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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. 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.
    2. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, Institute for the Study of Labor (IZA).
    3. repec:bpj:causin:v:4:y:2016:i:2:p:0:n:1 is not listed on IDEAS
    4. 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.
    5. 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, Department of Economics, University of Bristol, UK.
    6. 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.
    7. 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.
    8. 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.
    9. 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.

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