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Identification of causal effects on binary outcomes using structural mean models

  • Paul Clarke
  • Frank Windmeijer

    ()

    (Institute for Fiscal Studies and University of Bristol)

Structural mean models (SMMs) were originally formulated to estimate causal effects among those selecting treatment in randomised controlled trials affected by non-ignorable non-compliance. It has already been established that SMM estimators identify these causal effects in randomised placebo-controlled trials where no-one assigned to the control group can receive the treatment. However, SMMs are starting to be used for randomised controlled trials without placebo-controls, and for instrumental variable analysis of observational studies; for example, Mendelian randomisation studies, and studies where physicians select patients' treatments. In such scenarios, identification depends on the assumption of no effect modification, namely, the causal effect is equal for the subgroups defined by the instrument. We consider the nature of this assumption by showing how it depends crucially on the underlying causal model generating the data, which in applications is almost always unknown. If its no effect modification assumption does not hold then an SMM estimator does not estimate its associated causal effect. However, if treatment selection is monotonic we highlight that additive and multiplicative SMMs do identify local (or complier) causal effects, but that the double-logistic SMM estimator does not without further assumptions. We clarify the proper interpretation of inferences from SMM estimators using a data example and simulation study.

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File URL: http://cemmap.ifs.org.uk/wps/cwp0210.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP02/10.

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Date of creation: Mar 2010
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Handle: RePEc:ifs:cemmap:02/10
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  1. 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.
  2. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
  3. 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.
  4. 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.
  5. 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.
  6. Moodie, Erica E. M. & Platt, Robert W. & Kramer, Michael S., 2009. "Estimating Response-Maximized Decision Rules With Applications to Breastfeeding," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 155-165.
  7. Paul Clarke & Frank Windmeijer, 2009. "Instrumental Variable Estimators for Binary Outcomes," The Centre for Market and Public Organisation 09/209, Department of Economics, University of Bristol, UK.
  8. 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.
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