  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.
