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).

研究比较了二元预测变量的 ROC 曲线与 AUC 值之间的关系，在比较软件实现方法时发现线性插值法虽然最为普遍，但不一定得出最正确的性能评价。同时比较了阶梯函数插值法和 pessimistic 插值法的优缺点，建议在结果中说明插值法的使用方式。