Statisticians are frequently confronted with highly complex data such as clustered data, missing data or censored data. In this manuscript, we consider hierarchically clustered survival data. This type of data arises when a sample consists of clusters, and each cluster has several, correlated sub-clusters containing various, dependent survival times. Two approaches are commonly used to analysis such data and estimate the association between the survival times within a cluster and/or sub-cluster. The first approach is by using random effects in a frailty model while a second approach is by using copula models. Hereby we assume that the joint survival function is described by a copula function evaluated in the marginal survival functions of the different individuals within a cluster. In this manuscript, we introduce a copula model based on a nested Archimedean copula function for hierarchical survival data, where both the clusters and sub-clusters are allowed to be moderate to large and varying in size. We investigate one-stage, two-stage and three-stage parametric estimation procedures for the association parameters in this model. In a simulation study we check the finite sample properties of these estimators. Furthermore we illustrate the methods on a real life data-set on Chronic Granulomatous Disease.

统计人员经常面临高度复杂的数据，例如集群数据，缺失数据或审查数据。在本手稿中，我们考虑了分层聚类的生存数据。当样本由聚类组成，并且每个聚类有几个相关的子类，其中包含各种相关的生存时间时，就会出现这种类型的数据。通常使用两种方法来分析此类数据并估计群集和/或子群集内的生存时间之间的关联。第一种方法是在脆弱模型中使用随机效应，而第二种方法是使用copula模型。据此，我们假设关节生存功能由在群内不同个体的边缘生存功能中评估的系谱函数描述。在这份手稿中 我们针对嵌套式生存数据引入了基于嵌套的Archimedean copula函数的copula模型，在该模型中，集群和子集群均允许中等到较大且大小不等。我们研究此模型中关联参数的一阶段，两阶段和三阶段参数估计程序。在模拟研究中，我们检查了这些估计量的有限样本属性。此外，我们说明了关于慢性肉芽肿病的现实生活数据集的方法。在模拟研究中，我们检查了这些估计量的有限样本属性。此外，我们说明了关于慢性肉芽肿病的现实生活数据集的方法。在模拟研究中，我们检查了这些估计量的有限样本属性。此外，我们说明了关于慢性肉芽肿病的现实生活数据集的方法。