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Overestimation of the receiver operating characteristic curve for logistic regression

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  • J. B. Copas

Abstract

Logistic regression is often used to find a linear combination of covariates which best discriminates between two groups or populations. The ROC, receiver operating characteristic, curve is a good way of assessing the performance of the resulting score, but using the same data both to fit the score and to calculate its ROC leads to an over-optimistic estimate of the performance which the score would give if it were to be validated on a sample of future cases. The paper studies the extent of this overestimation, and suggests a shrinkage correction for the ROC curve itself and for the area under the curve. The correction is consistent with Efron's formula for the bias in the error rate of a binary prediction rule. Two medical examples are discussed. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • J. B. Copas, 2002. "Overestimation of the receiver operating characteristic curve for logistic regression," Biometrika, Biometrika Trust, vol. 89(2), pages 315-331, June.
  • Handle: RePEc:oup:biomet:v:89:y:2002:i:2:p:315-331
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    References listed on IDEAS

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    1. Eric Schoen, 1999. "Designing fractional two-level experiments with nested error structures," Journal of Applied Statistics, Taylor & Francis Journals, pages 495-508.
    2. GOOS, Peter, "undated". "The usefulness of optimal design for generating blocked and split-plot response surface experiments," Working Papers 2005033, University of Antwerp, Faculty of Applied Economics.
    3. D. R. Bingham & E. D. Schoen & R. R. Sitter, 2004. "Designing fractional factorial split-plot experiments with few whole-plot factors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(2), pages 325-339.
    4. Bradley Jones & Peter Goos, 2007. "A candidate-set-free algorithm for generating "D"-optimal split-plot designs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(3), pages 347-364.
    5. C. J. Brien & R. A. Bailey, 2006. "Multiple randomizations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 571-609.
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    Cited by:

    1. Margaret Pepe & Tianxi Cai & Zheng Zhang, 2004. "Combining Predictors for Classification Using the Area Under the ROC Curve," UW Biostatistics Working Paper Series 1021, Berkeley Electronic Press.
    2. Liang Li & Sheng Luo & Bo Hu & Tom Greene, 0. "Dynamic Prediction of Renal Failure Using Longitudinal Biomarkers in a Cohort Study of Chronic Kidney Disease," Statistics in Biosciences, Springer;International Chinese Statistical Association, pages 1-22.
    3. repec:spr:stabio:v:9:y:2017:i:2:d:10.1007_s12561-016-9183-7 is not listed on IDEAS

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