ROC plot

ROC (receiver operating characteristic) curves show the ability of a quantitative diagnostic test to classify subjects correctly as the decision threshold is varied.

The ROC plot shows sensitivity (true positive fraction) on the horizontal axis against 1-specificity (false positive fraction) on the vertical axis over all possible decision thresholds.

A diagnostic test able to perfectly identify subjects with and without the condition produces a curve that passes through the upper left corner (0, 1) of the plot. A diagnostic test with no ability to discriminate better than chance produces a diagonal line from the origin (0, 0) to the top right corner (1, 1) of the plot. Most tests lie somewhere between these extremes. If a curve lies below the diagonal line (0, 0 to 1, 1), you can invert it by swapping the decision criteria to produce a curve above the line.

An empirical ROC curve is the simplest to construct. Sensitivity and specificity are calculated using the empirical distributions for the subjects with and without the condition. This method is nonparametric because no parameters are needed to model the behavior of the curve, and it makes no assumptions about the underlying distribution of the two groups of subjects.