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 ((Formula presented.)) 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 (Formula presented.) curve, the simultaneous confidence band of the whole or partial (Formula presented.) 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 (Formula presented.) curve, there exists a Working-Hotelling type of method and the ellipse-envelope approach. However, these large-sample-based approaches do not provide satisfactory coverage for small to median samples. In this article, we propose a new confidence band for the binormal (Formula presented.) 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 dataset is used to illustrate these methods. 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. Supplementary materials for this article are available online.