Pseudo self-consistent estimation of a copula model with informative censoring

We consider the case where a terminal event censors a non-terminal event, but not vice versa. When the events are dependent, estimation of the distribution of the non-terminal event is a competing risks problem, while estimation of the distribution of the terminal event is not. The dependence structure of the event times is formulated with the gamma frailty copula on the upper wedge, with the marginal distributions unspecified. With a consistent estimator of the association parameter, pseudo self-consistency equations are derived and adapted to the semiparametric model. Existence, uniform consistency and weak convergence of the new estimator for the marginal distribution of the non-terminal event is established using theories of empirical processes, U-statistics and Z-estimation. The potential practical utility of the methodology is illustrated with simulated and real data sets.