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Confidence intervals and bands for the binormal ROC curve revisited

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  • Eugene Demidenko

Abstract

Two types of confidence intervals (CIs) and confidence bands (CBs) for the receiver operating characteristic (ROC) curve are studied: pointwise CIs and simultaneous CBs. An optimized version of the pointwise CI with the shortest width is developed. A new ellipse-envelope simultaneous CB for the ROC curve is suggested as an adaptation of the Working--Hotelling-type CB implemented in a paper by Ma and Hall (1993). Statistical simulations show that our ellipse-envelope CB covers the true ROC curve with a probability close to nominal while the coverage probability of the Ma and Hall CB is significantly smaller. Simulations also show that our CI for the area under the ROC curve is close to nominal while the coverage probability of the CI suggested by Hanley and McNail (1982) uniformly overestimates the nominal value. Two examples illustrate our simultaneous ROC bands: radiation dose estimation from time to vomiting and discrimination of breast cancer from benign abnormalities using electrical impedance measurements.

Suggested Citation

  • Eugene Demidenko, 2012. "Confidence intervals and bands for the binormal ROC curve revisited," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 67-79, March.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:1:p:67-79
    DOI: 10.1080/02664763.2011.578616
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    References listed on IDEAS

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    1. Peter G. Hall & Rob J. Hyndman & Yanan Fan, 2003. "Non Parametric Confidence Intervals for Receiver Operating Characteristic Curves," Monash Econometrics and Business Statistics Working Papers 12/03, Monash University, Department of Econometrics and Business Statistics.
    2. Peter Hall, 2004. "Nonparametric confidence intervals for receiver operating characteristic curves," Biometrika, Biometrika Trust, vol. 91(3), pages 743-750, September.
    3. Guangqin Ma & W.J. Hall, 1993. "Confidence Bands for Receiver Operating Characteristic Curves," Medical Decision Making, , vol. 13(3), pages 191-197, August.
    4. James A. Hanley, 1988. "The Robustness of the "Binormal" Assumptions Used in Fitting ROC Curves," Medical Decision Making, , vol. 8(3), pages 197-203, August.
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    Cited by:

    1. Kajal Lahiri & Liu Yang, 2018. "Confidence Bands for ROC Curves With Serially Dependent Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 115-130, January.
    2. Eugene Demidenko, 2016. "The p -Value You Can’t Buy," The American Statistician, Taylor & Francis Journals, vol. 70(1), pages 33-38, February.

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