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

We propose a class of estimators of a received 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 Robins and Rotnitzky (2004), our estimators are always consistent, asymptotically linear at the null hypothesis of no-treatment effect -- thereby providing valid testing procedures -- since, by construction, our model for the causal relative risk always includes the value 1.