Estimation of treatment effects in randomised trials with non-compliance and a dichotomous outcome using structural mean models

We consider estimation of the received treatment effect on a dichotomous outcome in randomised trials with non-compliance. We explore inference about the parameters of the structural mean models of Robins (1994, 1997) and Robins et al. (1999). We show that, in contrast to the additive and multiplicative structural mean models for continuous and count outcomes, unbiased estimating functions for a nonzero (structural) treatment effect parameter do not exist in the presence of many continuous and discrete baseline covariates, even when the randomisation probabilities are known. The best that can be hoped for are estimators, such as those proposed in this paper, that are guaranteed both to estimate consistently the (null) treatment effect when the null hypothesis of no treatment effect is true and to have small bias when the true treatment effect is close to but not equal to zero. Copyright 2004, Oxford University Press.

[1]  J. Angrist,et al.  Digitized by the Internet Archive in 2011 with Funding from Estimation of Limited-dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice , 2011 .

[2]  N. Jewell,et al.  Estimation of treatment effects in randomized trials with non‐compliance and a dichotomous outcome , 2004 .

[3]  J. Robins.  Correcting for non-compliance in randomized trials using structural nested mean models , 1994 .

[4]  W. Newey,et al.  Semiparametric Efficiency Bounds , 1990 .

[5]  Joshua D. Angrist,et al.  Identification of Causal Effects Using Instrumental Variables , 1993 .

[6]  J. Robins.  A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect , 1986 .

[7]  Donald B. Rubin,et al.  Bayesian Inference for Causal Effects: The Role of Randomization , 1978 .

[8]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[9]  D. Rubin,et al.  Assessing the effect of an influenza vaccine in an encouragement design. , 2000, Biostatistics.

[10]  A. Dawid.  Conditional Independence in Statistical Theory , 1979 .

[11]  J. Robins,et al.  Sensitivity Analysis for Selection bias and unmeasured Confounding in missing Data and Causal inference models , 2000 .

[12]  G. Chamberlain.  Asymptotic efficiency in estimation with conditional moment restrictions , 1987 .

[13]  Alberto Abadie.  Semiparametric instrumental variable estimation of treatment response models , 2003 .

[14]  Stijn Vansteelandt,et al.  Causal inference with generalized structural mean models , 2003 .