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L 1 Penalized Estimation in the Cox Proportional Hazards Model
Author(s) -
Goeman Jelle J.
Publication year - 2010
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200900028
Subject(s) - lasso (programming language) , mathematics , proportional hazards model , algorithm , feature selection , model selection , penalty method , r package , maximum likelihood , function (biology) , selection (genetic algorithm) , mathematical optimization , computer science , statistics , artificial intelligence , evolutionary biology , world wide web , biology
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.