Estimating the distribution of nonterminal event time in the presence of mortality or informative dropout.

We consider estimating the distribution of nonterminal event time that may be censored by a terminal event but not vice versa. This problem may arise in two scenarios: (1) clinical trials involving both terminal and nonterminal events, or (2) when the primary outcome of the trial is nonterminal but there exists informative dropout. Inference is complicated by the dependent censoring from mortality or informative dropout. In this paper, we show that the joint distribution of the events can be formulated such that only the association is parameterized, with the marginal distributions unspecified. A closed form estimator for the association parameter is obtained from a novel adaptation of Oakes' concordance estimating equation. Tests for independence and goodness-of-fit of the model are also developed. A computationally simple, consistent and asymptotically normal estimator for the marginal distribution of the nonterminal event is given. Simulations demonstrate that the methods work well with practical sample sizes. The proposals are illustrated with data from an AIDS clinical trial.