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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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    Cited by:

    1. Margaret Sullivan Pepe & Tianxi Cai & Gary Longton, 2006. "Combining Predictors for Classification Using the Area under the Receiver Operating Characteristic Curve," Biometrics, The International Biometric Society, vol. 62(1), pages 221-229, March.
    2. 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.
    3. Xin Huang & Gengsheng Qin & Yixin Fang, 2011. "Optimal Combinations of Diagnostic Tests Based on AUC," Biometrics, The International Biometric Society, vol. 67(2), pages 568-576, June.
    4. P. Saha & P. J. Heagerty, 2010. "Time-Dependent Predictive Accuracy in the Presence of Competing Risks," Biometrics, The International Biometric Society, vol. 66(4), pages 999-1011, December.
    5. Liang Li & Sheng Luo & Bo Hu & Tom Greene, 2017. "Dynamic Prediction of Renal Failure Using Longitudinal Biomarkers in a Cohort Study of Chronic Kidney Disease," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 357-378, December.
    6. Pablo Martínez-Camblor & Sonia Pérez-Fernández & Susana Díaz-Coto, 2021. "Optimal classification scores based on multivariate marker transformations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 581-599, December.

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