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Causal inference with generalized structural mean models

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  • S. Vansteelandt
  • E. Goetghebeur
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    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.

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

    Volume (Year): 65 (2003)
    Issue (Month): 4 ()
    Pages: 817-835

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    Handle: RePEc:bla:jorssb:v:65:y:2003:i:4:p:817-835

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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," The Centre for Market and Public Organisation, Department of Economics, University of Bristol, UK 11/266, Department of Economics, University of Bristol, UK.
    2. Paul Clarke & Frank Windmeijer, 2009. "Instrumental Variable Estimators for Binary Outcomes," The Centre for Market and Public Organisation, Department of Economics, University of Bristol, UK 09/209, Department of Economics, University of Bristol, UK.
    3. 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, Berkeley Electronic Press 1157, Berkeley Electronic Press.
    4. Paul Clarke & Frank Windmeijer, 2009. "Identification of Causal Effects on Binary Outcomes Using Structural Mean Models," The Centre for Market and Public Organisation, Department of Economics, University of Bristol, UK 09/217, Department of Economics, University of Bristol, UK.
    5. 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, Springer, Springer, vol. 114(2), pages 523-547, November.

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