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

Mark J. van der Laan, Division of Biostatistics, School of Public Health, University of California, Berkeley
Alan E. Hubbard, Division of Biostatistics, School of Public Health, University of California, Berkeley
Nicholas P. Jewell, Division of Biostatistics, School of Public Health, University of California, Berkeley

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 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.