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The Dantzig selector in Cox's proportional hazards model

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  • Antoniadis, Anestis
  • Fryzlewicz, Piotr
  • Letué, Frédérique

Abstract

The Dantzig selector (DS) is a recent approach of estimation in high-dimensional linear regression models with a large number of explanatory variables and a relatively small number of observations. As in the least absolute shrinkage and selection operator (LASSO), this approach sets certain regression coefficients exactly to zero, thus performing variable selection. However, such a framework, contrary to the LASSO, has never been used in regression models for survival data with censoring. A key motivation of this article is to study the estimation problem for Cox's proportional hazards (PH) function regression models using a framework that extends the theory, the computational advantages and the optimal asymptotic rate properties of the DS to the class of Cox's PH under appropriate sparsity scenarios. We perform a detailed simulation study to compare our approach with other methods and illustrate it on a well-known microarray gene expression data set for predicting survival from gene expressions.

Suggested Citation

  • Antoniadis, Anestis & Fryzlewicz, Piotr & Letué, Frédérique, 2010. "The Dantzig selector in Cox's proportional hazards model," LSE Research Online Documents on Economics 30992, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:30992
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    References listed on IDEAS

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    Cited by:

    1. Gerda Claeskens, 2012. "Focused estimation and model averaging with penalization methods: an overview," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(3), pages 272-287, August.
    2. Jianbo Li & Yuan Li & Riquan Zhang, 2017. "B spline variable selection for the single index models," Statistical Papers, Springer, vol. 58(3), pages 691-706, September.
    3. Li, Jianbo & Gu, Minggao & Zhang, Riquan, 2013. "Variable selection for general transformation models with right censored data via nonconcave penalties," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 445-456.
    4. Li, Jianbo & Gu, Minggao, 2012. "Adaptive LASSO for general transformation models with right censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2583-2597.

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    More about this item

    Keywords

    Dantzig selector; generalized linear models; LASSO; penalized partial likelihood; proportional hazards model; variable selection;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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