Consider a survival time T that is subject to random right censoring, and suppose that T is stochastically dependent on the censoring time C. We are interested in the marginal distribution of T. This situation is often encountered in practice. Consider for instance the case where T is the time to death of a patient suffering from a certain disease. Then, the censoring time C is for instance the time until the person leaves the study or the time until he/she dies from another disease. If the reason for leaving the study is related to the health condition of the patient or if he/she dies from a disease that has similar risk factors as the disease of interest, then T and C are likely dependent. In this paper we propose a new model that takes this dependence into account. The model is based on a parametric copula for the relationship between T and C, and on parametric marginal distributions for T and C. Unlike most other papers in the literature, we do not assume that the parameter defining the copula function is known. We give sufficient conditions on these parametric copula and marginals under which the bivariate distribution of (T;C) is identifed. These sufficient conditions are then checked for a wide range of common copulas and marginal distributions. We also study the estimation of the model, and carry out extensive simulations and the analysis of data on pancreas cancer to illustrate the proposed model and estimation procedure.

翻译：考虑一个生存时间 T, 该时间是随机右检查的, 并假设 T 是随机依赖检查时间的T。 我们对于T的边际分布感兴趣。 这种情况在实践中经常遇到。 例如, 考虑T是患有某种疾病的病人死亡的时间。 然后, C 检查时间是病人离开研究的时间, 或者他/她死于另一种疾病的时间。 如果离开研究的原因与病人的健康状况有关, 或者他/她死于一种具有类似风险因素的疾病, 与该疾病有关, 那么T和C很可能是依赖性的。 在本文中,我们提出了一个考虑到这种依赖性的新模式。 这个模式基于T和C之间的关系以及T和C的参数性边际分布的参数。 与文献中的多数其他文件不同, 我们并不认为确定Copula模式功能的参数是已知的。 我们给这些参数下的条件充足, 也就是具有类似病种风险因素的疾病, 那么T和C可能是依赖的。 在本文中, 我们提出了一个新的模型模式模式, 和边际分布的模型。