Yan HaiFollow

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics

First Advisor

Gengsheng Qin

Second Advisor

Xiaoyi Min


In the medical diagnostic study, the accuracy of a diagnostic test is commonly evaluated based on its sensitivity and specificity. Both sensitivity and specificity are not fixed but depend on the cutoff chosen for that test. The receiver operating characteristic (ROC) curve of the test is constructed to show how sensitivity and specificity change as the cutoff varies. The area under the ROC curve (AUC) can also be used to evaluate the discriminatory ability of diagnostic tests with continuous test results. In practice, however, the cutoff of a test is usually chosen so that the specificity is meaningfully high. Therefore, the sensitivity under a certain specificity serves as a diagnostic measure to evaluate the diagnostic tests.

In both two and three (the normal healthy stage, the early stage of the disease, and the stage of the full development of the disease) diagnostic classes studies, we propose a new influence function-based empirical likelihood method and Bayesian empirical likelihood methods. The proposed methods are shown to perform better than the existing methods in terms of both coverage probability and interval length in simulation studies. A real data set from Alzheimer's Disease Neuroimaging Initiative (ANDI) is analyzed by using the newly proposed methods.

In two-phase diagnostic studies with both screening test and gold standard test, verification of the true disease status might be partially missing based on the results of diagnostic tests and other subjects' characteristics. Because the estimators of AUC based on partially validated subjects are usually biased, it is usually necessary to estimate AUC by bias-corrected methods. We proposed direct estimators of the AUC based on hybrid imputation(FI and MSI), inverse probability weighting (IPW), and the semi-parametric efficient(SPE) approach with verification biased data when the test result is continuous under the assumption that the true disease status, if missing, is missing at random (MAR). Simulation results show that the proposed estimators are accurate for the biased sampling. We illustrate the proposed methods with a real data set of Neonatal Hearing Screening study.

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