Using regularization patterns from penalized regression in microarray experiments

Microarray experiments have been used to investigate the relationship between gene expression and survival in cancer patients. Many methods have been developed, but most of them do not take into account other prognostic variables and the interplay among genes. A solution consists in using penalized regression models for censored survival data. We propose a single graphical approach to complement penalized regression analysis. In this paper, we illustrate the methodology using a penalized Cox regression approach on two different microarray data sets (colon and lung cancer). A small simulation study completes the paper. On both data sets, we applied a L2 penalized Cox Regression, after having pre-selected the most relevant sets of gene expression data according to a generalized logrank test. The patterns of estimated gene expression coefficients were explored varying the penalty parameter. We compared these results with those obtained while using a L1 penalty and found that the two approaches gave consistent, but not identical, results. The simulation study confirms the results for three different correlation scenarios. Theoretical considerations indicate that the L2 penalized regression is a more appropriate approach in this context. We propose to consider the entire regularization pattern varying the penalty parameter as a graphical tool in a sensitivity analysis