Generalized Inference Confidence Band for binormal ROC curve

In medical practice, the diagnostic accuracy of a biomarker is usually measured by its sensitivity and specificity. The Receiver Operating Characteristic (<i>ROC</i>) curve is the graph of sensitivity against 1 − specificity as the cut-off point runs through all possible values. To account for sampling error and make inference about the true <i>ROC</i> curve, the simultaneous confidence band of the whole or partial <i>ROC</i> curve needs to be estimated across all values of specificity (can be within (0, 1) or some clinically-meaningful range). Particularly, for estimating the confidence band of the binormal <i>ROC</i> curve, there exists a Working-Hotelling type of method and the ellipse-envelop approach. However, these large-sample-based approaches do not provide satisfactory coverage for small to median samples. In this paper, we propose a new confidence band for the binormal <i>ROC</i> curve based on the generalized inference approach. Extensive simulation study is carried out to compare the performance of the proposed generalized confidence band with the existing large-sample-based confidence bands and a real data set is used to illustrate these methods. In conclusion, the proposed generalized confidence bands generally yield satisfactory coverage probabilities, while both large-sample-based confidence bands tend to be more liberal for most scenarios.