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

Summary. 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.