Dependent Censoring Based on Copulas

The paper considers survival models in which the survival time and the censoring time are stochastically dependent, which is referred to as dependent censoring. The non-identifiability of a fully nonparametric dependent censoring model leads to challenging problems. A common approach to handle this dependence is based on copulas. To overcome the non-identifiability of the model, the copula can be considered fully known. This is however a heavy assumption in practice, since the strength of the dependence is rarely known. Hence, it results in estimators that can be used for sensitivity analyses but rarely for point estimation of unknown quantities. Recently, a new approach to handle dependent censoring has been proposed, in which the copula is not fully known. The marginal distributions of the survival and censoring time can be modelled parametrically or semiparametrically. The paper describes the literature on these two streams of copula based models.