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.

翻译：接收者操作特征（ROC）曲线是跨学科领域中评估测试性能的重要图形工具。尽管ROC曲线具有实用价值，但其可能因呈现S形或在极端特异性处出现钩状弯曲而跨越机会线。根据决策理论，这些非凹形ROC曲线是次优的，因为总存在某些点，在相同灵敏度或特异性条件下，其性能优于机会线下方对应区段的点。本研究通过提出一种基于位置值的新方法扩展了现有文献，该方法能确保ROC曲线呈现凹形曲率，并利用贝叶斯范式在参数化和半参数化框架下进行估计。我们通过大量模拟研究评估了所提方法在不同场景下的性能，并将其应用于胰腺癌数据集的分析。