Empirical likelihood inference for area under the receiver operating characteristic curve using ranked set samples

Abstract

The area under a receiver operating characteristic curve (AUC) is a useful tool to assess the performance of continuous-scale diagnostic tests on binary classification. In this article, we propose an empirical likelihood (EL) method to construct confidence intervals for the AUC from data collected by ranked set sampling (RSS). The proposed EL-based method enables inferences without assumptions required in existing nonparametric methods and takes advantage of the sampling efficiency of RSS. We show that for both balanced and unbalanced RSS, the EL-based point estimate is the Mann-Whitney statistic, and confidence intervals can be obtained from a scaled chi-square distribution. Simulation studies and two case studies on diabetes and chronic kidney disease data suggest that using the proposed method and RSS enables more efficient inference on the AUC.

Keywords: AUC; Mann-Whitney statistic; diagnostic test; profile empirical likelihood; ranked set sampling.