The Kaplan-Meier estimator as an inverse-probability-of-censoring weightedaverage

The Kaplan-Meier (product-limit) estimator of the survival function of rand omly censored time-to-event data is a central quantity in survival analysis . It is usually introduced as a nonparametric maximum likelihood estimator, or else as the output of an imputation scheme for censored observations su ch as redistribute-to-the-right or self-consistency. Following recent work by Robins and Rotnitzky, we show that the Kaplan-Meier estimator can also b e represented as a weighted average of identically distributed terms, where the weights are related to the survival function of censoring times. We gi ve two demonstrations of this representation; the first assumes a Kaplan-Me ier form for the censoring time survival function, the second estimates the survival functions of failure and censoring times simultaneously and can b e developed without prior introduction to the Kaplan-Meier estimator.