Variable selection in ROC regression

Regression models are introduced into the receiver operating characteristic (ROC) analysis to accommodate effects of covariates, such as genes. If many covariates are available, the variable selection issue arises. The traditional induced methodology separately models outcomes of diseased and nondiseased groups; thus, separate application of variable selections to two models will bring barriers in interpretation, due to differences in selected models. Furthermore, in the ROC regression, the accuracy of area under the curve (AUC) should be the focus instead of aiming at the consistency of model selection or the good prediction performance. In this paper, we obtain one single objective function with the group SCAD to select grouped variables, which adapts to popular criteria of model selection, and propose a two-stage framework to apply the focused information criterion (FIC). Some asymptotic properties of the proposed methods are derived. Simulation studies show that the grouped variable selection is superior to separate model selections. Furthermore, the FIC improves the accuracy of the estimated AUC compared with other criteria.