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

Louis-Paul Rivest and Martin T. Wells

Journal of Multivariate Analysis, 2001, vol. 79, issue 1, 138-155

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.

Keywords: Archimedean; copula; competing; risks; dependent; censoring; identifiability; product-limit; estimator; martingale; Nelson-Aalen; estimator (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (43)

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