Estimating the survival distribution when ascertainment of vital status is subject to delay

During the interim stages of most large scale clinical trials, knowledge that a patient is alive or dead is usually not up to date. This is due to the pattern of patient visits to hospitals, as well as the administrative set-up used by the study to obtain the information on vital status. If the process of ascertaining vital status is not completely random, then the usual method of estimating the survival curve based on the Kaplan-Meier estimator may be biased. For this situation, we propose another estimator and show that it is consistent and asymptotically normal. Comparison with the Kaplan-Meier estimator is made for several patterns of ascertainment of vital status using numerical simulations.