Smooth estimation of the area under the ROC curve in multistage ranked set sampling

The receiver operating characteristic (ROC) curve is an important tool for assessing the discrimination power of a continuous biomarker. The area under the ROC curve is a well-known index for effectiveness of the biomarker. This article deals with estimating the aforesaid measure under a rank-based sampling design called multistage ranked set sampling. A nonparametric estimator using kernel density estimation is developed, and some theoretical results about it are established. Simulation studies show that the proposed estimator can be substantially more efficient than its alternative in simple random sampling. The methodology is illustrated with data from the National Health and Nutrition Examination Survey.