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Variable Selection in Threshold Regression Model with Applications to HIV Drug Adherence Data

Author

Listed:
  • Takumi Saegusa

    (University of Maryland)

  • Tianzhou Ma

    (University of Maryland)

  • Gang Li

    (University of California)

  • Ying Qing Chen

    (Fred Hutchinson Cancer Research Center)

  • Mei-Ling Ting Lee

    (University of Maryland)

Abstract

The threshold regression model is an effective alternative to the Cox proportional hazards regression model when the proportional hazards assumption is not met. This paper considers variable selection for threshold regression. This model has separate regression functions for the initial health status and the speed of degradation in health. This flexibility is an important advantage when considering relevant risk factors for a complex time-to-event model where one needs to decide which variables should be included in the regression function for the initial health status, in the function for the speed of degradation in health, or in both functions. In this paper, we extend the broken adaptive ridge (BAR) method, originally designed for variable selection for one regression function, to simultaneous variable selection for both regression functions needed in the threshold regression model. We establish variable selection consistency of the proposed method and asymptotic normality of the estimator of non-zero regression coefficients. Simulation results show that our method outperformed threshold regression without variable selection and variable selection based on the Akaike information criterion. We apply the proposed method to data from an HIV drug adherence study in which electronic monitoring of drug intake is used to identify risk factors for non-adherence.

Suggested Citation

  • Takumi Saegusa & Tianzhou Ma & Gang Li & Ying Qing Chen & Mei-Ling Ting Lee, 2020. "Variable Selection in Threshold Regression Model with Applications to HIV Drug Adherence Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(3), pages 376-398, December.
    • Handle: RePEc:spr:stabio:v:12:y:2020:i:3:d:10.1007_s12561-020-09284-1
    DOI: 10.1007/s12561-020-09284-1
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    References listed on IDEAS

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    1. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    2. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    3. Florian Frommlet & Grégory Nuel, 2016. "An Adaptive Ridge Procedure for L0 Regularization," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-23, February.
    4. Simon, Noah & Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2011. "Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i05).
    5. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    6. Tao Xiao & G. A. Whitmore & Xin He & Mei-Ling Ting Lee, 2012. "Threshold regression for time-to-event analysis: The stthreg package," Stata Journal, StataCorp LP, vol. 12(2), pages 257-283, June.
    7. Dai, Linlin & Chen, Kani & Sun, Zhihua & Liu, Zhenqiu & Li, Gang, 2018. "Broken adaptive ridge regression and its asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 334-351.
    8. 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.
    9. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    10. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    11. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    12. Lisha Chen & Jianhua Z. Huang, 2012. "Sparse Reduced-Rank Regression for Simultaneous Dimension Reduction and Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1533-1545, December.
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    Cited by:

    1. Mei-Ling Ting Lee & G. A. Whitmore, 2023. "Semiparametric predictive inference for failure data using first-hitting-time threshold regression," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 508-536, July.
    2. Yiming Chen & Paul J. Smith & Mei-Ling Ting Lee, 2023. "Causal Inference in Threshold Regression and the Neural Network Extension (TRNN)," Stats, MDPI, vol. 6(2), pages 1-24, April.
    3. Ying Qing Chen, 2020. "Introduction to Special Issue on ‘Statistical Methods for HIV/AIDS Research’," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(3), pages 263-266, December.

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