L1 penalized estimation in the Cox proportional hazards model

Biom J. 2010 Feb;52(1):70-84. doi: 10.1002/bimj.200900028.


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.

Publication types

  • Comparative Study

MeSH terms

  • Algorithms*
  • Breast Neoplasms / genetics
  • Computer Simulation
  • Female
  • Gene Expression Profiling / methods
  • Humans
  • Models, Genetic*
  • Proportional Hazards Models*
  • Survival Analysis