Estimation of Treatment Effects in Randomized Trials with Noncompliance and a Dichotomous Outcome

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 articles by Vansteelandt and Goethebeur (2003) and Robins and Rotnitzky (2004) 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 article 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 only rely on the correct specification of a model for the parameter of interest. As in Vansteelandt and Goethebeur (2003) and Robins and Rotnitzky (2004) our estimators are always consistent, 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