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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 1-20, April.
    • Handle: RePEc:bpj:sagmbi:v:8:y:2009:i:1:n:21
    DOI: 10.2202/1544-6115.1438
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    1. Laura J. van 't Veer & Hongyue Dai & Marc J. van de Vijver & Yudong D. He & Augustinus A. M. Hart & Mao Mao & Hans L. Peterse & Karin van der Kooy & Matthew J. Marton & Anke T. Witteveen & George J. S, 2002. "Gene expression profiling predicts clinical outcome of breast cancer," Nature, Nature, vol. 415(6871), pages 530-536, January.
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    3. Jing Zhang & Guosheng Yin & Yanyan Liu & Yuanshan Wu, 2018. "Censored cumulative residual independent screening for ultrahigh-dimensional survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(2), pages 273-292, April.
    4. Yang Qu & Yu Cheng, 2023. "Volume under the ROC surface for high-dimensional independent screening with ordinal competing risk outcomes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 735-751, October.
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    6. Xie Xiaodong & Zheng Shaozhi, 2017. "Group MCP for Cox Models with Time-Varying Coefficients," Journal of Systems Science and Information, De Gruyter, vol. 4(5), pages 476-488, October.
    7. 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.
    8. 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.
    9. 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.
    10. Lee Kyu Ha & Chakraborty Sounak & Sun Jianguo, 2011. "Bayesian Variable Selection in Semiparametric Proportional Hazards Model for High Dimensional Survival Data," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-32, April.
    11. Jing Zhang & Haibo Zhou & Yanyan Liu & Jianwen Cai, 2021. "Conditional screening for ultrahigh-dimensional survival data in case-cohort studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 632-661, October.
    12. Lee, Kyu Ha & Chakraborty, Sounak & Sun, Jianguo, 2017. "Variable selection for high-dimensional genomic data with censored outcomes using group lasso prior," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 1-13.
    13. Jing Zhang & Haibo Zhou & Yanyan Liu & Jianwen Cai, 2021. "Feature screening for case‐cohort studies with failure time outcome," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 349-370, March.
    14. Jing Zhang & Yanyan Liu & Hengjian Cui, 2021. "Model-free feature screening via distance correlation for ultrahigh dimensional survival data," Statistical Papers, Springer, vol. 62(6), pages 2711-2738, December.

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