What is a receiver operating characteristic curve?

• A. Plot of the sensitivity of a test versus the false positive rate (1 - specificity) computed at a number of different cutpoints to select optimum value for telling apart disease vs non disease
• B. Plot of the specificity versus disease prevalence
• C. Graph of positive predictive value against prevalence
• D. A curve showing likelihood ratios across test values

Answer: (A)

A receiver operating characteristic curve shows how well a diagnostic test distinguishes disease from no disease across all possible thresholds. It plots sensitivity (true positive rate) on the vertical axis against the false positive rate (1 minus specificity) on the horizontal axis, for every cutpoint you might use to declare a positive test. By moving the threshold, you get different pairs of sensitivity and specificity, and the ROC aggregates these into a single curve. A curve that hugs the top left corner indicates strong discrimination; the area under the curve (AUC) summarizes overall performance, with 1.0 being perfect and 0.5 representing no better than chance. In practice, you pick a threshold by balancing sensitivity and specificity according to the clinical context, sometimes using criteria like maximizing Youden’s index.

This matches the described choice because it is precisely the plot of sensitivity versus the false positive rate across varying cutpoints to separate disease from non-disease. The other concepts—specificity versus prevalence, positive predictive value versus prevalence, or likelihood ratios across test values—describe different relationships and are not what a ROC curve represents.