Variable Selection for Survival Data with A Class of Adaptive Elastic Net Techniques

Abstract: The accelerated failure time (AFT) models have proved useful in many contexts, though heavy censoring (as for example in cancer survival) and high dimensionality (as for example in microarray data) cause difficulties for model fitting and model selection. We propose new approaches to variable selection for censored data, based on AFT models optimized using regularized weighted least squares. The regularized technique uses a mixture of L1 and L2 norm penalties under two proposed elastic net type approaches. One is the the adaptive elastic net and the other is weighted elastic net. The approaches extend the original approaches proposed by Ghosh (2007), and Hong and Zhang (2010) respectively. We also extend the two proposed approaches by adding censoring observations as constraints into their model optimization frameworks. The approaches are evaluated on microarray and by simulation. We compare the performance of these approaches with six other variable selection techniques--three are generally used for censored data and the other three are correlation-based greedy methods used for high-dimensional data.