Novel harmonic regularization approach for variable selection in Cox's proportional hazards model.

Ge-Jin Chu,Jia-Xuan Wang,Yong Liang

doi:10.1155/2014/857398

Ge-Jin Chu, Jia-Xuan Wang + Show 1 more

Open Access

https://doi.org/10.1155/2014/857398

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Abstract

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 Lq (1/2 < q < 1) 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.

Highlights

One of the most important objectives for survival analysis is to select a small number of key risk factors from many potential predictors [1, 2]
Variable selection is a fundamental problem in statistics and machine learning, and the regularization method is one of the ways to solve this problem
In the procedure of variable selection, the harmonic regularization is like a net which can always catch the correct model

Summary

Introduction

One of the most important objectives for survival analysis is to select a small number of key risk factors from many potential predictors [1, 2]. The Cox proportional hazards model [3, 4] is used to study the relationship between predictor variables and survival time. A series of penalized partial likelihood methods, such as the L1 [5,6,7,8], Lq (0 < q < 1) [9] and L1/2 [10, 11] penalized methods were proposed for Cox’s proportional hazards model. These penalized partial likelihood methods find important risk factors by shrinking some regression coefficients to zero.

Harmonic Regularization

The Harmonic Regularization Algorithm for the Cox Model

Simulation

Conclusion