Dependent censoring based on parametric copulas

SummaryConsider a survival timethat is subject to random right censoring, and suppose thatis stochastically dependent on the censoring time . We are interested in the marginal distribution of . This situation is often encountered in practice. Consider, for example, the case whereis a patient’s time to death from a certain disease. Then the censoring timecould be the time until the patient leaves the study or the time until death from another cause. If the reason for leaving the study is related to the health condition of the patient, or if the patient dies from a disease that has similar risk factors to the disease of interest, thenandare likely to be dependent. In this paper we propose a new model that takes such dependence into account. The model is based on a parametric copula for the relationship betweenand , and on parametric marginal distributions forand . Unlike most other authors, we do not assume that the parameter defining the copula is known. We give sufficient conditions on these parametric copulas and marginals under which the bivariate distribution ofis identified. These sufficient conditions are then checked for a wide range of common copulas and marginals. We also study the estimation of the model, and carry out extensive simulations and analysis on a pancreatic cancer dataset to illustrate the proposed model and estimation procedure.