  Cross validation is commonly used for selecting tuning parameters in
penalized regression, but its use in penalized Cox regression models has
received relatively little attention in the literature. Due to its partial
likelihood construction, carrying out cross validation for Cox models is not
straightforward, and there are several potential approaches for implementation.
Here, we propose two new cross-validation methods for Cox regression and
compare them to approaches that have been proposed elsewhere. Our proposed
approach of cross-validating the linear predictors seems to offer an attractive
balance of performance and numerical stability. We illustrate these advantages
using simulated data as well as using them to analyze data from a
high-dimensional study of survival in lung cancer patients.
