Receiver Operating Characteristic Curves (ROC)

ROC curves were originally developed to analyze noisy radio signals. Today, however they are used in many disciplines to evaluate test results. For example, ROC curves are widely used to display a plot of the true positive rate against the false positive rate for the different possible cut-points of a diagnostic test

Consider that you are evaluating a diagnostic test for lung cancer. In addition to the test result, you also have the true answer, whether the patient did or did not have lung cancer.

• For every level of the test, you can now evaluate the number of true positives and the number of true negatives. These values are normally represented as fractions, i.e., the True Positive Fraction (TPF - also called sensitivity) and the True Negative Fraction (TNF - also called specificity).
• It is also defined that the False Negative Fraction (FNF) equals 1-TPF, and the False Positive Fraction (FPF) equals 1-TNF.
• In an ROC curve, for every level of the test, the TPF is plotted against the FPF. The goal is to find the threshold with the best compromise between TPF and FPF.

Aabel's implementation of ROC allows plotting:

• ROC for a single test
• ROC for two tests on paired samples. See the ROC curve and the corresponding ROC summary table in the top image below, from the published data of Hanley, J.A., McNeil, B.J. (1983)
• ROC for two tests on unpaired samples. See the right-hand side ROC curve in the bottom image below
• Aabel ROC (to directly visualize the optimal test value(s) on an ROC curve)
  • Aabel provides a specific implementation to allow projecting the values onto the diagonal line (see the left-hand side ROC curve in the bottom image below).