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Computational and Mathematical Methods in Medicine
Volume 2014, Article ID 857398, 9 pages
Research Article

Novel Harmonic Regularization Approach for Variable Selection in Cox’s Proportional Hazards Model

University Hospital, State Key Laboratory of Quality Research in Chinese Medicines, Faculty of Information Technology, Macau University of Science and Technology, Macau

Received 23 April 2014; Revised 13 July 2014; Accepted 25 July 2014; Published 24 November 2014

Academic Editor: Andrzej Kloczkowski

Copyright © 2014 Ge-Jin Chu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Variable selection is an important issue in regression and a number of variable selection methods have been proposed involving nonconvex penalty functions. In this paper, we investigate a novel harmonic regularization method, which can approximate nonconvex regularizations, to select key risk factors in the Cox’s proportional hazards model using microarray gene expression data. The harmonic regularization method can be efficiently solved using our proposed direct path seeking approach, which can produce solutions that closely approximate those for the convex loss function and the nonconvex regularization. Simulation results based on the artificial datasets and four real microarray gene expression datasets, such as real diffuse large B-cell lymphoma (DCBCL), the lung cancer, and the AML datasets, show that the harmonic regularization method can be more accurate for variable selection than existing Lasso series methods.