Semiparametric empirical likelihood confidence intervals for AUC under a density ratio model

Inferences on the area under a receiver operating characteristic curve (AUC) are usually based on a fully parametric approach or a fully nonparametric approach. A semiparametric empirical likelihood method is proposed to construct confidence intervals for AUC by assuming a density ratio model for the diseased and non-diseased population densities. The limiting distribution of the semiparametric empirical log likelihood ratio statistic for AUC has a scaled chi-square distribution. The proposed semiparametric empirical likelihood approach is shown, via a simulation study, to be more robust than a fully parametric approach and is more accurate than a fully nonparametric approach. Some results on simulation and an analysis of two real examples are presented.