ROC and AUC with a Binary Predictor: a Potentially Misleading Metric
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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 only as many thresholds as the one less than number of categories; 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 believe a linear interpolation from the ROC curve with binary predictors, which is most commonly done in software, corresponding to the estimated AUC. We believe these ROC curves and AUC can lead to misleading results. We compare R, Python, Stata, and SAS software implementations.
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