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Doubly robust estimation of generalized partial linear models for longitudinal data with dropouts

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  • Huiming Lin
  • Bo Fu
  • Guoyou Qin
  • Zhongyi Zhu

Abstract

We develop a doubly robust estimation of generalized partial linear models for longitudinal data with dropouts. Our method extends the highly efficient aggregate unbiased estimating function approach proposed in Qu et al. (2010) to a doubly robust one in the sense that under missing at random (MAR), our estimator is consistent when either the linear conditional mean condition is satisfied or a model for the dropout process is correctly specified. We begin with a generalized linear model for the marginal mean, and then move forward to a generalized partial linear model, allowing for nonparametric covariate effect by using the regression spline smoothing approximation. We establish the asymptotic theory for the proposed method and use simulation studies to compare its finite sample performance with that of Qu's method, the complete‐case generalized estimating equation (GEE) and the inverse‐probability weighted GEE. The proposed method is finally illustrated using data from a longitudinal cohort study.

Suggested Citation

  • Huiming Lin & Bo Fu & Guoyou Qin & Zhongyi Zhu, 2017. "Doubly robust estimation of generalized partial linear models for longitudinal data with dropouts," Biometrics, The International Biometric Society, vol. 73(4), pages 1132-1139, December.
    • Handle: RePEc:bla:biomet:v:73:y:2017:i:4:p:1132-1139
    DOI: 10.1111/biom.12703
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    References listed on IDEAS

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    1. Anastasios A. Tsiatis & Marie Davidian & Weihua Cao, 2011. "Improved Doubly Robust Estimation When Data Are Monotonely Coarsened, with Application to Longitudinal Studies with Dropout," Biometrics, The International Biometric Society, vol. 67(2), pages 536-545, June.
    2. Qin, Guoyou & Zhu, Zhongyi, 2007. "Robust estimation in generalized semiparametric mixed models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1658-1683, September.
    3. Zhiqiang Tan, 2010. "Bounded, efficient and doubly robust estimation with inverse weighting," Biometrika, Biometrika Trust, vol. 97(3), pages 661-682.
    4. James R. Carpenter & Michael G. Kenward & Stijn Vansteelandt, 2006. "A comparison of multiple imputation and doubly robust estimation for analyses with missing data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(3), pages 571-584, July.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Andrea Rotnitzky & Quanhong Lei & Mariela Sued & James M. Robins, 2012. "Improved double-robust estimation in missing data and causal inference models," Biometrika, Biometrika Trust, vol. 99(2), pages 439-456.
    10. 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.
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