may be approximated using Gaussian quadrature. The baseline rates are specified as piecewise constant functions, and the covariates are assumed to have multiplicative effects on the event rates. We assess the performance of the estimation procedure in a simulation study, and apply the method to estimate age-specific rates of recurrent urinary tract infections and mortality in an older population.
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