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Quantile forward regression for high-dimensional survival data

Author

Listed:
  • Eun Ryung Lee

    (Sungkyunkwan University)

  • Seyoung Park

    (Sungkyunkwan University)

  • Sang Kyu Lee

    (Michigan State University
    National Cancer Institute)

  • Hyokyoung G. Hong

    (National Cancer Institute)

Abstract

Despite the urgent need for an effective prediction model tailored to individual interests, existing models have mainly been developed for the mean outcome, targeting average people. Additionally, the direction and magnitude of covariates’ effects on the mean outcome may not hold across different quantiles of the outcome distribution. To accommodate the heterogeneous characteristics of covariates and provide a flexible risk model, we propose a quantile forward regression model for high-dimensional survival data. Our method selects variables by maximizing the likelihood of the asymmetric Laplace distribution (ALD) and derives the final model based on the extended Bayesian Information Criterion (EBIC). We demonstrate that the proposed method enjoys a sure screening property and selection consistency. We apply it to the national health survey dataset to show the advantages of a quantile-specific prediction model. Finally, we discuss potential extensions of our approach, including the nonlinear model and the globally concerned quantile regression coefficients model.

Suggested Citation

  • Eun Ryung Lee & Seyoung Park & Sang Kyu Lee & Hyokyoung G. Hong, 2023. "Quantile forward regression for high-dimensional survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 769-806, October.
    • Handle: RePEc:spr:lifeda:v:29:y:2023:i:4:d:10.1007_s10985-023-09603-w
    DOI: 10.1007/s10985-023-09603-w
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    References listed on IDEAS

    as
    1. Park, Seyoung & Lee, Eun Ryung, 2021. "Hypothesis testing of varying coefficients for regional quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    2. Kong, Yinfei & Li, Yujie & Zerom, Dawit, 2019. "Screening and selection for quantile regression using an alternative measure of variable importance," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 435-455.
    3. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    4. Nena Karavasiloglou & Giulia Pestoni & Miriam Wanner & David Faeh & Sabine Rohrmann, 2019. "Healthy lifestyle is inversely associated with mortality in cancer survivors: Results from the Third National Health and Nutrition Examination Survey (NHANES III)," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-11, June.
    5. Honda, Toshio & 本田, 敏雄 & Lin, Chien-Tong, 2022. "Forward variable selection for ultra-high dimensional quantile regression models," Discussion Papers 2021-02, Graduate School of Economics, Hitotsubashi University.
    6. Ming-Yen Cheng & Toshio Honda & Jin-Ting Zhang, 2016. "Forward Variable Selection for Sparse Ultra-High Dimensional Varying Coefficient Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1209-1221, July.
    7. Shan Luo & Zehua Chen, 2014. "Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1229-1240, September.
    8. Shujie Ma & Runze Li & Chih-Ling Tsai, 2017. "Variable Screening via Quantile Partial Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 650-663, April.
    9. Eun Ryung Lee & Hohsuk Noh & Byeong U. Park, 2014. "Model Selection via Bayesian Information Criterion for Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 216-229, March.
    10. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    11. Wang, Hansheng, 2009. "Forward Regression for Ultra-High Dimensional Variable Screening," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1512-1524.
    12. Hyokyoung G. Hong & Jian Kang & Yi Li, 2018. "Conditional screening for ultra-high dimensional covariates with survival outcomes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 45-71, January.
    13. Lan Wang & Yichao Wu & Runze Li, 2012. "Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 214-222, March.
    14. Qi Zheng & Hyokyoung G. Hong & Yi Li, 2020. "Building generalized linear models with ultrahigh dimensional features: A sequentially conditional approach," Biometrics, The International Biometric Society, vol. 76(1), pages 47-60, March.
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