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Causal inference with generalized structural mean models

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  • S. Vansteelandt
  • E. Goetghebeur

Abstract

We estimate cause-effect relationships in empirical research where exposures are not completely controlled, as in observational studies or with patient non-compliance and self-selected treatment switches in randomized clinical trials. Additive and multiplicative structural mean models have proved useful for this but suffer from the classical limitations of linear and log-linear models when accommodating binary data. We propose the generalized structural mean model to overcome these limitations. This is a semiparametric two-stage model which extends the structural mean model to handle non-linear average exposure effects. The first-stage structural model describes the causal effect of received exposure by contrasting the means of observed and potential exposure-free outcomes in exposed subsets of the population. For identification of the structural parameters, a second stage 'nuisance' model is introduced. This takes the form of a classical association model for expected outcomes given observed exposure. Under the model, we derive estimating equations which yield consistent, asymptotically normal and efficient estimators of the structural effects. We examine their robustness to model misspecification and construct robust estimators in the absence of any exposure effect. The double-logistic structural mean model is developed in more detail to estimate the effect of observed exposure on the success of treatment in a randomized controlled blood pressure reduction trial with self-selected non-compliance. Copyright 2003 Royal Statistical Society.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssb:v:65:y:2003:i:4:p:817-835
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    1. repec:bla:jorssa:v:180:y:2017:i:2:p:569-586 is not listed on IDEAS
    2. Rosalba Radice & Luca Zanin & Giampiero Marra, 2013. "On the effect of obesity on employment in the presence of observed and unobserved confounding," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 436-455, November.
    3. 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.
    4. 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.
    5. 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.
    6. Daniel Almirall & Thomas Ten Have & Susan A. Murphy, 2010. "Structural Nested Mean Models for Assessing Time-Varying Effect Moderation," Biometrics, The International Biometric Society, vol. 66(1), pages 131-139, March.
    7. 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.
    8. 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.
    9. Shinohara Russell T. & Frangakis Constantine E. & Platz Elizabeth & Tsilidis Konstantinos, 2012. "Designs Combining Instrumental Variables with Case-Control: Estimating Principal Strata Causal Effects," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-21, January.
    10. Sylvie Goetgeluk & Stijn Vansteelandt, 2008. "Conditional Generalized Estimating Equations for the Analysis of Clustered and Longitudinal Data," Biometrics, The International Biometric Society, vol. 64(3), pages 772-780, September.
    11. Luca Zanin & Rosalba Radice & Giampiero Marra, 2013. "Estimating the Effect of Perceived Risk of Crime on Social Trust in the Presence of Endogeneity Bias," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 114(2), pages 523-547, November.

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