On the convexity of ROC curves estimated from radiological test results.
On the convexity of ROC curves estimated from radiological test results.
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DOI：
10.1016/j.acra.2010.04.001
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发表时间：
2010-08
影响因子：
4.8
通讯作者：
Berbaum, Kevin S.
中科院分区：
文献类型：
--
作者：
Pesce, Lorenzo L.;Metz, Charles E.;Berbaum, Kevin S.
关键词：
尽管理想观察者的接收器工作特性(ROC)曲线必须是凸的--也就是说，它的斜率必须单调地减小--但已发表的与经验数据的拟合往往显示出“钩子”。这种拟合有时被接受的理由是，实验是在真实的观察者身上进行的，而不是理想的观察者。然而，理想观察者必须产生凸曲线这一事实并不意味着凸曲线只描述理想观察者。本文旨在识别非凸ROC曲线的实际含义，以及导致经验ROC曲线和/或拟合ROC曲线不凸的条件。本文从历史、理论和统计三个角度对非凸ROC曲线进行了分析，并对其进行了简要的描述。然后，我们考虑各种形状的人口ROC曲线，并分析它们所暗示的医疗决策的类型。最后，我们描述了抽样可变性和曲线拟合算法如何产生包含挂钩的ROC曲线估计。我们表明，人口ROC曲线中的钩子意味着使用非理性的决策策略，即使曲线没有越过机会线，因此在医疗环境中通常是站不住脚的。此外，我们还提出了一种简单的方法，通过在决策过程中加入统计变量来改进任何非凸ROC曲线。最后，我们描述了如何测试ROC数据中存在的钩子是否可能是由偶然引起的，以及如何轻松地将文献中发现的一些钩状ROC解释为拟合伪影或建模问题。总体而言，ROC曲线表明，除非其他理由证明它们的存在是合理的，否则应该以怀疑的眼光看待这些钩子。
Although an ideal observer’s receiver operating characteristic (ROC) curve must be convex — i.e., its slope must decrease monotonically — published fits to empirical data often display “hooks.” Such fits sometimes are accepted on the basis of an argument that experiments are done with real, rather than ideal, observers. However, the fact that ideal observers must produce convex curves does not imply that convex curves describe only ideal observers. This paper aims to identify the practical implications of non-convex ROC curves and the conditions that can lead to empirical and/or fitted ROC curves that are not convex. This paper views non-convex ROC curves from historical, theoretical and statistical perspectives, which we describe briefly. We then consider population ROC curves with various shapes and analyze the types of medical decisions that they imply. Finally, we describe how sampling variability and curve-fitting algorithms can produce ROC curve estimates that include hooks. We show that hooks in population ROC curves imply the use of an irrational decision strategy, even when the curve doesn’t cross the chance line, and therefore usually are untenable in medical settings. Moreover, we sketch a simple approach to improve any non-convex ROC curve by adding statistical variation to the decision process. Finally, we sketch how to test whether hooks present in ROC data are likely to have been caused by chance alone and how some hooked ROCs found in the literature can be easily explained as fitting artifacts or modeling issues. In general, ROC curve fits that show hooks should be looked upon with suspicion unless other arguments justify their presence.
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