In this article we extend the factor copula model to deal with right-censored event time data grouped in clusters. The new methodology allows for clusters to have variable sizes ranging from small to large and intracluster dependence to be flexibly modeled by any parametric family of bivariate copulas, thus encompassing a wide range of dependence structures. Incorporation of covariates (possibly time dependent) in the margins is also supported. Three estimation procedures are proposed: both one- and two-stage parametric and a two-stage semiparametric method where marginal survival functions are estimated by using a Cox proportional hazards model. We prove that the estimators are consistent and asymptotically normally distributed, and assess their finite sample behavior with simulation studies. Furthermore, we illustrate the proposed methods on a data set containing the time to first insemination after calving in dairy cattle clustered in herds of different sizes.

在本文中，我们扩展了因子 copula 模型来处理分组在集群中的右删失事件时间数据。新方法允许集群具有从小到大的可变大小，并且集群内依赖可以通过任何双变量 copula 的参数族灵活建模，从而包含广泛的依赖结构。还支持在边距中加入协变量（可能是时间相关的）。提出了三种估计程序：一阶段和两阶段参数和两阶段半参数方法，其中使用 Cox 比例风险模型估计边际生存函数。我们证明估计量是一致且渐近正态分布的，并通过模拟研究评估它们的有限样本行为。此外，