An area under the ROC curve value of 0.5 indicates which of the following about a diagnostic test?

• A. The test has perfect discrimination.
• B. The test has moderate discrimination.
• C. The test performs better than chance but not perfect.
• D. The test performs no better than random chance.

Answer: (D)

The key idea is what the area under the ROC curve tells you about a test’s ability to distinguish between diseased and non-diseased individuals. The AUC represents the probability that the test will assign a higher score to a randomly chosen diseased person than to a randomly chosen non-diseased person. An AUC of 0.5 corresponds to a straight diagonal line, meaning the test has no ability to discriminate at all and performs like random guessing. In other words, it does not provide any useful information beyond chance. By contrast, an AUC of 1.0 would indicate perfect discrimination, while any value above 0.5 indicates some ability to separate cases from controls, with higher values showing stronger discrimination.