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The concordance index C and the Mann-Whitney parameter Pr(X>Y) with randomly censored data

James A Koziol1, Zhenyu Jia

  • 1Department of Molecular and Experimental Medicine, The Scripps Research Institute, La Jolla, CA 92037, USA.

Biometrical Journal. Biometrische Zeitschrift
|July 10, 2009
PubMed

Insights

Harrell's c-index estimates survival distribution separation without censoring. However, with random censoring, it no longer estimates the Mann-Whitney parameter, unlike Efron's recommended estimator.

Area of Science:

  • Statistics
  • Biostatistics
  • Survival Analysis

Background:

  • Harrell's c-index (concordance C) is a common metric for assessing separation between two survival distributions.
  • In scenarios without data censoring, the c-index accurately estimates the Mann-Whitney parameter, Pr(X>Y).
  • This parameter has broad applications across various statistical fields.

Purpose of the Study:

  • To clarify the behavior of Harrell's c-index in the presence of randomly censored data.
  • To highlight the distinction between the c-index and the Mann-Whitney parameter under random censorship.
  • To introduce Efron's maximum likelihood estimator as a recommended alternative for the Mann-Whitney parameter in censored data settings.

Main Methods:

  • Comparative analysis of Harrell's c-index and Efron's maximum likelihood estimator.
  • Theoretical examination of survival distribution separation metrics.
  • Evaluation of parameter estimation under random censorship.

Main Results:

  • Harrell's c-index does not estimate the Mann-Whitney parameter Pr(X>Y) when data is randomly censored.
  • Under random censorship, the c-index estimates a different parameter influenced by censoring distributions.
  • Efron's maximum likelihood estimator remains a valid method for estimating the Mann-Whitney parameter with censored data.

Conclusions:

  • Harrell's c-index interpretation requires careful consideration of data censoring.
  • Efron's estimator is preferred for accurate Mann-Whitney parameter estimation in the presence of random censorship.
  • Understanding these distinctions is crucial for reliable survival data analysis.

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