Properties of the marginal survival functions for dependent censored data under an assumed Archimedean copula

Given a random sample from a dependent censored variable ( X, δ) = ( min ( T, C) , 1 ( T < C) ) , general formulas are given for possible marginal survival functions of the failure time T and the censoring time C under the assumption that their underlying copula is Archimedean. These formulas are used to establish the relationship between these possible survival functions, along with useful identifiability results. A new estimator of the marginal survival functions is also proposed, under the assumption that the underlying Archimedean copula is known. Bias formulas for this estimator and other existing estimators are derived. Simulation studies show that the new estimator is comparable with the copula-graphic estimator proposed by Zheng and Klein (1995) and Rivest and Wells (2001), as well as with the estimator of Zheng and Klein (1994) under the Archimedean copula assumption.