Empirical Likelihood Inference for Area under the ROC Curve using Ranked Set Samples

TL;DR

This paper introduces an empirical likelihood method for constructing confidence intervals for the AUC in binary classification, utilizing ranked set sampling to improve inference efficiency without strict assumptions.

Contribution

It develops a novel EL-based approach for AUC inference from RSS data, providing more efficient and assumption-free confidence intervals compared to existing methods.

Findings

EL-based point estimate equals Mann-Whitney statistic

Confidence intervals derived from scaled chi-square distribution

Simulation and case studies show improved inference efficiency

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.