In meta-analysis of individual patient data with semi-competing risks, the joint frailty–copula model has been proposed, where frailty terms account for the between-study heterogeneity and copulas account for dependence between terminal and nonterminal event times. In the previous works, the baseline hazard functions in the joint frailty–copula model are estimated by the nonparametric model or the penalized spline model, which requires complex maximization schemes and resampling-based interval estimation. In this article, we propose the Weibull distribution for the baseline hazard functions under the joint frailty–copula model. We show that the Weibull model constitutes a conjugate model for the gamma frailty, leading to explicit expressions for the moments, survival functions, hazard functions, quantiles, and mean residual lifetimes. These results facilitate the parameter interpretation of prognostic inference. We propose a maximum likelihood estimation method and make our computer programs available in the R package, joint.Cox . We also show that the delta method is feasible to calculate interval estimates, which is a useful alternative to the resampling-based method. We conduct simulation studies to examine the accuracy of the proposed methods. Finally, we use the data on ovarian cancer patients to illustrate the proposed method.

中文翻译：

---

Weibull关节脆弱-copula模型下具有半竞争风险的单个患者数据的Meta分析

在对具有半竞争风险的单个患者数据进行荟萃分析时，提出了联合脆弱-copula模型，其中脆弱术语解释了研究之间的异质性，copula解释了最终事件和非最终事件之间的依赖性。在先前的工作中，通过非参数模型或惩罚样条模型来估计脆弱联合模型中的基线危害函数，这需要复杂的最大化方案和基于重采样的区间估计。在本文中，我们提出了脆弱联合体模型下基线危害函数的威布尔分布。我们表明，威布尔模型构成了伽玛脆弱的共轭模型，导致了力矩，生存函数，危害函数，分位数和平均剩余寿命的明确表达。这些结果有助于对预后推断的参数解释。我们提出了一种最大似然估计方法，并在R包中提供了我们的计算机程序， joint.Cox 。我们还表明，增量法对计算区间估计值是可行的，这是基于重采样的方法的有用替代方法。我们进行仿真研究，以检验所提出方法的准确性。最后，我们使用卵巢癌患者的数据来说明所提出的方法。