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The Kaplan-Meier Estimator as an Inverse-Probability-of-Censoring Weighted Average

Glen A. Satten and Somnath Datta
The American Statistician
Vol. 55, No. 3 (Aug., 2001), pp. 207-210
Stable URL: http://www.jstor.org/stable/2685801
Page Count: 4
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The Kaplan-Meier Estimator as an Inverse-Probability-of-Censoring Weighted Average
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Abstract

The Kaplan-Meier (product-limit) estimator of the survival function of randomly 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 out-put of an imputation scheme for censored observations such as redistribute-to-the-right or self-consistency. Following recent work by Robins and Rotnitzky, we show that the Kaplan-Meier estimator can also be represented as a weighted average of identically distributed terms, where the weights are related to the survival function of censoring times. We give two demonstrations of this representation; the first assumes a Kaplan-Meier form for the censoring time survival function, the second estimates the survival functions of failure and censoring times simultaneously and can be developed without prior introduction to the Kaplan-Meier estimator.

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