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**\(L_{1}\) penalized estimation in the Cox proportional hazards model.**
*(English)*
Zbl 1207.62185

Summary: 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.

### MSC:

62N02 | Estimation in survival analysis and censored data |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

65K10 | Numerical optimization and variational techniques |

62J12 | Generalized linear models (logistic models) |

92C50 | Medical applications (general) |

65C60 | Computational problems in statistics (MSC2010) |

Full Text:
DOI

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