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

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, Biometrika82, 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 copula-graphic 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.