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Cox regression with dependent error in covariates

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  • Yijian Huang
  • Ching†Yun Wang

Abstract

Many survival studies have error†contaminated covariates due to the lack of a gold standard of measurement. Furthermore, the error distribution can depend on the true covariates but the structure may be difficult to characterize; heteroscedasticity is a common manifestation. We suggest a novel dependent measurement error model with minimal assumptions on the dependence structure, and propose a new functional modeling method for Cox regression when an instrumental variable is available. This proposal accommodates much more general error contamination than existing approaches including nonparametric correction methods of Huang and Wang (2000, Journal of the American Statistical Association 95, 1209–1219; 2006, Statistica Sinica 16, 861–881). The estimated regression coefficients are consistent and asymptotically normal, and a consistent variance estimate is provided for inference. Simulations demonstrate that the procedure performs well even under substantial error contamination. Illustration with a clinical study is provided.

Suggested Citation

  • Yijian Huang & Ching†Yun Wang, 2018. "Cox regression with dependent error in covariates," Biometrics, The International Biometric Society, vol. 74(1), pages 118-126, March.
    • Handle: RePEc:bla:biomet:v:74:y:2018:i:1:p:118-126
    DOI: 10.1111/biom.12741
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    References listed on IDEAS

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    1. Sharon X. Xie & C. Y. Wang & Ross L. Prentice, 2001. "A risk set calibration method for failure time regression by using a covariate reliability sample," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 855-870.
    2. Xiao Song & Ching-Yun Wang, 2014. "Proportional Hazards Model With Covariate Measurement Error and Instrumental Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1636-1646, December.
    3. Yi Li & Louise Ryan, 2004. "Survival Analysis With Heterogeneous Covariate Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 724-735, January.
    4. Hu, Chengcheng & Lin, D.Y., 2004. "Semiparametric Failure Time Regression With Replicates of Mismeasured Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 105-118, January.
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    Cited by:

    1. William Liu, 2023. "A Theory Guide to Using Control Functions to Instrument Hazard Models," Papers 2312.03165, arXiv.org.

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