Southwest Jiaotong University, School of Mathematics, Department of Statistics, Chengdu, China.
Duke University NUS Graduate Medical School, Singapore Eye Research Institute, National University of Singapore, Singapore, Singapore.
Stat Methods Med Res. 2019 Dec;28(12):3627-3648. doi: 10.1177/0962280218812211. Epub 2018 Nov 20.
It is often necessary to differentiate subjects from multiple categories using medical tests. We may then adopt statistical measures to characterize the performance of these tests. The three-way ROC analysis has been proposed to evaluate the diagnostic accuracy of medical tests with three categories, reflecting the correct classification probabilities across all possible decision thresholds. The geometry of the ROC surface is carefully studied, leading to numerical summary measures such as the volume under the surface. This paper generalizes the global volume under the surface of three-way ROC analysis to the weighted volume under the surface (WVUS) by introducing a weight function emphasizing particular regions of correct classification probabilities. This generalization practically allows researchers to calculate the diagnostic accuracy for a medical or clinical biomarker while satisfactorily high probabilities of correct classification for one or two classes are conditionally ensured. We provide the asymptotic properties of the proposed nonparametric and parametric estimators of WVUS, which could easily lend support to statistical inferences. Some simulations have been conducted to assess the proposed estimators and also to demonstrate the necessity of WVUS. A real data analysis about liver cancer illustrates our methodology.
通常需要使用医学测试将受试者分为多个类别。然后，我们可以采用统计措施来描述这些测试的性能。已经提出了三向 ROC 分析来评估具有三个类别的医学测试的诊断准确性，反映了所有可能决策阈值的正确分类概率。仔细研究了 ROC 曲面的几何形状，导致了数值摘要度量，例如曲面下的体积。本文通过引入一个权重函数来强调正确分类概率的特定区域，将三向 ROC 分析的全局曲面下体积推广为加权曲面下体积（WVUS）。这种推广实际上允许研究人员在一个或两个类别具有较高的正确分类概率的条件下，计算医学或临床生物标志物的诊断准确性。我们提供了 WVUS 的拟议和参数估计量的渐近性质，这可以很容易地为统计推断提供支持。进行了一些模拟以评估所提出的估计量，并还证明了 WVUS 的必要性。一个关于肝癌的真实数据分析说明了我们的方法。
