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Robust sandwich covariance estimation for regression calibration estimator in Cox regression with measurement error

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  • Wang, C. Y.

Abstract

Prentice (1982) proposed a regression calibration estimator in Cox regression when covariate variables are measured with error. However, estimation of the covariance of this estimator has not yet been discussed in the literature. The regression calibration estimator is to replace an unobserved covariate variable by its conditional expectation given observed covariate variables. Therefore, a standard Cox (1972) regression program based on the partial-likelihood estimating equation (such as the coxreg function in S-plus) may be applied to the replacement data for parameter estimation. However, covariance estimation of the regression estimator based on a standard Cox regression program may lead to bias estimation. This paper provides a simple sandwich formula for the covariance estimation. The covariance estimator is valid under a possibly misspecified Cox proportional hazards model when repeated measurements are available for the covariate that is measured with error. This method is important in practice since it is easy to implement, and inference based on it is valid if the hazard ratio parameter for the mismeasured covariate is not large. Results from intensive simulation studies are given.

Suggested Citation

  • Wang, C. Y., 1999. "Robust sandwich covariance estimation for regression calibration estimator in Cox regression with measurement error," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 371-378, December.
    • Handle: RePEc:eee:stapro:v:45:y:1999:i:4:p:371-378
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    Citations

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    Cited by:

    1. C. Y. Wang & Naisyin Wang & Suojin Wang, 2000. "Regression Analysis When Covariates Are Regression Parameters of a Random Effects Model for Observed Longitudinal Measurements," Biometrics, The International Biometric Society, vol. 56(2), pages 487-495, June.
    2. Yu Hsiang & Cheng Yu-Jen & Wang Ching-Yun, 2016. "Semiparametric Regression Estimation for Recurrent Event Data with Errors in Covariates under Informative Censoring," The International Journal of Biostatistics, De Gruyter, vol. 12(2), pages 1-18, November.
    3. Ching-Yun Wang & Harry Cullings & Xiao Song & Kenneth J. Kopecky, 2017. "Joint non-parametric correction estimator for excess relative risk regression in survival analysis with exposure measurement error," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1583-1599, November.
    4. 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.
    5. Li‐Pang Chen & Grace Y. Yi, 2021. "Analysis of noisy survival data with graphical proportional hazards measurement error models," Biometrics, The International Biometric Society, vol. 77(3), pages 956-969, September.
    6. 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.

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