ROCcurves

ROC curves, or receiver operating characteristic curves, are graphical representations of the performance of a binary classifier as its discrimination threshold is varied. The curve plots the true positive rate (sensitivity) against the false positive rate (1 − specificity) at each threshold. A classifier that assigns higher scores to positive cases will have a curve closer to the top-left corner.

The area under the curve (AUC) summarizes the curve into a single number. An AUC of 0.5 indicates random performance, while an AUC of 1 represents perfect discrimination. The AUC can be interpreted as the probability that a randomly chosen positive instance receives a higher score than a randomly chosen negative one. Computation is typically nonparametric via the trapezoidal rule; ties are handled by standard methods in the software.

ROC curves are widely used to compare binary classifiers across domains such as medicine, finance, and machine learning. They are insensitive to class distribution to some extent, and allow threshold-free comparison; however, they do not reflect calibration, i.e., whether predicted probabilities match actual frequencies. The curves can be extended to multi-class problems (one-vs-rest) and to macro or micro averaging. Alternative evaluation curves, such as precision-recall curves, may be preferred when the positive class is rare.

Limitations and considerations: ROC performance may be misleading if costs of false positives and false negatives differ greatly; the curve treats all thresholds equally. In practice, both discrimination and calibration should be assessed, using additional metrics and calibration plots. Bootstrap methods are often used to estimate confidence intervals for the AUC.