A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring

✍ Scribed by Louis-Paul Rivest; Martin T. Wells

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 154 KB
• Volume: 79
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.2000.1959

✦ Synopsis

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 between censoring and survival using a copula function. This work investigates their proposal. First it derives a closed form expression for the copulagraphic estimator when the joint survival function is modeled with an Archimedean copula. The copula-graphic estimator is then shown to be uniformly 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.