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ROC and AUC with a Binary Predictor: a Potentially Misleading Metric

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  • John Muschelli

    (Johns Hopkins Bloomberg School of Public Health)

Abstract

In analysis of binary outcomes, the receiver operator characteristic (ROC) curve is heavily used to show the performance of a model or algorithm. The ROC curve is informative about the performance over a series of thresholds and can be summarized by the area under the curve (AUC), a single number. When a predictor is categorical, the ROC curve has one less than number of categories as potential thresholds; when the predictor is binary, there is only one threshold. As the AUC may be used in decision-making processes on determining the best model, it important to discuss how it agrees with the intuition from the ROC curve. We discuss how the interpolation of the curve between thresholds with binary predictors can largely change the AUC. Overall, we show using a linear interpolation from the ROC curve with binary predictors corresponds to the estimated AUC, which is most commonly done in software, which we believe can lead to misleading results. We compare R, Python, Stata, and SAS software implementations. We recommend using reporting the interpolation used and discuss the merit of using the step function interpolator, also referred to as the “pessimistic” approach by Fawcett (2006).

Suggested Citation

  • John Muschelli, 2020. "ROC and AUC with a Binary Predictor: a Potentially Misleading Metric," Journal of Classification, Springer;The Classification Society, vol. 37(3), pages 696-708, October.
    • Handle: RePEc:spr:jclass:v:37:y:2020:i:3:d:10.1007_s00357-019-09345-1
    DOI: 10.1007/s00357-019-09345-1
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    References listed on IDEAS

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    1. Margaret S. Pepe & Gary Longton & Holly Janes, 2009. "Estimation and comparison of receiver operating characteristic curves," Stata Journal, StataCorp LP, vol. 9(1), pages 1-16, March.
    2. Takaya Saito & Marc Rehmsmeier, 2015. "The Precision-Recall Plot Is More Informative than the ROC Plot When Evaluating Binary Classifiers on Imbalanced Datasets," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-21, March.
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    Cited by:

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    2. Pierre Durand & Gaëtan Le Quang & Arnold Vialfont, 2023. "Are Basel III requirements up to the task? Evidence from bankruptcy prediction models," Working Papers 2308, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    3. Battiston, Pietro & Gamba, Simona & Santoro, Alessandro, 2024. "Machine learning and the optimization of prediction-based policies," Technological Forecasting and Social Change, Elsevier, vol. 199(C).

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    Keywords

    ROC; AUC; Area under the curve; R;
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