Hybrid L_{1/2  + 2} method for gene selection in the Cox proportional hazards model

An important issue in genomic research is to identify the significant genes that related to survival from tens of thousands of genes. Although Cox proportional hazards model is a conventional survival analysis method, it does not induce the gene selection.

In this paper, we extend the hybrid L_{1/2  + 2} regularization (HLR) idea to the censored survival situation, a new edition of sparse Cox model based on the HLR method has been proposed. We develop two algorithms for solving the HLR penalized Cox model; one is the coordinate descent algorithm with HLR thresholding operator, the other is the weight iteration method.

The proposed method was tested on six public mRNA data sets of serval kinds of cancers, AML, Breast cancer, Pancreatic cancer, DLBCL and Melanoma. The test results indicate that the method identified a small subset of genes but essential while giving best or equivalent predictive performance, as compared to some popular methods.

The results of empirical and simulations imply that the proposed strategy is highly competitive in studying high dimensional survival data among several state-of-the-art methods.