Efficient confidence bounds for ROC curves.

The specificity and sensitivity of a quantitative diagnostic marker depends on the selected cut-off point. The ROC curve is generated by plotting sensitivity against specificity as the cut-off point runs through the whole range of possible marker values. Confidence bounds for ROC curves may be constructed by combining two separate confidence intervals for sensitivity and specificity. In the present paper, a more efficient method, which is based on a statistical test introduced by Greenhouse and Mantel, is presented. The resulting 95 per cent confidence intervals are up to 40 per cent smaller. A formula is given to calculate the sample size necessary to obtain a confidence interval of a stipulated length at a specified point of the ROC curve. As an example, the performance of a tumour marker in the diagnosis of bone marrow metastases is investigated.