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Identification of Causal Effects on Binary Outcomes Using Structural Mean Models

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  • Paul Clarke
  • Frank Windmeijer

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Abstract

Structural mean models (SMMs) are used to estimate causal effects among those selecting treatment in randomised controlled trials affected by non-ignorable non-compliance. These causal effects can be identified by assuming that there is no effect modification, namely, that the causal effect is equal for the treated subgroups randomised to treatment and to control. By analysing simple structural models for binary outcomes, we argue that the no effect modification assumption does not hold in general, and so SMMs do not estimate causal effects for the treated. An exception is for designs in which those randomised to control can be completely excluded from receiving the treatment. However, when there is non-compliance in the control arm, local (or complier) causal effects can be identified provided that the further assumption of monotonic selection into treatment holds. We demonstrate these issues using numerical examples.

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Bibliographic Info

Paper provided by Department of Economics, University of Bristol, UK in its series The Centre for Market and Public Organisation with number 09/217.

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Length: 20 pages
Date of creation: Jun 2009
Date of revision:
Handle: RePEc:bri:cmpowp:09/217

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Keywords: structural mean models; identification; local average treatment effects; complier average treatment effects;

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  1. 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.
  2. Joshua D. Angrist, 2000. "Estimation of Limited-Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice," NBER Technical Working Papers 0248, National Bureau of Economic Research, Inc.
  3. S. Vansteelandt & E. Goetghebeur, 2003. "Causal inference with generalized structural mean models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 817-835.
  4. 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.
  5. Joshua D. Angrist & Guido W. Imbens, 1995. "Identification and Estimation of Local Average Treatment Effects," NBER Technical Working Papers 0118, National Bureau of Economic Research, Inc.
  6. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
  7. Mark J. van der Laan & Alan Hubbard & Nicholas P. Jewell, 2007. "Estimation of treatment effects in randomized trials with non-compliance and a dichotomous outcome," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 463-482.
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