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Survival Prediction Based on Compound Covariate under Cox Proportional Hazard Models

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  • Takeshi Emura
  • Yi-Hau Chen
  • Hsuan-Yu Chen

Abstract

Survival prediction from a large number of covariates is a current focus of statistical and medical research. In this paper, we study a methodology known as the compound covariate prediction performed under univariate Cox proportional hazard models. We demonstrate via simulations and real data analysis that the compound covariate method generally competes well with ridge regression and Lasso methods, both already well-studied methods for predicting survival outcomes with a large number of covariates. Furthermore, we develop a refinement of the compound covariate method by incorporating likelihood information from multivariate Cox models. The new proposal is an adaptive method that borrows information contained in both the univariate and multivariate Cox regression estimators. We show that the new proposal has a theoretical justification from a statistical large sample theory and is naturally interpreted as a shrinkage-type estimator, a popular class of estimators in statistical literature. Two datasets, the primary biliary cirrhosis of the liver data and the non-small-cell lung cancer data, are used for illustration. The proposed method is implemented in R package “compound.Cox” available in CRAN at http://cran.r-project.org/.

Suggested Citation

  • Takeshi Emura & Yi-Hau Chen & Hsuan-Yu Chen, 2012. "Survival Prediction Based on Compound Covariate under Cox Proportional Hazard Models," PLOS ONE, Public Library of Science, vol. 7(10), pages 1-12, October.
    • Handle: RePEc:plo:pone00:0047627
    DOI: 10.1371/journal.pone.0047627
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    1. Xi Zhao & Einar Andreas Rødland & Therese Sørlie & Bjørn Naume & Anita Langerød & Arnoldo Frigessi & Vessela N Kristensen & Anne-Lise Børresen-Dale & Ole Christian Lingjærde, 2011. "Combining Gene Signatures Improves Prediction of Breast Cancer Survival," PLOS ONE, Public Library of Science, vol. 6(3), pages 1-15, March.
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    Cited by:

    1. Ahmed A. Ewees & Mohammed A. A. Al-qaness & Laith Abualigah & Diego Oliva & Zakariya Yahya Algamal & Ahmed M. Anter & Rehab Ali Ibrahim & Rania M. Ghoniem & Mohamed Abd Elaziz, 2021. "Boosting Arithmetic Optimization Algorithm with Genetic Algorithm Operators for Feature Selection: Case Study on Cox Proportional Hazards Model," Mathematics, MDPI, vol. 9(18), pages 1-22, September.
    2. Emura, Takeshi & Chen, Yi-Hau, 2014. "Gene selection for survival data under dependent censoring: a copula-based approach," MPRA Paper 58043, University Library of Munich, Germany.
    3. Jialiang Li & Tonghui Yu & Jing Lv & Mei‐Ling Ting Lee, 2021. "Semiparametric model averaging prediction for lifetime data via hazards regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(5), pages 1187-1209, November.
    4. Emura, Takeshi & Kao, Fan-Hsuan & Michimae, Hirofumi, 2014. "An improved nonparametric estimator of sub-distribution function for bivariate competing risk models," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 229-241.

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    1. 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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