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Univariate Shrinkage in the Cox Model for High Dimensional Data

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  • Tibshirani Robert J.

    (Stanford University)

Abstract

We propose a method for prediction in Cox's proportional model, when the number of features (regressors), p, exceeds the number of observations, n. The method assumes that the features are independent in each risk set, so that the partial likelihood factors into a product. As such, it is analogous to univariate thresholding in linear regression and nearest shrunken centroids in classification. We call the procedure Cox univariate shrinkage and demonstrate its usefulness on real and simulated data. The method has the attractive property of being essentially univariate in its operation: the features are entered into the model based on the size of their Cox score statistics. We illustrate the new method on real and simulated data, and compare it to other proposed methods for survival prediction with a large number of predictors.

Suggested Citation

  • Tibshirani Robert J., 2009. "Univariate Shrinkage in the Cox Model for High Dimensional Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-18, April.
  • Handle: RePEc:bpj:sagmbi:v:8:y:2009:i:1:n:21
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    Cited by:

    1. Chakraborty, Sounak & Guo, Ruixin, 2011. "A Bayesian hybrid Huberized support vector machine and its applications in high-dimensional medical data," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1342-1356, March.
    2. Zhao, Sihai Dave & Li, Yi, 2012. "Principled sure independence screening for Cox models with ultra-high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 397-411.
    3. repec:eee:csdana:v:112:y:2017:i:c:p:1-13 is not listed on IDEAS
    4. repec:eee:csdana:v:119:y:2018:i:c:p:74-85 is not listed on IDEAS
    5. Emura, Takeshi & Chen, Yi-Hau & Chen, Hsuan-Yu, 2012. "Survival prediction based on compound covariate under cox proportional hazard models," MPRA Paper 41149, University Library of Munich, Germany.

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