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Integrative Analysis of Cancer Diagnosis Studies with Composite Penalization

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  • Jin Liu
  • Shuangge Ma
  • Jian Huang

Abstract

xml:id="sjos816-abs-0001" type="main" xml:lang="en"> In cancer diagnosis studies, high-throughput gene profiling has been extensively conducted, searching for genes whose expressions may serve as markers. Data generated from such studies have the ‘large d, small n’ feature, with the number of genes profiled much larger than the sample size. Penalization has been extensively adopted for simultaneous estimation and marker selection. Because of small sample sizes, markers identified from the analysis of single data sets can be unsatisfactory. A cost-effective remedy is to conduct integrative analysis of multiple heterogeneous data sets. In this article, we investigate composite penalization methods for estimation and marker selection in integrative analysis. The proposed methods use the minimax concave penalty (MCP) as the outer penalty. Under the homogeneity model, the ridge penalty is adopted as the inner penalty. Under the heterogeneity model, the Lasso penalty and MCP are adopted as the inner penalty. Effective computational algorithms based on coordinate descent are developed. Numerical studies, including simulation and analysis of practical cancer data sets, show satisfactory performance of the proposed methods.

Suggested Citation

  • Jin Liu & Shuangge Ma & Jian Huang, 2014. "Integrative Analysis of Cancer Diagnosis Studies with Composite Penalization," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 87-103, March.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:1:p:87-103
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    File URL: http://hdl.handle.net/10.1111/j.1467-9469.2012.00816.x
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    References listed on IDEAS

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    1. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    2. Mazumder, Rahul & Friedman, Jerome H. & Hastie, Trevor, 2011. "SparseNet: Coordinate Descent With Nonconvex Penalties," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1125-1138.
    3. Jian Huang & Shuange Ma & Huiliang Xie & Cun-Hui Zhang, 2009. "A group bridge approach for variable selection," Biometrika, Biometrika Trust, vol. 96(2), pages 339-355.
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    Cited by:

    1. Wu, Cen & Zhang, Qingzhao & Jiang, Yu & Ma, Shuangge, 2018. "Robust network-based analysis of the associations between (epi)genetic measurements," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 119-130.
    2. Jin Liu & Jian Huang & Yawei Zhang & Qing Lan & Nathaniel Rothman & Tongzhang Zheng & Shuangge Ma, 2014. "Integrative analysis of prognosis data on multiple cancer subtypes," Biometrics, The International Biometric Society, vol. 70(3), pages 480-488, September.
    3. Zhang, Qingzhao & Ma, Shuangge & Huang, Yuan, 2021. "Promote sign consistency in the joint estimation of precision matrices," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    4. Gregory Vaughan & Robert Aseltine & Kun Chen & Jun Yan, 2017. "Stagewise generalized estimating equations with grouped variables," Biometrics, The International Biometric Society, vol. 73(4), pages 1332-1342, December.
    5. Fang, Kuangnan & Fan, Xinyan & Zhang, Qingzhao & Ma, Shuangge, 2018. "Integrative sparse principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 1-16.
    6. Shirong Deng & Jie Chen & Huidong Shi, 2021. "Integrative analysis of multiple types of genomic data using an accelerated failure time frailty model," Computational Statistics, Springer, vol. 36(2), pages 1499-1532, June.

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