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Estimation of treatment effects in randomized trials with non-compliance and a dichotomous outcome

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  • Mark J. van der Laan
  • Alan Hubbard
  • Nicholas P. Jewell
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    Abstract

    We propose a class of estimators of the treatment effect on a dichotomous outcome among the treated subjects within covariate and treatment arm strata in randomized trials with non-compliance. Recent papers by Vansteelandt and Goetghebeur, and Robins and Rotnitzky have presented consistent and asymptotically linear estimators of a causal odds ratio, which rely, beyond correct specification of a model for the causal odds ratio, on a correctly specified model for a potentially high dimensional nuisance parameter. In this paper we propose consistent, asymptotically linear and locally efficient estimators of a causal relative risk and a new parameter-called a switch causal relative risk-which relies only on the correct specification of a model for the parameter of interest. Our estimators are always consistent and asymptotically linear at the null hypothesis of no-treatment effect, thereby providing valid testing procedures. We examine the finite sample properties of these instrumental-variable-based estimators and the associated testing procedures in simulations and a data analysis of decaffeinated coffee consumption and miscarriage. Copyright 2007 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): 69 (2007)
    Issue (Month): 3 ()
    Pages: 463-482

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    Handle: RePEc:bla:jorssb:v:69:y:2007:i:3:p:463-482

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    Cited by:
    1. Paul S. Clarke; & Tom M. Palmer; & Frank Windmeijer, 2012. "Estimating structural mean models with multiple instrumental variables using the generalised method of moments," Health, Econometrics and Data Group (HEDG) Working Papers 12/23, HEDG, c/o Department of Economics, University of York.
    2. 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.
    3. 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.

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