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The Area under an ROC Curve with Limited Information

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  • Wilbert B. van den Hout

Abstract

The area under the receiver operating characteristic (ROC) curve of a diagnostic test can be used as a summary measure for its discriminative ability. If only a single point of an ROC curve is available, then the entire form of the ROC curve is unknown and the area under it cannot be calculated. Assuming that the unknown ROC curve is either monotone or concave, lower and upper bounds are derived for the area. From these bounds, the minmax approximations are obtained. Compared to only assuming monotonicity, assuming that the unknown ROC curve is concave renders a higher minmax approximation for the area under it, with tighter bounds.

Suggested Citation

  • Wilbert B. van den Hout, 2003. "The Area under an ROC Curve with Limited Information," Medical Decision Making, , vol. 23(2), pages 160-166, March.
    • Handle: RePEc:sae:medema:v:23:y:2003:i:2:p:160-166
    DOI: 10.1177/0272989X03251246
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    References listed on IDEAS

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    1. Scott B. Cantor & Michael W. Kattan, 2000. "Determining the Area under the ROC Curve for a Binary Diagnostic Test," Medical Decision Making, , vol. 20(4), pages 468-470, October.
    2. Anna N. Angelos Tosteson & Colin B. Begg, 1988. "A General Regression Methodology for ROC Curve Estimation," Medical Decision Making, , vol. 8(3), pages 204-215, August.
    3. Yvonne T. Van Der Schouw & Huub Straatman & Andre L.M. Verbeek, 1994. "ROC Curves and the Areas under Them for Dichotomized Tests," Medical Decision Making, , vol. 14(4), pages 374-381, October.
    4. Jørgen Hilden, 1991. "The Area under the ROC Curve and Its Competitors," Medical Decision Making, , vol. 11(2), pages 95-101, June.
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