Estimating the area under a receiver operating characteristic curve using partially ordered sets

Zamanzade Ehsan () and Wang Xinlei ()
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Zamanzade Ehsan: Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, 81746-73441, Iran
Wang Xinlei: Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, Dallas, 75275-0332, TX, USA

The International Journal of Biostatistics, 2021, vol. 17, issue 1, 139-152

Abstract: 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.

Keywords: imperfect ranking; isotonic estimation; maximum likelihood; nonparametric estimation; relative efficiency; tie information (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1515/ijb-2019-0127

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