Asymptotically efficient estimation of a survival function in the missing censoring indicator model

We propose and analyze a new estimator of a survival function in the random censorship model when the censoring indicator is missing at random for some study subjects. The proposed approach appeals to a known representation for the survival function, expressible as a smooth functional of a certain conditional probability and the cumulative hazard function of the observed minimum. Well-known estimators are substituted into this representation leading to a simple estimator of the survival function. The new estimator, whose asymptotic variance reduces to that of the Kaplan-Meier estimator when all the censoring indicators are observed, is shown to achieve the efficiency bound derived by van der Laan and McKeague.