Nonparametric survival estimation when death is reported with delay

In disease registries there can be a delay between death of a subject and the reporting of this death to the data analyst. If researchers use the Kaplan-Meier estimator and implicitly assumed that subjects who have yet to have death reported are still alive, i.e. are censored at the time of analysis, the Kaplan-Meier estimator is typically inconsistent. Assuming censoring is independent of failure, we provide a simple estimator that is consistent and asymptotically efficient. We also provide estimates of the asymptotic variance of our estimator and simulations that demonstrate the favorable performance of these estimators. Finally, we demonstrate our methods by analyzing AIDS survival data. This analysis underscores the pitfalls of not accounting for delay when estimating the survival distribution and suggests a significant reduction in bias by using our estimator.