A martingale approach to the copula-graphic estimator for the survival function under dependent censoring
A martingale approach to the copula-graphic estimator for the survival function under dependent censoring
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DOI：
10.1006/jmva.2000.1959
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发表时间：
2001-10-01
影响因子：
1.6
通讯作者：
Wells, MT
中科院分区：
文献类型：
--
作者：
Rivest, LP;Wells, MT
产品极限估计是估计齐次样本中生存概率最常用的方法，当生存时间和审查时间相关时，产品极限估计是边际生存函数的不一致估计。最近，M. Zheng和J. P. Klein （1995, Biometrika 82, 127 138）提出了一种用copula函数来模拟依赖关系和生存关系的copula图估计器。这项工作调查了他们的建议。首先导出了用阿基米德联结法对联合生存函数进行建模时的共轭估计量的封闭表达式。然后证明了联图估计量是一致一致和渐近正态的。当生存时间和审查时间相互独立时，它也等价于通常的产品极限估计。本文还对关联模型的规格进行了敏感性分析。(C) 2001学术出版社。
The product limit estimator is arguably the most popular method of estimating survival probabilities in homogeneous samples, When the survival time and the censoring time are dependent, the product-limit estimator is an inconsistent estimator of the marginal survival function. Recently M. Zheng and J. P. Klein (1995, Biometrika 82, 127 138) proposed a copula-graphic estimator that models the dependency bet een censoring and survival using a copula function. This work investigates their proposal. First it derives a closed form expression for the copulagraphic estimator Mien the joint survival function is modeled with in Archimedean copula. The copula-graphic estimator is then shown to be unifomily consistent and asymptotically normal. It is also equivalent to the usual product-limit estimator when the survival and censoring times are assumed to be independent. A sensitivity analysis of the specification of the copula model for the dependency is also presented. (C) 2001 Academic Press.