Environmental and Ecological Statistics (13528505)(4)
The volume under the receiver operating characteristic (ROC) surface (VUS) is a natural generalization of a classical tool, the area under the ROC curve from a disease with two statuses (e.g., healthy and diseased) to a disease with a three-class status (e.g., healthy, intermediate, and diseased) for evaluating the effectiveness of a continuous biomarker in discriminating the disease status. In this work, we discuss the problem of estimating VUS using ranked set sampling (RSS), a cost-efficient alternative to simple random sampling (SRS), which is applicable in situations in which the actual quantification of the biomarker is hard, time-consuming, costly or tedious but a small number of sample units can still be ordered without referring to their precise values. We develop several nonparametric estimators when SRS or RSS design is applied to each of the healthy, intermediate and diseased subpopulations. We study the properties of the proposed estimators, including unbiasedness, variance expression, asymptotic normality, and efficiency. Specifically, we show that the introduced estimators are at least as efficient as their SRS counterparts and often far more efficient under a large class of imperfect ranking models. Lastly, to demonstrate the applicability and efficiency of the introduced procedures in an environmental context, we apply them to a real environmental dataset, utilizing three of its five classes. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
