Copula based Cox proportional hazards models for dependent censoring

Most existing copula models for dependent censoring in the literature assume that the parameter defining the copula is known. However, prior knowledge on this dependence parameter is often unavailable. In this paper we propose a novel model under which the copula parameter does not need to be known. The model is based on a parametric copula model for the relation between the survival time (<i>T</i>) and the censoring time (<i>C</i>), whereas the marginal distributions of <i>T</i> and <i>C</i> follow a semiparametric Cox proportional hazards model and a parametric model, respectively. We show that this model is identified, and propose estimators of the nonparametric cumulative hazard and the finite-dimensional parameters. It is shown that the estimators of the model parameters and the cumulative hazard function are consistent and asymptotically normal. We also investigate the performance of the proposed method using finite-sample simulations. Finally, we apply our model and estimation procedure to a follicular cell lymphoma data set.

现有文献中针对相依删失问题的多数连接函数（copula）模型，均假设定义该连接函数的参数为已知量。然而，该相依参数的先验知识往往难以获取。本文提出一种全新模型，无需预设该连接函数参数的取值。该模型以生存时间（T）与删失时间（C）间关系的参数化连接函数模型为基础，其中T与C的边缘分布分别服从半参数Cox比例风险模型与参数模型。本文证明了该模型的可识别性，并提出了非参数累积风险函数与有限维参数的估计方法。研究表明，模型参数与累积风险函数的估计量具备相合性与渐近正态性。此外，本文通过有限样本模拟实验验证了所提方法的性能表现。最后，本文将所提模型与估计流程应用于滤泡性淋巴瘤（follicular cell lymphoma）数据集。