Empirical likelihood inference for the area under the receiver operating characteristic (ROC) curve with verification biased data

In medical diagnostic studies, the area under the receiver operating characteristic curve (AUC) is a widely used metric that captures a continuous test’s overall ability to discriminate between diseased and non-diseased individuals across all possible cutoffs. However, in practice, disease status is sometimes only partially verified, introducing verification bias that undermines the validity of AUC estimation. While numerous methods address bias correction for AUC estimation, approaches that directly construct confidence intervals for the AUC remain limited. This paper proposes two robust methods for constructing bias-corrected confidence intervals for the AUC under the missing-at-random assumption: one based on bootstrap resampling and the other on empirical likelihood. Both approaches accommodate missing disease verification by leveraging the bias-corrected ROC estimators introduced by Alonzo and Pepe. Extensive simulation studies and real-world data analyses demonstrate that our proposed methods yield valid and precise interval estimates for the AUC under various clinically relevant settings.