Empirical likelihood-based inferences for the area under the ROC curve with covariates

In the receiver operating characteristic (ROC) analysis, the area under the ROC curve (AUC) is a popular summary index of discriminatory accuracy of a diagnostic test. Incorporating covariates into ROC analysis can improve the diagnostic accuracy of the test. Regression model for the AUC is a tool to evaluate the effects of the covariates on the diagnostic accuracy. In this paper, empirical likelihood (EL) method is proposed for the AUC regression model. For the regression parameter vector, it can be shown that the asymptotic distribution of its EL ratio statistic is a weighted sum of independent chi-square distributions. Confidence regions are constructed for the parameter vector based on the newly developed empirical likelihood theorem, as well as for the covariate-specific AUC. Simulation studies were conducted to compare the relative performance of the proposed EL-based methods with the existing method in AUC regression. Finally, the proposed methods are illustrated with a real data set.