The 'receiver operating characteristic' (ROC) curve of a diagnostic test has an area under the curve (AUC) of 0.88. This indicates that:
- A The test correctly classifies 88% of all subjects
- B The sensitivity of the test is 88%
- C There is an 88% probability that a randomly chosen diseased person has a higher test score than a randomly chosen non-diseased person ✓
- D The test has a 12% false positive rate at the optimal cut-off
Correct answer: C. There is an 88% probability that a randomly chosen diseased person has a higher test score than a randomly chosen non-diseased person
Explanation
AUC (c-statistic) is interpreted as the probability that a randomly selected case (diseased) has a higher test value than a randomly selected control (non-diseased). AUC 0.88 means an 88% probability of correct ranking — indicating good discriminatory ability. AUC = 0.5 means no discrimination (same as chance); AUC = 1.0 means perfect discrimination. AUC ≥ 0.8 is considered good; ≥ 0.9 excellent. Option A confuses AUC with overall accuracy. The optimal cut-off maximises sensitivity + specificity (Youden index).
Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.
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