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Kaplan–Meier Estimator

  1. Ørnulf Borgan

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a11042

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Borgan, Ø. 2005. Kaplan–Meier Estimator. Encyclopedia of Biostatistics. 4.

Author Information

  1. University of Oslo, Oslo, Norway

Publication History

  1. Published Online: 15 JUL 2005

Abstract

It is described how the Kaplan–Meier estimator can be used to provide a nonparametric estimate of the survival distribution from right- censored data. Problems with estimating the survival distribution with left-truncated data are considered, and it is pointed out that for such data, it may be more useful to estimate conditional survival distributions. Estimation of the median and mean survival times is discussed, and it is described how the Kaplan–Meier estimator may be derived by the redistribute-to-the-right algorithm and how it is the unique self-consistent estimator for right-censored survival data. It is shown how the Kaplan–Meier estimator can be given as the product-integral of the Nelson–Aalen estimator for the cumulative hazard rate, and it is indicated how the product-integral formulation is helpful in the study the of statistical properties of the estimator. Finally, the construction of confidence bands for the survival distribution is considered.

Keywords:

  • censored survival data;
  • confidence bands;
  • Greenwood's formula;
  • mean survival time, median survival time;
  • Nelson–Aalen estimator;
  • product-limit estimator;
  • product-integral