University of Barcelona, Medicine Faculty, Public Health Department, Casanova 143, 08036 Barcelona, Spain.
Stat Med. 2012 May 20;31(11-12):1098-109. doi: 10.1002/sim.4369. Epub 2011 Sep 21.
In the diagnostic area, the usual setting considers two populations: nondiseased and diseased. The use of the standard ROC analysis methodology is well established. Sometimes, however, diagnostic problems inherently include more than two classification states. For example, 'yes, uncertain, no' or 'low, normal, high'. Here we consider a three-normal distribution setting and derive estimators for the optimum thresholds between states based on a cost function. These estimators can be extended for clinical contexts with more than three states. This approach is well known for the two-state setting and its advantage lies in the fact that it accounts for the specific context's properties, such as disease prevalence and classification costs. Here we calculated the variance of the estimators by the use of parametric methods on nonlinear equations and we constructed confidence intervals accounting for possible uncertainty in the threshold estimation. We conducted a simulation study to assess the performance of these estimators and the confidence intervals. Comparisons with the naive threshold estimation method of joining the distributions two-by-two and applying standard ROC techniques proved that the latter method is not reliable for all parameter combinations and should be avoided.
在诊断领域，通常的设定考虑两种情况：无病和有病。标准的 ROC 分析方法已经得到很好的确立。然而，有时诊断问题本身包括超过两种分类状态。例如，“是，不确定，否”或“低，正常，高”。在这里，我们考虑一个三正态分布的情况，并根据成本函数为状态之间的最优阈值推导出估计器。这些估计器可以扩展到具有三个以上状态的临床环境中。这种方法在两状态设置中是众所周知的，其优点在于它考虑了特定环境的属性，如疾病流行率和分类成本。在这里，我们通过使用非线性方程的参数方法计算了估计器的方差，并构建了考虑阈值估计可能存在不确定性的置信区间。我们进行了一项模拟研究，以评估这些估计器和置信区间的性能。与将分布两两合并并应用标准 ROC 技术的简单阈值估计方法进行比较，证明后者对于所有参数组合都不可靠，应避免使用。
