Ranked set sampling (RSS), known as a cost-effective sampling technique, requires that the ranker gives a complete ranking of the units in each set. Frey (2012) proposed a modification of RSS based on partially ordered sets, referred to as RSS-t in this paper, to allow the ranker to declare ties as much as he/she wishes. We consider the problem of estimating the area under a receiver operating characteristics (ROC) curve using RSS-t samples. The area under the ROC curve (AUC) is commonly used as a measure for the effectiveness of diagnostic markers. We develop six nonparametric estimators of the AUC with/without utilizing tie information based on different approaches. We then compare the estimators using a Monte Carlo simulation and an empirical study with real data from the National Health and Nutrition Examination Survey. The results show that utilizing tie information increases the efficiency of estimating the AUC. Suggestions about when to choose which estimator are also made available to practitioners.

中文翻译：

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使用偏序集估计接收器操作特征曲线下的面积

排名集抽样 (RSS)，被称为具有成本效益的抽样技术，要求排名者给出每个集合中单元的完整排名。Frey (2012) 提出了一种基于偏序集的 RSS 修改，在本文中称为 RSS-t，以允许排名者根据他/她的意愿声明联系。我们考虑使用 RSS-t 样本估计接收者操作特征 (ROC) 曲线下面积的问题。ROC 曲线下面积 (AUC) 通常用作衡量诊断标志物有效性的指标。我们开发了六个 AUC 的非参数估计器，使用/不使用基于不同方法的联系信息。然后，我们将使用蒙特卡罗模拟和实证研究的估计值与来自国家健康和营养检查调查的真实数据进行比较。结果表明，利用平局信息提高了估计 AUC 的效率。还向从业者提供有关何时选择哪个估算器的建议。