  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 instance the case where T is the time to
death of a patient suffering from a certain disease. Then, the censoring time C
is for instance the time until the person leaves the study or the time until
he/she dies from another disease. If the reason for leaving the study is
related to the health condition of the patient or if he/she dies from a disease
that has similar risk factors as the disease of interest, then T and C are
likely dependent. In this paper we propose a new model that takes this
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 papers in the literature, we do not assume that the
parameter defining the copula function is known. We give sufficient conditions
on these parametric copula and marginals under which the bivariate distribution
of (T;C) is identifed. These sufficient conditions are then checked for a wide
range of common copulas and marginal distributions. We also study the
estimation of the model, and carry out extensive simulations and the analysis
of data on pancreas cancer to illustrate the proposed model and estimation
procedure.
