Confidence Intervals for AUC and pAUC by Empirical Likelihood

The area under the receiver operating characteristic curve (AUC) and Partial AUC (pAUC) are often used to measure the performance of medical diagnostic tests. Under nonparametric settings, we propose and illustrate in this paper a two-sample empirical likelihood approach to test hypotheses and construct confidence intervals for AUC and pAUC. The empirical likelihood ratio test in our setup yields an asymptotic chi-square distribution under null hypothesis. Thus, there is no need to estimate the complicated scale factor or the variance of the nonparametric AUC/pAUC estimators like most other competing methods do. Simulations show our method is very competitive. In fact, our method tops competitors in every situation we simulated. Real data examples (with R code) are presented illustrating the statistical tests and confidence intervals for AUC and pAUC.