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Biometrika 2002 89(2):315-331; doi:10.1093/biomet/89.2.315
© 2002 by Biometrika Trust
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Overestimation of the receiver operating characteristic curve for logistic regression

J.B. Copas1 and P.Corbett1

1 Department of Statistics, University of Warwick, Coventry, CV4 7AL, U.K.jbc@stats.warwick.ac.ukphil@stats.warwick.ac.uk

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.

Key Words: Logistic regression; ROC; Screening score; Shrinkage

Received April 2000. Revised September 2001


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