In receiver operating characteristic (ROC) curve analysis, the area under the curve (AUC) is undoubtedly the most widely used index of diagnostic accuracy for the assessment of the utility of a biomarker or for the comparison of competing biomarkers. Along with the AUC, the maximum of the Youden index, J, is often used both as an index of diagnostic accuracy and as a tool useful for the estimation of an optimal cutoff point that can be used for diagnostic purposes based on the biomarker under consideration. In this work, we study the utility of the length of the binormal model-based ROC curve (LoC) as an index of diagnostic accuracy for biomarker evaluation. Estimation procedures for LoC, described in this article, are based either on normality assumptions or on the same assumptions after a Box–Cox transformation to normality. Two simulation studies are considered. In the first, the estimation procedures for LoC are compared in terms of bias and root mean squared error, while in the second one, the performance of LoC is compared with approaches based on AUC and J, both for the case of the assessment of a single biomarker and for the comparison of two biomarkers, in a parametric framework. We provide an interpretation for the proposed index and illustrate with an application on biomarkers from a colorectal cancer study.

在接收器工作特性（ROC）曲线分析中，曲线下面积（AUC）无疑是诊断准确性最广泛使用的指标，用于评估生物标记物的效用或比较竞争性生物标记物。连同AUC，Youden指数的最大值J通常既用作诊断准确性的指标，又用作可用于评估最佳截止点的工具，该工具可根据所考虑的生物标记物用于诊断目的。在这项工作中，我们研究了基于双正态模型的ROC曲线（LoC）的长度作为生物标志物评估的诊断准确性指标的效用。本文介绍的LoC估算程序是基于正态性假设或Box-Cox转换为正态性后的相同假设。考虑了两个仿真研究。第一种方法是根据偏倚和均方根误差对LoC的估计程序进行比较，而第二种方法是将LoC的性能与基于AUC和J的方法进行比较，无论是评估单个生物标记还是在参数框架中比较两个生物标记。我们为拟议的索引提供了解释，并举例说明了来自结肠直肠癌研究的生物标志物。