Max Planck Institute for Demographic Research, Rostock, Germany.
Department of Biomedical Data Sciences, Leiden University Medical Center, Leiden, The Netherlands.
Lifetime Data Anal. 2023 Jul;29(3):585-607. doi: 10.1007/s10985-022-09587-z. Epub 2023 Jan 18.
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, samples are often selected at a later time, which results in delayed entry so that only individuals who have not yet experienced the terminal event will be included. In joint frailty models such left truncation has effects on the frailty distribution that need to be accounted for in both the recurrence process and the terminal event process, if the two are associated. We demonstrate, in a comprehensive simulation study, the effects that not adjusting for late entry can have and derive the correctly adjusted marginal likelihood, which can be expressed as a ratio of two integrals over the frailty distribution. We extend the estimation method of Liu and Huang (Stat Med 27:2665-2683, 2008. https://doi.org/10.1002/sim.3077 ) to include potential left truncation. Numerical integration is performed by Gaussian quadrature, the baseline intensities are specified as piecewise constant functions, potential covariates are assumed to have multiplicative effects on the intensities. We apply the method to estimate age-specific intensities of recurrent urinary tract infections and mortality in an older population.
在复发事件的研究中，通常需要联合建模方法来允许潜在的与终端事件（如死亡）相关的删失。对于从事件过程开始就对个体进行观察的情况，已经研究了用于复发事件和死亡的联合脆弱性模型，以及额外的依赖参数。然而，样本通常是在稍后的时间选择的，这导致延迟进入，只有尚未经历终端事件的个体才会被包括在内。在联合脆弱性模型中，如左截断，对脆弱性分布有影响，需要在复发过程和终端事件过程中进行考虑，如果这两个过程相关的话。我们在一项全面的模拟研究中展示了不调整晚期进入可能产生的影响，并推导出正确调整的边际似然，它可以表示为两个关于脆弱性分布的积分之比。我们扩展了 Liu 和 Huang（统计医学 27:2665-2683，2008. https://doi.org/10.1002/sim.3077）的估计方法，以包括潜在的左截断。数值积分通过高斯求积法进行，基线强度被指定为分段常数函数，潜在协变量被假设对强度有乘法效应。我们将该方法应用于估计老年人群中复发性尿路感染和死亡率的年龄特异性强度。
