A placement-value based approach to concave ROC analysis

Abstract: The receiver operating characteristic (ROC) curve is an important graphic tool for evaluating a test in a wide range of disciplines. While useful, an ROC curve can cross the chance line, either by having an S-shape or a hook at the extreme specificity. These non-concave ROC curves are sub-optimal according to decision theory, as there are points that are superior than those corresponding to the portions below the chance line with either the same sensitivity or specificity. We extend the literature by proposing a novel placement value-based approach to ensure concave curvature of the ROC curve, and utilize Bayesian paradigm to make estimations under both a parametric and a semiparametric framework. We conduct extensive simulation studies to assess the performance of the proposed methodology under various scenarios, and apply it to a pancreatic cancer dataset.