  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).
