Efficient Estimation from Right-Censored Data When Failure Indicators are Missing at Random
The Kaplan-Meier estimator of a survival function is well known to be asymp- totically efficient when cause of failure is always observed. It has been an open problem, however, to find an efficient estimator when failure indicators are missing at random. Lo (1991) showed that nonparametric maximum likelihood estimators are inconsistent, and this has led to several proposals of ad hoc estimators, none of which are efficient. We now introduce a sieved-nonparametric maximum likelihood estimator, and show that it is efficient. Our approach is related to the estimation of a bivariate survival function from bivariate right-censored data.
Statistical Methodology | Statistical Theory
van der Laan, Mark J. and McKeague, Ian W., "Efficient Estimation from Right-Censored Data When Failure Indicators are Missing at Random" (August 1997). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 59.