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Estimation of treatment effects in randomised trials with non-compliance and a dichotomous outcome using structural mean models

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  • James Robins
  • Andrea Rotnitzky

Abstract

We consider estimation of the received treatment effect on a dichotomous outcome in randomised trials with non-compliance. We explore inference about the parameters of the structural mean models of Robins (1994, 1997) and Robins et al. (1999). We show that, in contrast to the additive and multiplicative structural mean models for continuous and count outcomes, unbiased estimating functions for a nonzero (structural) treatment effect parameter do not exist in the presence of many continuous and discrete baseline covariates, even when the randomisation probabilities are known. The best that can be hoped for are estimators, such as those proposed in this paper, that are guaranteed both to estimate consistently the (null) treatment effect when the null hypothesis of no treatment effect is true and to have small bias when the true treatment effect is close to but not equal to zero. Copyright 2004, Oxford University Press.

Suggested Citation

  • James Robins & Andrea Rotnitzky, 2004. "Estimation of treatment effects in randomised trials with non-compliance and a dichotomous outcome using structural mean models," Biometrika, Biometrika Trust, vol. 91(4), pages 763-783, December.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:4:p:763-783
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    File URL: http://hdl.handle.net/10.1093/biomet/91.4.763
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    Cited by:

    1. He Jiwei & Stephens-Shields Alisa & Joffe Marshall, 2015. "Structural Nested Mean Models to Estimate the Effects of Time-Varying Treatments on Clustered Outcomes," The International Journal of Biostatistics, De Gruyter, vol. 11(2), pages 203-222, November.
    2. Paul S. Clarke & Frank Windmeijer, 2012. "Instrumental Variable Estimators for Binary Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1638-1652, December.
    3. Han, Sukjin, 2021. "Identification in nonparametric models for dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 132-147.
    4. Faerber Jennifer A. & Joffe Marshall M. & Small Dylan S. & Zhang Rongmei & Brown Gregory K. & Ten Have Thomas R., 2017. "A Simple Model Allowing Modification of the Effect of a Randomized Intervention by Post-Randomization Variables," Journal of Causal Inference, De Gruyter, vol. 5(2), pages 1-16, September.
    5. Ali Reza Soltanian & Soghrat Faghihzadeh, 2012. "A generalization of the Grizzle model to the estimation of treatment effects in crossover trials with non-compliance," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1037-1048, October.
    6. Mark van der Laan & Alan Hubbard & Nicholas Jewell, 2004. "Estimation of Treatment Effects in Randomized Trials with Noncompliance and a Dichotomous Outcome," U.C. Berkeley Division of Biostatistics Working Paper Series 1157, Berkeley Electronic Press.
    7. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, Institute of Labor Economics (IZA).
    8. Stephens Alisa & Joffe Marshall & Keele Luke, 2016. "Generalized Structural Mean Models for Evaluating Depression as a Post-treatment Effect Modifier of a Jobs Training Intervention," Journal of Causal Inference, De Gruyter, vol. 4(2), pages 1, September.
    9. Kern, Holger & Hainmueller, Jens, 2007. "Opium for the Masses: How Foreign Free Media Can Stabilize Authoritarian Regimes," MPRA Paper 2702, University Library of Munich, Germany.
    10. Paul S. Clarke & Tom M. Palmer & Frank Windmeijer, 2011. "Estimating structural mean models with multiple instrumental variables using the generalised method of moments," CeMMAP working papers CWP28/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Paul Clarke & Frank Windmeijer, 2009. "Identification of Causal Effects on Binary Outcomes Using Structural Mean Models," The Centre for Market and Public Organisation 09/217, The Centre for Market and Public Organisation, University of Bristol, UK.
    12. Matthew Blackwell & Anton Strezhnev, 2022. "Telescope matching for reducing model dependence in the estimation of the effects of time‐varying treatments: An application to negative advertising," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(1), pages 377-399, January.
    13. Joffe Marshall M & Small Dylan & Ten Have Thomas & Brunelli Steve & Feldman Harold I, 2008. "Extended Instrumental Variables Estimation for Overall Effects," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-20, April.
    14. Hua Chen & Zhi Geng & Xiao-Hua Zhou, 2009. "Identifiability and Estimation of Causal Effects in Randomized Trials with Noncompliance and Completely Nonignorable Missing Data," Biometrics, The International Biometric Society, vol. 65(3), pages 675-682, September.
    15. Murielle Bochud & Valentin Rousson, 2010. "Usefulness of Mendelian Randomization in Observational Epidemiology," IJERPH, MDPI, vol. 7(3), pages 1-18, February.
    16. Linbo Wang & Xiang Meng & Thomas S. Richardson & James M. Robins, 2023. "Coherent modeling of longitudinal causal effects on binary outcomes," Biometrics, The International Biometric Society, vol. 79(2), pages 775-787, June.
    17. Ditte Nørbo Sørensen & Torben Martinussen & Eric Tchetgen Tchetgen, 2019. "A causal proportional hazards estimator under homogeneous or heterogeneous selection in an IV setting," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(4), pages 639-659, October.

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