A NOTE ON THE KAPLAN-MEIER ESTIMATOR

An anomalous feature of the Kaplan-Meier-estimator is that certain estimated survival probabilities can be decreased when the data are perturbed in a way that improves the overall group survival. All alternative estimator based on the so-called reduced-sample method does not have this disadvantage. However, its construction requires knowledge of the potential censoring times of subjects who were actually observed to fail. If these censoring times are unknown, it is natural to proceed by imputing them. A self-consistency argument shows that this leads back to the Kaplan-Meier estimator. Although the method does not yield a new estimator, it gives some insight into the anomalous behavior of the original one.