Asymptotically efficient product-limit estimators with censoring indicators missing at random

Abstract

In this paper, we develop methods for estimating a survival function with censoring indicators missing at random. The resulting methods lead to the use of imputation and inverse probability weighting. We give several asymptotically efficient PL estimators. All the estimators are proved to be strongly uniformly consistent and weakly convergent to a Gaussian process. Further, it is shown that these estimators are asymptotically efficient. A simulation study was carried out to evaluate the finite sample performances of the proposed estimators and compare the proposed estimators with van der Laan and McKeague's (1998) estimator under missing at random (MAR) and missing completely at random (MCAR) assumptions, respectively.