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Comparing Three-class Diagnostic Tests by Three-way ROC Analysis

Author

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  • Stephan Dreiseitl
  • Lucila Ohno-Machado
  • Michael Binder

Abstract

Three-way ROC surfaces are based on a generalization of dichotomous ROC analysis to three-class diagnostic tests. The discriminatory power of three-class diagnostic tests is measured by the volume under the ROC surface. This measure can be given a probabilistic interpretation similar to the equivalence of the c-index to the area under the ROC curve. This article presents a method to calculate nonparametric estimates of the variance of the volume under the surface using Mann-Whitney U statistics. As a simple extension of this result, it is possible to calculate covariance estimates for the volume under the surface. This allows the statistical comparison of two tests used for diagnostic tasks with three possible outcomes. The formulas derived are validated on synthetic data and applied to a three-class data set of pigmented skin lesions. It is shown that a neural network algorithm trained on clinical data and lesion features performs better than one trained on only the lesion features. Key words: Receiver operating characteristic curves; trichotomous ROC analysis. (Med Decis Making 2000; 20:323-331)

Suggested Citation

  • Stephan Dreiseitl & Lucila Ohno-Machado & Michael Binder, 2000. "Comparing Three-class Diagnostic Tests by Three-way ROC Analysis," Medical Decision Making, , vol. 20(3), pages 323-331, July.
    • Handle: RePEc:sae:medema:v:20:y:2000:i:3:p:323-331
    DOI: 10.1177/0272989X0002000309
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    Cited by:

    1. Waegeman, Willem & De Baets, Bernard & Boullart, Luc, 2008. "On the scalability of ordered multi-class ROC analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3371-3388, March.
    2. Wan, Shuwen & Zhang, Biao, 2015. "Using proportional odds models for semiparametric ROC surface estimation," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 74-79.
    3. Òscar Jordà & Alan M. Taylor, 2011. "Performance Evaluation of Zero Net-Investment Strategies," NBER Working Papers 17150, National Bureau of Economic Research, Inc.
    4. Song Zhang & Yang Qu & Yu Cheng & Oscar L. Lopez & Abdus S. Wahed, 2022. "Prognostic accuracy for predicting ordinal competing risk outcomes using ROC surfaces," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(1), pages 1-22, January.

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