A Comparison of the Lehmann and GLM ROC Models

Recently, several regression methods have been developed to model the receiver operating characteristic curve (ROC), as a measure of accuracy for potential biomarker use in diagnostic testing and disease detection. In this paper, we investigate the Lehmann ROC regression model and compare it to more commonly used ROC regression methods that are found in the literature. The comparative performance of the methods are evaluated using simulated data from the normal, extreme value, and the Weibull distributions. Theory suggests that the Lehmann method should only work well when using the Weibull distribution. Our simulation results suggest that the performance of these methods is more complicated than the theory might suggest. The methods were demonstrated using data from a study concerning the clinical effectiveness of leukocyte elastase determination in the diagnosis of coronary artery disease (CAD).