ROC curve

ROC curve

The ROC curve (Receiver Operating Characteristic curve) is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied. The ROC curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings. The ROC curve is used in medicine, radiology, biometrics, and other areas of classification.

History

The ROC curve was first developed during World War II for the analysis of radar signals before it was employed in signal detection theory. Following the attack on Pearl Harbor in 1941, the United States army began new research to increase the prediction of correctly detected Japanese aircraft. ROC analysis provided the tools for optimizing radar signal detection.

Definition and construction

An ROC space is defined by FPR and TPR as x and y axes respectively, which depicts relative trade-offs between true positive (benefits) and false positive (costs). Each prediction result or instance of a confusion matrix represents one point in the ROC space.

Interpretation

The best possible prediction method would yield a point in the upper left corner or coordinate (0,1) of the ROC space, representing 100% sensitivity (no false negatives) and 100% specificity (no false positives). The (0,1) point is also called a perfect classification. A random guess would give a point along a diagonal line (the so-called line of no-discrimination) from the left bottom to the top right corners.

See also

• Sensitivity and specificity
• Positive and negative predictive values
• Likelihood ratios in diagnostic testing
• Diagnostic odds ratio
• Receiver operating characteristic

References

ROC curve Resources
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