Nonparametric Estimation of AUC and Partial AUC under Test-Result-Dependent Sampling

The area under a ROC curve (AUC) and partial area under a ROC curve (pAUC) are important summary measures useful in assessing the accuracy of a diagnostic test or a biomarker in discriminating true disease status. We consider nonparametric estimation of AUC and pAUC under a test-result-dependent sampling (TDS) design, which consists of a simple random component and a test-result-dependent component. A TDS design can yield better efficiency and reduced study cost by oversampling or undersampling subjects falling into specified ranges of test results. We obtain a nonparametric empirical likelihood estimate of the test-result distribution under the TDS design. The estimated test-result distribution is then used to construct consistent estimators for AUC and pAUC. We establish asymptotic properties of the proposed estimators. Simulation shows that the proposed estimators have good finite sample properties and that the TDS design is more efficient than a simple random sampling (SRS) design. A data example based on an ongoing lung cancer trial is provided to illustrate the TDS design and the proposed estimators.