The L(1/2) regularization approach for survival analysis in the accelerated failure time model.

The analysis of high-dimensional and low-sample size microarray data for survival analysis of cancer patients is an important problem. It is a huge challenge to select the significantly relevant bio-marks from microarray gene expression datasets, in which the number of genes is far more than the size of samples. In this article, we develop a robust prediction approach for survival time of patient by a L(1/2) regularization estimator with the accelerated failure time (AFT) model. The L(1/2) regularization could be seen as a typical delegate of L(q)(0<q<1) regularization methods and it has shown many attractive features. In order to optimize the problem of the relevant gene selection in high-dimensional biological data, we implemented the L(1/2) regularized AFT model by the coordinate descent algorithm with a renewed half thresholding operator. The results of the simulation experiment showed that we could obtain more accurate and sparse predictor for survival analysis by the L(1/2) regularized AFT model compared with other L1 type regularization methods. The proposed procedures are applied to five real DNA microarray datasets to efficiently predict the survival time of patient based on a set of clinical prognostic factors and gene signatures.