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Empirical and weighted conditional likelihoods for matched case-control studies with missing covariates

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  • Liu, Tianqing
  • Yuan, Xiaohui
  • Li, Zhaohai
  • Li, Yuanzhang

Abstract

In clinical and epidemiological studies, matched case-control designs have been used extensively to investigate the relationships between disease/response and exposure/covariate. Due to the retrospective nature of the study, some covariates may not be observed for all study subjects and missing covariate information may create bias and reduce the efficiency of the parameter estimates. We explore the use of profile empirical likelihood (EL) to cope with this situation by combining unbiased estimating equations when the number of estimating equations is greater than the number of unknown parameters. For high dimensional covariates, we propose a weighted conditional likelihood (WCL) method to solve the computational problem of the profile EL method. The proposed EL and WCL methods can achieve semiparametric efficiency if the probability of missingness is correctly specified. Based on the EL and WCL functions, we also develop Wilks’ type tests and corresponding confidence regions for the model parameters. A simulation study is conducted to assess the performance of the proposed methods in terms of robustness and efficiency.

Suggested Citation

  • Liu, Tianqing & Yuan, Xiaohui & Li, Zhaohai & Li, Yuanzhang, 2013. "Empirical and weighted conditional likelihoods for matched case-control studies with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 185-199.
    • Handle: RePEc:eee:jmvana:v:119:y:2013:i:c:p:185-199
    DOI: 10.1016/j.jmva.2013.04.010
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    References listed on IDEAS

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    1. Paul J. Rathouz, 2003. "Likelihood methods for missing covariate data in highly stratified studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 711-723, August.
    2. 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.
    3. Qin, Jing & Shao, Jun & Zhang, Biao, 2008. "Efficient and Doubly Robust Imputation for Covariate-Dependent Missing Responses," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 797-810, June.
    4. Yuan, Xiaohui & Liu, Tianqing & Lin, Nan & Zhang, Baoxue, 2010. "Combining conditional and unconditional moment restrictions with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2420-2433, November.
    5. Qin, Jing & Zhang, Biao & Leung, Denis H. Y., 2009. "Empirical Likelihood in Missing Data Problems," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1492-1503.
    6. M. C. Paik & R. L. Sacco, 2000. "Matched case–control data analyses with missing covariates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(1), pages 145-156.
    7. Paul J. Rathouz, 2002. "Semiparametric inference in matched case-control studies with missing covariate data," Biometrika, Biometrika Trust, vol. 89(4), pages 905-916, December.
    8. Glen A. Satten & Raymond J. Carroll, 2000. "Conditional and Unconditional Categorical Regression Models with Missing Covariates," Biometrics, The International Biometric Society, vol. 56(2), pages 384-388, June.
    9. Sinha, Samiran & Mukherjee, Bhramar & Ghosh, Malay & Mallick, Bani K. & Carroll, Raymond J., 2005. "Semiparametric Bayesian Analysis of Matched Case-Control Studies With Missing Exposure," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 591-601, June.
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    Cited by:

    1. Tianqing Liu & Xiaohui Yuan, 2020. "Empirical likelihood-based weighted rank regression with missing covariates," Statistical Papers, Springer, vol. 61(2), pages 697-725, April.

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