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Identification of Causal Effects on Binary Outcomes Using Structural Mean Models

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  • Paul Clarke
  • Frank Windmeijer

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.

Suggested Citation

  • 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.
    • Handle: RePEc:bri:cmpowp:09/217
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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.
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    4. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    5. 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.
    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. 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, November.
    8. Ten Have, Thomas R. & Elliott, Michael R. & Joffe, Marshall & Zanutto, Elaine & Datto, Catherine, 2004. "Causal Models for Randomized Physician Encouragement Trials in Treating Primary Care Depression," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 16-25, January.
    9. Angrist, Joshua D, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 27-28, January.
    10. 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, June.
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    Cited by:

    1. Luke Keele & Dylan Small & Richard Grieve, 2017. "Randomization-based instrumental variables methods for binary outcomes with an application to the ‘IMPROVE’ trial," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(2), pages 569-586, February.
    2. 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.
    3. Geneletti, Sara & Baio, Gianluca & O'Keeffe, Aidan & Ricciardi, Federico, 2019. "Bayesian modelling for binary outcomes in the regression discontinuity design," LSE Research Online Documents on Economics 100096, London School of Economics and Political Science, LSE Library.
    4. Taguri Masataka & Chiba Yasutaka, 2012. "Instruments and Bounds for Causal Effects under the Monotonic Selection Assumption," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-23, August.
    5. Masataka Taguri & Yutaka Matsuyama & Yasuo Ohashi, 2014. "Model selection criterion for causal parameters in structural mean models based on a quasi-likelihood," Biometrics, The International Biometric Society, vol. 70(3), pages 721-730, September.
    6. Mariam O. Adeleke & Gianluca Baio & Aidan G. O'Keeffe, 2022. "Regression discontinuity designs for time‐to‐event outcomes: An approach using accelerated failure time models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1216-1246, July.
    7. 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.
    8. Robert Carroll & Chris Metcalfe & Sarah Steeg & Neil M Davies & Jayne Cooper & Nav Kapur & David Gunnell, 2016. "Psychosocial Assessment of Self-Harm Patients and Risk of Repeat Presentation: An Instrumental Variable Analysis Using Time of Hospital Presentation," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-13, February.

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    More about this item

    Keywords

    structural mean models; identification; local average treatment effects; complier average treatment effects;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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