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Estimation of Treatment Effects in Randomized Trials with Non-Compliance and a Dichotomous Outcome

Mark J. van der Laan, Alan Hubbard and Nicholas P. Jewell
Journal of the Royal Statistical Society. Series B (Statistical Methodology)
Vol. 69, No. 3 (2007), pp. 463-482
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/4623279
Page Count: 20
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Estimation of Treatment Effects in Randomized Trials with Non-Compliance and a Dichotomous Outcome
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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.

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