Dependent censoring based on parametric copulas

Abstract

Summary Consider a survival time $T$ that is subject to random right censoring, and suppose that $T$ is stochastically dependent on the censoring time $C$. We are interested in the marginal distribution of $T$. This situation is often encountered in practice. Consider, for example, the case where $T$ is a patient’s time to death from a certain disease. Then the censoring time $C$ could 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, then $T$ and $C$ are 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 between $T$ and $C$, and on parametric marginal distributions for $T$ and $C$. 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 of $(T,C)$ is 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.