Empirical Likelihood-Based Inferences in ROC Analysis with Covariates

• Activity Number: 342
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Gengsheng Qin*+ and Baoying Yang
• Companies: Georgia State University and Southwest Jiaotong University
• Keywords: AUC regression ; empirical likelihood ; ROC regression ; bootstrap ; confidence region

Abstract

In ROC analysis, the area under the ROC curve (AUC) is a popular one number summary index of the discriminatory accuracy of a diagnostic test. Accounting for covariates can improve diagnostic accuracy of the test. Regression models for the ROC curve and the AUC are two means to evaluate the effects of the covariates on the diagnostic accuracy. In this paper, empirical likelihood (EL) methods are proposed for the AUC regression model and the ROC regression model respectively. For both of the regression parameter vectors in the AUC regression model and the ROC regression model, it is shown that the limiting distributions of their EL ratio statistics are the weighted sum of independent chi-square distributions. Confidence regions can be constructed for the parameter vectors in the regression models based on the newly developed empirical likelihood theories. We can also construct confidence interval for the covariate-specific AUC. Simulation studies are conducted to compare the relative performance of the proposed EL-based methods with the existing method in AUC regression. Finally, we illustrate the proposed methods with a real data set.