An important application of genomic studies is to discover genomic biomarkers, among tens of thousands of genes assayed, for disease classification. There is a need for statistical methods that can efficiently use such high-throughput data, select biomarkers with discriminant power and construct classification rules. The ROC (receiving operator characteristic) technique has been widely used in disease classification with low dimensional biomarkers because (1).it does not assume a parametric form of the class probability; (2).it accommodates case-control designs; and (3).it allows treating false positives and false negatives differently. However, due to computational difficulties, the ROC based classification has not been used with genomic data. Moreover, the standard ROC technique does not incorporate built-in biomarker selection.

We propose a novel method for biomarker selection and classification using the ROC technique for genomic data. The proposed method uses a sigmoid approximation to the area under the ROC curve as the objective function for classification and the threshold gradient descent regularization method for estimation and biomarker selection. Tuning parameter selection based on the V-fold cross validation and predictive performance evaluation are also investigated. The proposed approach is demonstrated with the Colon cancer study and a HIV vaccine study. The proposed approach yields parsimonious models with excellent classification performance.