Regular Article
“Proper” Binormal ROC Curves: Theory and Maximum-Likelihood Estimation

https://doi.org/10.1006/jmps.1998.1218Get rights and content

Abstract

The conventional binormal model, which assumes that a pair of latent normal decision-variable distributions underlies ROC data, has been used successfully for many years to fit smooth ROC curves. However, if the conventional binormal model is used for small data sets or ordinal-category data with poorly allocated category boundaries, a “hook” in the fitted ROC may be evident near the upper-right or lower-left corner of the unit square. To overcome this curve-fitting artifact, we developed a “proper” binormal model and a new algorithm for maximum-likelihood (ML) estimation of the corresponding ROC curves. Extensive simulation studies have shown the algorithm to be highly reliable. ML estimates of the proper and conventional binormal ROC curves are virtually identical when the conventional binormal ROC shows no “hook,” but the proper binormal curves have monotonic slope for all data sets, including those for which the conventional model produces degenerate fits.

References (31)

  • ICRU Report 54

    (1996)
  • M. Kendall et al.

    The advanced theory of statistics

    (1979)
  • D.K. McClish

    Analyzing a portion of the ROC curve

    Medical Decision Making

    (1989)
  • C.E. Metz

    ROC methodology in radiologic imaging

    Investigative Radiology

    (1986)
  • C.E. Metz

    Statistical analysis of ROC data in evaluating diagnostic performance

  • Cited by (272)

    • Comparison of the binormal and Lehman receiver operating characteristic curves

      2024, Communications in Statistics: Simulation and Computation
    View all citing articles on Scopus

    J. A. SwetsR. M. Pickett

    f1

    The authors are grateful to Donald D. Dorfman (The University of Iowa) for stimulating discussions; to John A. Swets (BBN Technologies, Inc.) for pointing out Theodore G. Birdsall's pioneering work on proper binormal ROC curves; and to Benjamin A. Herman (The University of Chicago) for porting PROPROC to the Windows 95 and Macintosh operating systems. This work was supported by Grant DE FG02-94ER6186 from the U. S. Department of Energy. Reprint requests should be addressed to Charles E. Metz, Ph.D., Department of Radiology, MC 2026, The University of Chicago Medical Center, 5841 South Maryland Avenue, Chicago, IL 60637-1470.

    View full text