Efficient Estimation from Right-Censored Data when  
Failure Indicators are Missing at Random

Mark J. van der Laan  and Ian W. McKeague

Abstract:

The Kaplan-Meier estimator of a survival function 
is well known to be asymptotically 
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.