L1 Penalized Estimation in the Cox Proportional Hazards Model

This article presents a novel algorithm that efficiently computes L-1 penalized (lasso) estimates of parameters in high-dimensional models. The lasso has the property that it simultaneously performs variable selection and shrinkage, which makes it very useful for finding interpretable prediction rules in high-dimensional data. The new algorithm is based on a combination of gradient ascent optimization with the Newton-Raphson algorithm. It is described for a general likelihood function and can be applied in generalized linear models and other models with an L-1 penalty. The algorithm is demonstrated in the Cox proportional hazards model, predicting survival of breast cancer patients using gene expression data, and its performance is compared with competing approaches. An R package, penalized, that implements the method, is available on CRAN.