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Cox Regression with Covariate Measurement Error

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  • CHENGCHENG HU
  • D. Y. LIN

Abstract

This article deals with parameter estimation in the Cox proportional hazards model when covariates are measured with error. We consider both the classical additive measurement error model and a more general model which represents the mis‐measured version of the covariate as an arbitrary linear function of the true covariate plus random noise. Only moment conditions are imposed on the distributions of the covariates and measurement error. Under the assumption that the covariates are measured precisely for a validation set, we develop a class of estimating equations for the vector‐valued regression parameter by correcting the partial likelihood score function. The resultant estimators are proven to be consistent and asymptotically normal with easily estimated variances. Furthermore, a corrected version of the Breslow estimator for the cumulative hazard function is developed, which is shown to be uniformly consistent and, upon proper normalization, converges weakly to a zero‐mean Gaussian process. Simulation studies indicate that the asymptotic approximations work well for practical sample sizes. The situation in which replicate measurements (instead of a validation set) are available is also studied.

Suggested Citation

  • Chengcheng Hu & D. Y. Lin, 2002. "Cox Regression with Covariate Measurement Error," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(4), pages 637-655, December.
    • Handle: RePEc:bla:scjsta:v:29:y:2002:i:4:p:637-655
    DOI: 10.1111/1467-9469.00310
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    Cited by:

    1. Cheng Zheng & Yingye Zheng, 2019. "Calibrating Variations in Biomarker Measures for Improving Prediction with Time-to-event Outcomes," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(3), pages 477-503, December.
    2. Yanqing Sun & Qingning Zhou & Peter B. Gilbert, 2023. "Analysis of the Cox Model with Longitudinal Covariates with Measurement Errors and Partly Interval Censored Failure Times, with Application to an AIDS Clinical Trial," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 430-454, July.
    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. Menggang Yu & Bin Nan, 2010. "Regression Calibration in Semiparametric Accelerated Failure Time Models," Biometrics, The International Biometric Society, vol. 66(2), pages 405-414, June.
    5. Yanyan Liu & Haibo Zhou & Jianwen Cai, 2009. "Estimated Pseudopartial-Likelihood Method for Correlated Failure Time Data with Auxiliary Covariates," Biometrics, The International Biometric Society, vol. 65(4), pages 1184-1193, December.
    6. Chen, Yurong & Feng, Yanqin & Sun, Jianguo, 2015. "Regression analysis of multivariate current status data with auxiliary covariates under the additive hazards model," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 34-45.
    7. Pamela A. Shaw & Ross L. Prentice, 2012. "Hazard Ratio Estimation for Biomarker-Calibrated Dietary Exposures," Biometrics, The International Biometric Society, vol. 68(2), pages 397-407, June.
    8. Chi-Chung Wen, 2010. "Semiparametric maximum likelihood estimation in Cox proportional hazards model with covariate measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(2), pages 199-217, September.
    9. Yanqin Feng & Yurong Chen, 2018. "Regression analysis of current status data with auxiliary covariates and informative observation times," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(2), pages 293-309, April.
    10. Cheng Zheng & Yiwen Zhang & Ying Huang & Ross Prentice, 2023. "Using Controlled Feeding Study for Biomarker Development in Regression Calibration for Disease Association Estimation," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 57-113, April.
    11. Li-Pang Chen & Grace Y. Yi, 2021. "Semiparametric methods for left-truncated and right-censored survival data with covariate measurement error," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 481-517, June.
    12. Yanqin Feng & Ling Ma & Jianguo Sun, 2015. "Regression Analysis of Current Status Data Under the Additive Hazards Model with Auxiliary Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 118-136, March.

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