Area under curve (AUC)

The area under (a ROC) curve is a summary measure of the accuracy of a quantitative diagnostic test.

A point estimate of the AUC of the empirical ROC curve is the Mann-Whitney U estimator (DeLong et. al., 1988). The confidence interval for AUC indicates the uncertainty of the estimate and uses the Wald Z large sample normal approximation (DeLong et al., 1998). A test with no better accuracy than chance has an AUC of 0.5, a test with perfect accuracy has an AUC of 1.

The interpretation of the AUC is:
  • The average value of sensitivity for all possible values of specificity (Zhou, Obuchowski, McClish, 2001).
  • The average value of specificity for all possible values of sensitivity (Zhou, Obuchowski, McClish, 2001).
  • The probability that a randomly selected subject with the condition has a test result indicating greater suspicion than that of a randomly chosen subject without the condition (Hanley & McNeil, 1982).

AUC can be misleading as it gives equal weight to the full range of sensitivity and specificity values even though a limited range, or specific threshold, may be of practical interest.