Bayesian and Influence Function-Based Empirical Likelihoods for Inference of Sensitivity to the Early Diseased Stage in Diagnostic Tests

• Activity Number: 108 - Innovations in Testing and Inference
• Type: Contributed
• Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Gengsheng Qin* and Yan Hai and Shuangfei Shi
• Companies: Georgia State University and Georgia State University and Georgia State University
• Keywords: Sensitivity ; Bayesian Inference; Empirical Likelihood; Influence Function; Confidence Interval

Abstract

In practice, a disease process might involve three ordinal diagnostic stages: the normal healthy stage, the early stage of the disease, and the stage of full development of the disease. Early detection is critical for some diseases since it often means an optimal time window for therapeutic treatments of the diseases. In this study, we propose a new influence function-based empirical likelihood method and Bayesian empirical likelihood methods to construct confidence intervals for the sensitivity of a test to patients in the early diseased stage given a specificity and a sensitivity of the test to patients in the fully diseased stage. Numerical studies are performed to compare the finite sample performances of the proposed approaches with existing methods. The proposed methods are shown to outperform existing methods in terms of both coverage probability and interval length. A real data set from the Alzheimer's Disease Neuroimaging Initiative (ANDI) is analyzed by using the proposed methods.