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. 1. Introduction In modern medical diagnosis or genetic studies, the receiver operating characteristic (ROC) curve is a popular tool to evaluate the discrimination performance of a certain biomarker on a disease status or a phenotype. For example, in a continuous-scale test, the diagnosis of a disease is dependent upon whether a test result is above or below a specified cutoff value. Also, genome-wide association studies in human populations aim at creating genomic profiles which combine the effects of many associated genetic variants to predict the disease risk of a new subject with high discriminative accuracy [1]. For a given cutoff value of a biomarker or a combination of biomarkers, the sensitivity and the specificity are employed to quantitatively evaluate the discriminative performance. By varying cutoff values throughout the entire real line, the resulting plot of sensitivity against 1-specificity is a ROC curve. The area under the ROC curve (AUC) is an important one-number summary index of the overall discriminative accuracy of a ROC curve, by taking the influence of all cutoff values into account. Let be the response of a diseased subject, and let be the response of a nondiseased subject; then, the AUC can be expressed as [2]. Pepe [3] and Zhou et al. [4] provided broad reviews on many statistical methods for the evaluation of diagnostic tests. Traditional ROC analyses do not consider the effect of characteristics of
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