  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.
