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A modified adaptive Lasso for identifying interactions in the Cox model with the heredity constraint

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  • Wang, Lu
  • Shen, Jincheng
  • Thall, Peter F.

Abstract

In many biomedical studies, identifying effects of covariate interactions on survival is a major goal. Important examples are treatment–subgroup interactions in clinical trials, and gene–gene or gene–environment interactions in genomic studies. A common problem when implementing a variable selection algorithm in such settings is the requirement that the model must satisfy the strong heredity constraint, wherein an interaction may be included in the model only if the interaction’s component variables are included as main effects. We propose a modified Lasso method for the Cox regression model that adaptively selects important single covariates and pairwise interactions while enforcing the strong heredity constraint. The proposed method is based on a modified log partial likelihood including two adaptively weighted penalties, one for main effects and one for interactions. A two-dimensional tuning parameter for the penalties is determined by generalized cross-validation. Asymptotic properties are established, including consistency and rate of convergence, and it is shown that the proposed selection procedure has oracle properties, given proper choice of regularization parameters. Simulations illustrate that the proposed method performs reliably across a range of different scenarios.

Suggested Citation

  • Wang, Lu & Shen, Jincheng & Thall, Peter F., 2014. "A modified adaptive Lasso for identifying interactions in the Cox model with the heredity constraint," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 126-133.
    • Handle: RePEc:eee:stapro:v:93:y:2014:i:c:p:126-133
    DOI: 10.1016/j.spl.2014.06.024
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    References listed on IDEAS

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    1. 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.
    2. Radchenko, Peter & James, Gareth M., 2010. "Variable Selection Using Adaptive Nonlinear Interaction Structures in High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1541-1553.
    3. 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.
    4. Wei Lin & Jinchi Lv, 2013. "High-Dimensional Sparse Additive Hazards Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 247-264, March.
    5. Hao Helen Zhang & Wenbin Lu, 2007. "Adaptive Lasso for Cox's proportional hazards model," Biometrika, Biometrika Trust, vol. 94(3), pages 691-703.
    6. Choi, Nam Hee & Li, William & Zhu, Ji, 2010. "Variable Selection With the Strong Heredity Constraint and Its Oracle Property," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 354-364.
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    Cited by:

    1. Du, Mingyue & Zhao, Xingqiu & Sun, Jianguo, 2022. "Variable selection for case-cohort studies with informatively interval-censored outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
    2. Xing Qin & Shuangge Ma & Mengyun Wu, 2023. "Two‐level Bayesian interaction analysis for survival data incorporating pathway information," Biometrics, The International Biometric Society, vol. 79(3), pages 1761-1774, September.

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