For a continuous-scale diagnostic test, the most commonly used summary index of the receiver operating characteristic (ROC) curve is the area under the curve (AUC) that measures the accuracy of the diagnostic test. In this paper we propose an empirical likelihood approach for the inference of AUC. We first define an empirical likelihood ratio for AUC and show that its limiting distribution is a scaled chi-square distribution. We then obtain an empirical likelihood based confidence interval for AUC using the scaled chi-square distribution. This empirical likelihood inference for AUC can be extended to stratified samples and the resulting limiting distribution is a weighted sum of independent chi-square distributions. We also conduct simulation studies to compare the relative performance of the proposed empirical likelihood based interval with the existing normal approximation based intervals and bootstrap intervals for AUC.
Statistical Methodology | Statistical Theory
Qin, Gengsheng and Zhou, Xiao-Hua, "Empirical Likelihood Inference for the Area Under the ROC Curve" (December 2005). UW Biostatistics Working Paper Series. Working Paper 268.