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Multiple robust estimation of marginal structural mean models for unconstrained outcomes

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  • Lucia Babino
  • Andrea Rotnitzky
  • James Robins

Abstract

We consider estimation, from longitudinal observational data, of the parameters of marginal structural mean models for unconstrained outcomes. Current proposals include inverse probability of treatment weighted and double robust (DR) estimators. A difficulty with DR estimation is that it requires postulating a sequence of models, one for the each mean of the counterfactual outcome given covariate and treatment history up to each exposure time point. Most natural models for such means are often incompatible. Robins et al., (2000b) proposed a parameterization of the likelihood which implies compatible parametric models for such means. Their parameterization has not been exploited to construct DR estimators and one goal of this article is to fill this gap. More importantly, exploiting this parameterization we propose a multiple robust (MR) estimator that confers even more protection against model misspecification than DR estimators. Our methods are easy to implement as they are based on the iterative fit of a sequence of weighted regressions.

Suggested Citation

  • Lucia Babino & Andrea Rotnitzky & James Robins, 2019. "Multiple robust estimation of marginal structural mean models for unconstrained outcomes," Biometrics, The International Biometric Society, vol. 75(1), pages 90-99, March.
    • Handle: RePEc:bla:biomet:v:75:y:2019:i:1:p:90-99
    DOI: 10.1111/biom.12924
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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. Murphy S.A. & van der Laan M.J. & Robins J.M., 2001. "Marginal Mean Models for Dynamic Regimes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1410-1423, December.
    3. Zheng Wenjing & van der Laan Mark J., 2012. "Targeted Maximum Likelihood Estimation of Natural Direct Effects," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-40, January.
    4. E. J. Tchetgen Tchetgen & I. Shpitser, 2014. "Estimation of a semiparametric natural direct effect model incorporating baseline covariates," Biometrika, Biometrika Trust, vol. 101(4), pages 849-864.
    5. Stijn Vansteelandt & Andrea Rotnitzky & James Robins, 2007. "Estimation of Regression Models for the Mean of Repeated Outcomes Under Nonignorable Nonmonotone Nonresponse," Biometrika, Biometrika Trust, vol. 94(4), pages 841-860.
    6. Peisong Han & Lu Wang, 2013. "Estimation with missing data: beyond double robustness," Biometrika, Biometrika Trust, vol. 100(2), pages 417-430.
    7. Peisong Han, 2016. "Intrinsic efficiency and multiple robustness in longitudinal studies with drop-out," Biometrika, Biometrika Trust, vol. 103(3), pages 683-700.
    8. Gruber Susan & van der Laan Mark J., 2010. "A Targeted Maximum Likelihood Estimator of a Causal Effect on a Bounded Continuous Outcome," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-18, August.
    9. J. Molina & A. Rotnitzky & M. Sued & J. M. Robins, 2017. "Multiple robustness in factorized likelihood models," Biometrika, Biometrika Trust, vol. 104(3), pages 561-581.
    10. Peisong Han, 2014. "Multiply Robust Estimation in Regression Analysis With Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1159-1173, September.
    11. Vansteelandt, Stijn & VanderWeele, Tyler J. & Tchetgen, Eric J. & Robins, James M., 2008. "Multiply Robust Inference for Statistical Interactions," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1693-1704.
    12. Orellana Liliana & Rotnitzky Andrea & Robins James M., 2010. "Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part II: Proofs of Results," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-19, March.
    13. Orellana Liliana & Rotnitzky Andrea & Robins James M., 2010. "Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part I: Main Content," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-49, March.
    14. 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.
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    Cited by:

    1. Yuqian Zhang & Weijie Ji & Jelena Bradic, 2021. "Dynamic treatment effects: high-dimensional inference under model misspecification," Papers 2111.06818, arXiv.org, revised Jun 2023.
    2. Jelena Bradic & Weijie Ji & Yuqian Zhang, 2021. "High-dimensional Inference for Dynamic Treatment Effects," Papers 2110.04924, arXiv.org, revised May 2023.

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