Receiver operating characteristic

A receiver operating characteristic curve, or ROC curve, is a graphical plot that illustrates the performance of a binary classifier model (although it can be generalized to multiple classes) at varying threshold values. ROC analysis is commonly applied in the assessment of diagnostic test performance in clinical epidemiology.

The ROC curve is the plot of the true positive rate (TPR) against the false positive rate (FPR) at each threshold setting.

The ROC can also be thought of as a plot of the statistical power as a function of the Type I Error of the decision rule (when the performance is calculated from just a sample of the population, it can be thought of as estimators of these quantities). The ROC curve is thus the sensitivity as a function of false positive rate.

Given that the probability distributions for both true positive and false positive are known, the ROC curve is obtained as the cumulative distribution function (CDF, area under the probability distribution from

−

∞

{\displaystyle -\infty }

to the discrimination threshold) of the detection probability in the y-axis versus the CDF of the false positive probability on the x-axis.

ROC analysis provides tools to select possibly optimal models and to discard suboptimal ones independently from (and prior to specifying) the cost context or the class distribution. ROC analysis is related in a direct and natural way to the cost/benefit analysis of diagnostic decision making.

Terminology

The true-positive rate is also known as sensitivity or probability of detection. The false-positive rate is also known as the probability of false alarm and equals (1 − specificity).