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Empirical Likelihood in Nonignorable Covariate-Missing Data Problems

Author

Listed:
  • Xie Yanmei

    (Department of Mathematics and Statistics, The University of Toledo, Toledo, OH 43606, USA)

  • Zhang Biao

    (Department of Mathematics and Statistics, The University of Toledo, Toledo, OH 43606, USA)

Abstract

Missing covariate data occurs often in regression analysis, which frequently arises in the health and social sciences as well as in survey sampling. We study methods for the analysis of a nonignorable covariate-missing data problem in an assumed conditional mean function when some covariates are completely observed but other covariates are missing for some subjects. We adopt the semiparametric perspective of Bartlett et al. (Improving upon the efficiency of complete case analysis when covariates are MNAR. Biostatistics 2014;15:719–30) on regression analyses with nonignorable missing covariates, in which they have introduced the use of two working models, the working probability model of missingness and the working conditional score model. In this paper, we study an empirical likelihood approach to nonignorable covariate-missing data problems with the objective of effectively utilizing the two working models in the analysis of covariate-missing data. We propose a unified approach to constructing a system of unbiased estimating equations, where there are more equations than unknown parameters of interest. One useful feature of these unbiased estimating equations is that they naturally incorporate the incomplete data into the data analysis, making it possible to seek efficient estimation of the parameter of interest even when the working regression function is not specified to be the optimal regression function. We apply the general methodology of empirical likelihood to optimally combine these unbiased estimating equations. We propose three maximum empirical likelihood estimators of the underlying regression parameters and compare their efficiencies with other existing competitors. We present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification. The proposed empirical likelihood method is also illustrated by an analysis of a data set from the US National Health and Nutrition Examination Survey (NHANES).

Suggested Citation

  • Xie Yanmei & Zhang Biao, 2017. "Empirical Likelihood in Nonignorable Covariate-Missing Data Problems," The International Journal of Biostatistics, De Gruyter, vol. 13(1), pages 1-20, May.
    • Handle: RePEc:bpj:ijbist:v:13:y:2017:i:1:p:20:n:6
    DOI: 10.1515/ijb-2016-0053
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    References listed on IDEAS

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    1. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz & Amy H. Herring, 2005. "Missing-Data Methods for Generalized Linear Models: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 332-346, March.
    2. Chen S.X. & Leung D.H.Y. & Qin J., 2003. "Information Recovery in a Study With Surrogate Endpoints," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1052-1062, January.
    3. Qihua Wang & Pengjie Dai, 2008. "Semiparametric model-based inference in the presence of missing responses," Biometrika, Biometrika Trust, vol. 95(3), pages 721-734.
    4. Jing Qin & Biao Zhang, 2007. "Empirical‐likelihood‐based inference in missing response problems and its application in observational studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 101-122, February.
    5. Qihua Wang, 2002. "Empirical likelihood-based inference in linear errors-in-covariables models with validation data," Biometrika, Biometrika Trust, vol. 89(2), pages 345-358, June.
    6. Hua Liang & Suojin Wang & Raymond J. Carroll, 2007. "Partially linear models with missing response variables and error-prone covariates," Biometrika, Biometrika Trust, vol. 94(1), pages 185-198.
    7. Stute, Winfried & Xue, Liugen & Zhu, Lixing, 2007. "Empirical Likelihood Inference in Nonlinear Errors-in-Covariables Models With Validation Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 332-346, March.
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