标题： 风险分布曲线及其导数 显示英文标题

标题： The Risk Distribution Curve and its Derivatives

摘要： 风险分层最直接且信息量最大的总结是作为风险分布曲线。 从这条曲线可以推导出ROC曲线、预测曲线以及其他描述风险分层的曲线，这表明它们呈现类似的信息。 给出了ROC曲线的数学表达式，AUC由此得出，这阐明了这一区分度的衡量指标如何量化有事件和无事件患者之间的重叠。 该表达式用于定义风险分布曲线的离散性与ROC曲线AUC之间的正相关关系。 由于更离散的风险分布以及有事件和无事件患者之间的更大分离度体现了更优的风险分层，因此ROC曲线AUC提供了有用的信息。 显示英文摘要

摘要： Risk stratification is most directly and informatively summarized as a risk distribution curve. From this curve the ROC curve, predictiveness curve, and other curves depicting risk stratification can be derived, demonstrating that they present similar information. A mathematical expression for the ROC curve AUC is derived which clarifies how this measure of discrimination quantifies the overlap between patients who have and don't have events. This expression is used to define the positive correlation between the dispersion of the risk distribution curve and the ROC curve AUC. As more disperse risk distributions and greater separation between patients with and without events characterize superior risk stratification, the ROC curve AUC provides useful information.