Locally Efficient Estimation of a Multivariate Survival Function in Longitudinal Studies
In this paper we develop a locally efficient 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 up. The estimator requires substitution of an estimator of the censoring mechanism, assuming that it satisfies 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 efficient one-step estimator is consistent and asymptotically normal if the censoring process is estimated consistently and it is efficient 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.
Longitudinal Data Analysis and Time Series | Multivariate Analysis | Statistical Methodology | Statistical Models | Statistical Theory | Survival Analysis
van der Laan, Mark J.; Hubbard, Alan E.; and Robins, James M., "Locally Efficient Estimation of a Multivariate Survival Function in Longitudinal Studies" (February 2000). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 82.