Kaplan–Meier Estimator

The Kaplan–Meier estimator is a nonparametric estimator which may be used to estimate the survival distribution function from censored data. The estimator may be obtained as the limiting case of the classical actuarial (life table) estimator, and it seems to have been first proposed by Böhmer [2]. It was, however, lost sight of by later researchers and not investigated further until the important paper by Kaplan & Meier [12] appeared. Today the estimator is usually named after these two authors, although sometimes it is denoted the product–limit estimator (see Aalen–Johansen Estimator). Below we describe the Kaplan–Meier estimator, illustrate its use in one particular case, and discuss estimation of the median and mean survival times. Furthermore, we show how the Kaplan–Meier estimator can be given as the product–integral of the Nelson–Aalen estimator, and indicate how this may be used to study its statistical properties. For almost four decades the Kaplan–Meier estimator has been one of the key statistical methods for analyzing censored survival data, and it is discussed in most textbooks on survival analysis. Rigorous derivations of the statistical properties of the estimator are provided in the books by Fleming & Harrington [7] and Andersen et al. [1]. In particular the latter presents formal proofs of almost all the results reviewed below as well as an extensive bibliography.