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Simultaneous mean and covariance estimation of partially linear models for longitudinal data with missing responses and covariate measurement error

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  • Qin, Guoyou
  • Zhang, Jiajia
  • Zhu, Zhongyi

Abstract

Missing responses and covariate measurement error are very commonly seen in practice. New estimating equations are developed to simultaneously estimate the mean and covariance under a partially linear model for longitudinal data with missing responses and covariate measurement error. Specifically, a novel approach is proposed to handle measurement error by using independent replicate measurements. Compared with existing methods, the proposed method requires fewer assumptions. For example, it does not require to specify the distribution of the mismeasured covariate or the measurement error, and does not need a parametric model to estimate the probability of being observed or to impute the missing responses. Additionally, the proposed estimating equations are easy to implement in most popular statistical softwares by applying existing algorithms for standard generalized estimating equations. The asymptotic properties of the proposed estimators are established under regularity conditions, and simulation studies demonstrate desired properties. Finally, the proposed method is applied to data from the Lifestyle Education for Activity and Nutrition (LEAN) study. This data analysis confirms the effectiveness of the intervention in producing weight loss at month nine.

Suggested Citation

  • Qin, Guoyou & Zhang, Jiajia & Zhu, Zhongyi, 2016. "Simultaneous mean and covariance estimation of partially linear models for longitudinal data with missing responses and covariate measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 24-39.
    • Handle: RePEc:eee:csdana:v:96:y:2016:i:c:p:24-39
    DOI: 10.1016/j.csda.2015.11.001
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    References listed on IDEAS

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    1. G. Y. Yi & W. Liu & Lang Wu, 2011. "Simultaneous Inference and Bias Analysis for Longitudinal Data with Covariate Measurement Error and Missing Responses," Biometrics, The International Biometric Society, vol. 67(1), pages 67-75, March.
    2. Jianhua Z. Huang & Liangyue Zhang & Lan Zhou, 2007. "Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(3), pages 451-477, September.
    3. He, Xuming & Fung, Wing K. & Zhu, Zhongyi, 2005. "Robust Estimation in Generalized Partial Linear Models for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1176-1184, December.
    4. Qu, Annie & Lindsay, Bruce G. & Lu, Lin, 2010. "Highly Efficient Aggregate Unbiased Estimating Functions Approach for Correlated Data With Missing at Random," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 194-204.
    5. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
    6. Zhongyi Zhu & Wing K. Fung & Xuming He, 2008. "On the asymptotics of marginal regression splines with longitudinal data," Biometrika, Biometrika Trust, vol. 95(4), pages 907-917.
    7. Baojiang Chen & Xiao-Hua Zhou, 2013. "Generalized Partially Linear Models for Incomplete Longitudinal Data In the Presence of Population-Level Information," Biometrics, The International Biometric Society, vol. 69(2), pages 386-395, June.
    8. Huang Y. & Wang C.Y., 2001. "Consistent Functional Methods for Logistic Regression With Errors in Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1469-1482, December.
    9. He, Xuming & Shi, Peide, 1996. "Bivariate Tensor-Product B-Splines in a Partly Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 162-181, August.
    10. Wenqin Pan & Donglin Zeng & Xihong Lin, 2009. "Estimation in Semiparametric Transition Measurement Error Models for Longitudinal Data," Biometrics, The International Biometric Society, vol. 65(3), pages 728-736, September.
    11. C. Y. Wang & Yijian Huang & Edward C. Chao & Marjorie K. Jeffcoat, 2008. "Expected Estimating Equations for Missing Data, Measurement Error, and Misclassification, with Application to Longitudinal Nonignorable Missing Data," Biometrics, The International Biometric Society, vol. 64(1), pages 85-95, March.
    12. Grace Y. Yi & Yanyuan Ma & Raymond J. Carroll, 2012. "A functional generalized method of moments approach for longitudinal studies with missing responses and covariate measurement error," Biometrika, Biometrika Trust, vol. 99(1), pages 151-165.
    13. Wei Liu & Lang Wu, 2007. "Simultaneous Inference for Semiparametric Nonlinear Mixed-Effects Models with Covariate Measurement Errors and Missing Responses," Biometrics, The International Biometric Society, vol. 63(2), pages 342-350, June.
    14. Samiran Sinha & Yanyuan Ma, 2014. "Semiparametric analysis of linear transformation models with covariate measurement errors," Biometrics, The International Biometric Society, vol. 70(1), pages 21-32, March.
    15. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
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    Cited by:

    1. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Zhang, Jiajia, 2022. "Empirical likelihood inference for longitudinal data with covariate measurement errors: An application to the LEAN study," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    2. Lin, Huiming & Qin, Guoyou & Zhang, Jiajia & Zhu, Zhongyi, 2018. "Analysis of longitudinal data with covariate measurement error and missing responses: An improved unbiased estimating equation," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 104-112.
    3. Mengli Zhang & Yang Bai, 2021. "On the use of repeated measurement errors in linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 779-803, July.
    4. 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.
    5. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Xu, Wanghong, 2019. "A novel robust approach for analysis of longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 83-95.

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