Regularized ROC Estimation: With Applications to Disease Classification Using Microarray Data

Summary Microarrays capable of monitoring gene expression on a large scale are becoming a routing tool in biomedical research. An important application of microarrays is to discover genomic biomarkers, among tens of thousands of genes assayed, for disease classification and prediction. Thus there is a need for novel statistical methods that can efficiently use such high-throughput genomic data, are suitable for disease classification, and are able to select important biomarkers among thousands of genes. We propose a sigmoid approximation to a widely used accuracy measure based on the receiver operating characteristic (ROC) curve, the area under the ROC curve (AUC), as the objective function for these purposes. We show that the proposed method consistently estimate the AUC when the number of covariates is fixed and the sample size is large. The proposed sigmoid objective function makes it computationally feasible for variable selection in high-dimensional settings. We investigate gradient directed techniques, including the L1 boosting based LASSO (least absolute shrinkage and selection operator) and the TGDR (threshold gradient descent regularization), that can identify the important genomic biomarkers from the data. The proposed methods yield parsimonious models with excellent classification performance measured by the AUC. We demonstrate the proposed methods with two cancer studies that use Affymetrix genechip expression data