Statistical theory and the evaluation of Cox's proportional hazards model regularized by various penalties for survival DNA microarray expression data

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In this study, we created programs using the R language to calculate statistical properties of Cox's proportional hazards model regularized by various penalties, including the statistical power based on the prognostic index, and conducted simulation experiments under various conditions of DNA microarray expression data with survival time. The results showed that when the number of candidate genes is larger than the sample size, the power of a validation set for penalized methods is greater than for stepwise methods in many cases. This tendency is most remarkable for the penalized methods including both the L1-norm and the L2-norm. Furthermore, we verified our programs to actual microarray gene expression data with survival time data to confirm their validity. Our simulation programs for Cox's proportional hazards model regularized by various penalties are very useful for planning DNA microarray studies or for evaluating the results of such studies.