The receiver operating characteristic (ROC) curve is a tool of particular use in disease status classification with a continuous medical test (marker). A variety of statistical regression models have been proposed for the comparison of ROC curves for different markers across covariate groups. A full parametric modeling of the marker distribution has been generally found to be overly reliant on the strong parametric assumptions. Pepe (2003) has instead developed parametric models for the ROC curve that induce a semi-parametric model for the marker distributions. The estimating equations proposed for use in these ROC-GLM models may differ from commonly used estimating equations in those same probability models. In this paper, we investigate the analysis of the power ROC curve when based on the parametric exponential model and the broader semi-parametric proportional hazards probability model. In the case of the latter, we consider estimating equations derived from the usual partial likelihood methods in time-to-event analyses and the ROC-GLM approach of Pepe, et al. In exploring the robustness of these ROC analysis approaches to violations of the distributional assumptions, we find that the ROC-GLM estimating equation provides an extra measure of robustness when compared to the Cox proportional hazards estimating equation.
Devlin, Sean ; Thomas, Elizabeth; and Emerson, Scott S., "Robustness of approaches to ROC curve modeling under misspecification of the underlying probability model" (January 2010). UW Biostatistics Working Paper Series. Working Paper 355.