Mossman Douglas, Peng Hongying
Department of Psychiatry and Behavioral Neuroscience, University of Cincinnati College of Medicine, Cincinnati, OH, USA. (DM)
Department of Environmental Health, University of Cincinnati College of Medicine, Cincinnati, OH, USA. (HP)
Med Decis Making. 2016 Apr;36(3):349-65. doi: 10.1177/0272989X15582210. Epub 2015 Apr 24.
Receiver operating characteristic (ROC) analysis helps investigators quantify and describe how well a diagnostic system discriminates between 2 mutually exclusive conditions. The conventional binormal (CvB) curve-fitting model usually produces ROCs that are improper in that they do not have the ever-decreasing slope required by signal detection theory. When data sets evaluated under the CvB model have hooks, the resulting ROCs can contain misleading information about the diagnostic performance of the method at low and high false positive rates.
To present and evaluate a dual beta (DB) ROC model that assumes diagnostic data arise from 2 β distributions. The DB model's parameter constraints assure that the resulting ROC curve has a positive, monotonically decreasing slope.
DESIGN/METHOD: Computer simulation study comparing results from CvB, DB, and weighted power function (WPF) models.
The DB model produces results that are as good as or better than those from the WPF model, and less biased and closer to the true values than curves obtained using the CvB model.
The DB ROC model expresses the relationship between the false positive rate and true positive rate in closed form and allows for quick ROC area calculations using spreadsheet functions. Because it posits simple relationships among the decision axis, operating points, and model parameters, the DB model offers investigators a flexible, easy-to-grasp ROC form that is simpler to implement than other proper ROC models.
受试者工作特征（ROC）分析有助于研究人员量化和描述诊断系统区分两种相互排斥情况的能力。传统的双正态（CvB）曲线拟合模型通常产生的ROC曲线是不合适的，因为它们不具备信号检测理论所要求的斜率不断减小的特征。当在CvB模型下评估的数据集有弯钩时，所得的ROC曲线可能会在低假阳性率和高假阳性率下包含有关该方法诊断性能的误导性信息。
提出并评估一种双β（DB）ROC模型，该模型假设诊断数据来自两个β分布。DB模型的参数约束可确保所得的ROC曲线具有正的、单调递减的斜率。
设计/方法：计算机模拟研究，比较CvB、DB和加权幂函数（WPF）模型的结果。
DB模型产生的结果与WPF模型的结果一样好或更好，并且比使用CvB模型获得的曲线偏差更小且更接近真实值。
DB ROC模型以封闭形式表达了假阳性率和真阳性率之间的关系，并允许使用电子表格函数快速计算ROC面积。由于它在决策轴、操作点和模型参数之间建立了简单的关系，DB模型为研究人员提供了一种灵活、易于理解的ROC形式，比其他合适的ROC模型更易于实现。
