ABSTRACT: 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.
Journal of Multivariate Analysis.