Mossman D
Division of Forensic Psychiatry, Wright State University School of Medicine, Dayton, Ohio 45401-0927, USA.
Med Decis Making. 1999 Jan-Mar;19(1):78-89. doi: 10.1177/0272989X9901900110.
Receiver operating characteristic (ROC) analysis traditionally has dealt with dichotomous diagnostic tasks (e.g., determining whether a disorder is present or absent). Often, however, medical problems involve distinguishing among more than two diagnostic alternatives. This article extends ROC concepts to diagnostic enterprises with three possible outcomes. For a trichotomous decision task, one can plot a ROC surface on three-dimensional coordinates; the volume under the ROC surface (VUS) equals the probability that test values will allow a decision maker to correctly sort a trio of items containing a randomly-selected member from each of three populations. Thus, the VUS summarizes global diagnostic accuracy for trichotomous tests, just as the area under a ROC curve does for a two-alternative diagnostic task. Information gain at points on the surface can be calculated just as is done for two-dimensional ROC curves, and investigators can thus compare three-way ROCs by comparing maximum information gain on each ROC surface.
传统上，接受者操作特征（ROC）分析处理的是二分诊断任务（例如，确定疾病是否存在）。然而，医学问题通常涉及区分两种以上的诊断选项。本文将ROC概念扩展到具有三种可能结果的诊断工作中。对于三分决策任务，可以在三维坐标上绘制ROC曲面；ROC曲面下的体积（VUS）等于测试值将使决策者能够正确对包含从三个总体中随机选择的成员的三个项目进行排序的概率。因此，VUS总结了三分测试的整体诊断准确性，就像ROC曲线下的面积对二分诊断任务所做的那样。曲面上各点的信息增益可以像二维ROC曲线那样计算，因此研究人员可以通过比较每个ROC曲面上的最大信息增益来比较三分ROC。
