Variable Selection and Outlier Detection in Regularized Survival Models: Application to Melanoma Gene Expression Data

The importance of gene expression data analysis for oncological diagnosis and treatment has become widely accepted in recent years. One of the main associated challenges is the development of mathematical and statistical methods for data analysis to improve prognosis and guide treatment decisions. One of the difficulties that researchers face when dealing with gene expression datasets concerns their high-dimensionality. In this context, the goal of this work is to reduce the dimensionality of gene expression data using regularization techniques such as Lasso and Elastic net, complemented with DegreeCox, a network-based regularization method for survival analysis recently proposed. Also identification of long or short-term survivors (outliers) may lead to the detection of new prognostic factors, and the Rank Product test is used to identify those observations. An example based on the The Cancer Genome Atlas (TCGA) Melanoma dataset is presented, where the covariates are patients’ gene expression. The application of data reduction techniques to the Melanoma dataset enabled the selection of relevant genes over a range of parameters evaluated, with 5 in common between elastic net regularization and DegreeCox for one of the two models further evaluated. Moreover, a long term survivor was detected as outlier by the Rank Product test, being systematically highly ranked for the martingale residuals of the models evaluated.