Estimating the Area under the ROC Curve with Modified Profile Likelihoods

Receiver operating characteristic (ROC) curves are a frequent tool to study the discriminating ability of a certain characteristic. The area under the ROC curve (AUC) is a widely used measure of statistical accuracy of continuous markers for diagnostic tests, and has the advantage of providing a single summary index of overall performance of the test. Recent studies have shown some critical issues related to traditional point and interval estimates for the AUC, especially for small samples, more complex models, unbalanced samples or values near the boundary of the parameter space, i.e., when the AUC approaches the values 0.5 or 1. Parametric models for the AUC have shown to be powerful when the underlying distributional assumptions are not misspecified. However, in the above circumstances parametric inference may be not accurate, sometimes yielding misleading conclusions. The objective of the paper is to propose an alternative inferential approach based on modified profile likelihoods, which provides more accurate statistical results in any parametric settings, including the above circumstances. The proposed method is illustrated for the binormal model, but can potentially be used in any other complex model and for any other parametric distribution. We report simulation studies to show the improved performance of the proposed approach, when compared to classical first-order likelihood theory. An application to real-life data in a small sample setting is also discussed, to provide practical guidelines.