Empirical Likelihood-Based NonParametric Inference for the Difference between Two Partial AUCS

Compare the accuracy of two continuous-scale tests is increasing important when a new test is developed. The traditional approach that compares the entire areas under two Receiver Operating Characteristic (ROC) curves is not sensitive when two ROC curves cross each other. A better approach to compare the accuracy of two diagnostic tests is to compare the areas under two ROC curves (AUCs) in the interested specificity interval. In this thesis, we have proposed bootstrap and empirical likelihood (EL) approach for inference of the difference between two partial AUCs. The empirical likelihood ratio for the difference between two partial AUCs is defined and its limiting distribution is shown to be a scaled chi-square distribution. The EL based confidence intervals for the difference between two partial AUCs are obtained. Additionally we have conducted simulation studies to compare four proposed EL and bootstrap based intervals. INDEX WORDS: ROC curve, AUC, PAUC, Partial AUC, Empirical Likelihood, Bootstrap, Confidence Interval. EMPIRICAL LIKELIHOOD-BASED NONPARAMETRIC INFERENCE FOR THE DIFFERENCE BETWEEN TWO PARTIAL AUCS