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Semiparametric regression calibration for general hazard models in survival analysis with covariate measurement error; surprising performance under linear hazard

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  • Ching‐Yun Wang
  • Xiao Song

Abstract

Observational epidemiological studies often confront the problem of estimating exposure‐disease relationships when the exposure is not measured exactly. Regression calibration (RC) is a common approach to correct for bias in regression analysis with covariate measurement error. In survival analysis with covariate measurement error, it is well known that the RC estimator may be biased when the hazard is an exponential function of the covariates. In the paper, we investigate the RC estimator with general hazard functions, including exponential and linear functions of the covariates. When the hazard is a linear function of the covariates, we show that a risk set regression calibration (RRC) is consistent and robust to a working model for the calibration function. Under exponential hazard models, there is a trade‐off between bias and efficiency when comparing RC and RRC. However, one surprising finding is that the trade‐off between bias and efficiency in measurement error research is not seen under linear hazard when the unobserved covariate is from a uniform or normal distribution. Under this situation, the RRC estimator is in general slightly better than the RC estimator in terms of both bias and efficiency. The methods are applied to the Nutritional Biomarkers Study of the Women's Health Initiative.

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  • Ching‐Yun Wang & Xiao Song, 2021. "Semiparametric regression calibration for general hazard models in survival analysis with covariate measurement error; surprising performance under linear hazard," Biometrics, The International Biometric Society, vol. 77(2), pages 561-572, June.
    • Handle: RePEc:bla:biomet:v:77:y:2021:i:2:p:561-572
    DOI: 10.1111/biom.13318
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    References listed on IDEAS

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    5. Qi, Lihong & Wang, C.Y. & Prentice, Ross L., 2005. "Weighted Estimators for Proportional Hazards Regression With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1250-1263, December.
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    1. Ching-Yun Wang & Jean de Dieu Tapsoba & Catherine Duggan & Anne McTiernan, 2024. "Generalized Linear Models with Covariate Measurement Error and Zero-Inflated Surrogates," Mathematics, MDPI, vol. 12(2), pages 1-14, January.

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