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Medical Decision Making
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Parametric Three-Way Receiver Operating Characteristic Surface Analysis Using Mathematica

Paul S. Heckerling, MD

Section of General Internal Medicine, Department of Medicine, University of Illinois at Chicago

Three-way receiver operating characteristic (ROC) surface analysis involves the calculation of a volume under an ROC surface (VUS), which is a measure of discriminatory accuracy of 2 diagnostic tests for 3 diseases. Nonparametric methods for calculating VUS and its standard error have been developed. The author presents the code for roc3D, a Mathematica computer program for performing parametric ROC surface analysis. roc3D calculates VUS assuming a multinormal distribution of test results in the 3 diseased populations, provides user-specified pointwise confidence limits for VUS, and displays a 3-dimensional plot of the ROC surface. Limitations of the roc3D program are discussed.

Key Words: three-way receiver operating characteristic • computer programs • Mathematica

Medical Decision Making, Vol. 21, No. 5, 409-417 (2001)
DOI: 10.1177/0272989X0102100507
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