cient Estimation of a MultivariateSurvival Function in Longitudinal Studies

In this paper we develop a locally eecient one-step estimator of a multivariate survival function and functionals thereof when all time-variables are subject to right-censoring by a common censoring variable. In particular, this estimator can be applied to estimate the gap time distributions corresponding with an ordered sequence of events. This estimator can incorporate a time-dependent covariate process measured to end of follow. The estimator requires substitution of an estimator of the censoring mechanism, assuming that it satisses coarsening at random, and an estimator of the full-data distribution of ~ T , given an observed full-data history at various points in time. Our proposed locally eecient one-step estimator is consistent and asymptotically normal if the censoring process is estimated consistently and it is eecient if the conditional distribution of ~ T , given the full-data history, is estimated consistently as well. In addition, we show that the estimator is consistent and asymptotically normal if the conditional distribution of ~ T , given the covariates, is estimated consistently, even when the censoring mechanism is estimated inconsistently. The practical performance of the method is tested with a simulation study. We also provide a data analysis applying the proposed methodology.