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Expected estimating equations to accommodate covariate measurement error

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  • C.‐Y. Wang
  • Margaret Sullivan Pepe

Abstract

Estimating equations which are not necessarily likelihood‐based score equations are becoming increasingly popular for estimating regression model parameters. This paper is concerned with estimation based on general estimating equations when true covariate data are missing for all the study subjects, but surrogate or mismeasured covariates are available instead. The method is motivated by the covariate measurement error problem in marginal or partly conditional regression of longitudinal data. We propose to base estimation on the expectation of the complete data estimating equation conditioned on available data. The regression parameters and other nuisance parameters are estimated simultaneously by solving the resulting estimating equations. The expected estimating equation (EEE) estimator is equal to the maximum likelihood estimator if the complete data scores are likelihood scores and conditioning is with respect to all the available data. A pseudo‐EEE estimator, which requires less computation, is also investigated. Asymptotic distribution theory is derived. Small sample simulations are conducted when the error process is an order 1 autoregressive model. Regression calibration is extended to this setting and compared with the EEE approach. We demonstrate the methods on data from a longitudinal study of the relationship between childhood growth and adult obesity.

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  • C.‐Y. Wang & Margaret Sullivan Pepe, 2000. "Expected estimating equations to accommodate covariate measurement error," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 509-524.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:3:p:509-524
    DOI: 10.1111/1467-9868.00247
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    Cited by:

    1. Tsimikas, John V. & Bantis, Leonidas E. & Georgiou, Stelios D., 2012. "Inference in generalized linear regression models with a censored covariate," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1854-1868.
    2. Glen McGee & Marianthi‐Anna Kioumourtzoglou & Marc G. Weisskopf & Sebastien Haneuse & Brent A. Coull, 2020. "On the interplay between exposure misclassification and informative cluster size," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1209-1226, November.
    3. Yutaka Yasui & Margaret Pepe & Li Hsu & Bao-Ling Adam & Ziding Feng, 2004. "Partially Supervised Learning Using an EM-Boosting Algorithm," Biometrics, The International Biometric Society, vol. 60(1), pages 199-206, March.
    4. Wang, C. Y. & Huang, Yijian, 2001. "Functional methods for logistic regression on random-effect-coefficients for longitudinal measurements," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 347-356, July.
    5. Wang, Qihua & Yu, Keming, 2007. "Likelihood-based kernel estimation in semiparametric errors-in-covariables models with validation data," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 455-480, March.
    6. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Zhang, Jiajia, 2018. "Robust estimation in linear regression models for longitudinal data with covariate measurement errors and outliers," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 261-275.

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