Weighted empirical likelihood inference for the area under the ROC curve

• A new method for estimation of the AUC for right-censored data is presented.
• Based on a log-ratio, nonparametric confidence intervals for the AUC are constructed.
• The intervals perform better than the existing ones based on normal theory or resampling.
• An asymptotic distribution of the log-ratio statistic used is established.

Interval estimation of the area under the receiver operating characteristic (ROC) curve is difficult when working with right-censored data. An empirical likelihood method is not advisable in this case due to severe computational issues. In this paper we propose an extension of a so-called weighted empirical likelihood (WEL) method for interval estimation of this parameter. We define the WEL ratio and show that it has a limiting scaled chi-square distribution. This result allows us to construct a confidence interval for the area under the ROC curve. Finally we conduct a simulation study to compare the performance of the proposed WEL-based interval with the one based on already existing plug-in method.