Efficient Method to Optimally Identify Important Biomarkers for Disease Outcomes with High-Dimensional Data

• Activity Number: 303
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Mental Health Statistics Section
• Author(s): Xiang Li* and Shanghong Xie and Donglin Zeng and Yuanjia Wang
• Companies: Columbia University and Columbia University and The University of North Carolina at Chapel Hill and Columbia University
• Keywords: ADMM Algorithm ; Biomarker Signature ; Censored Data ; High-dimensional Data ; L0-Penalty ; Variable Selection

Abstract

Advances in high-throughput technologies in genomics and imaging yield unprecedentedly large number of prognostic biomarkers. The ideal variable selection procedure would search for the best subset of predictors, which is equivalent to imposing an L0-penalty on the regression coefficients. Since this optimization is a NP-hard problem, we propose a two-stage procedure for L0-penalty variable selection based on an alternating direction method of multipliers (ADMM) algorithm with an augmented penalization (ADMM-L0). Our method iterates between a convex regularized regression and a simple hard-thresholding estimation. We propose to simultaneously select regularization tuning parameter and thresholding parameter based on cross-validation. A one-step coordinate descent algorithm is used in the first stage to significantly improve computational efficiency. Through extensive simulation studies and real data application in Huntington's disease, we demonstrate superior performance of the proposed method in terms of selection accuracy and computational speed as compared to existing methods. The ADMM-L0 procedure outlined here is implemented in the R-package ADMMnet.