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

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 69; no. 3; pp. 463 - 482
• Main Authors: van der Laan, Mark J, Hubbard, Alan, Jewell, Nicholas P
• Format: Journal Article
• Language: English
• Published: Oxford, UK Oxford, UK : Blackwell Publishing Ltd 01.06.2007; Blackwell Publishing Ltd; Blackwell Publishers; Blackwell; Royal Statistical Society; Oxford University Press
• Series: Journal of the Royal Statistical Society Series B
• Subjects: abortion (animals); Assumption of risk; Binary outcome; Causal treatment effect; Coffee; Compliance; Consistent estimators; Counterfactual; Data analysis; Decaffeinated coffees; Estimators; Exact sciences and technology; Functional analysis; Functions of a complex variable; General topics; Generalized quantile; Health; Inference; Instrumental variable; Instrumental variables; Instrumental variables estimation; Mathematical analysis; Mathematical independent variables; Mathematical models; Mathematics; Medical treatment; Multivariate analysis; Non-compliance; Noncompliance; Null hypothesis; odds ratio; Parametric models; Probability and statistics; quantile function; Quantitative analysis; relative risk; Research methods; Risk factors; Sample size; Sciences and techniques of general use; Specification; Statistical methods; Statistics; Studies; Nuisance parameter; Generalized function; Covariate; Asymptotic convergence; Hypothesis test; Statistical test; Counterfactual; Estimator efficiency; Consistent estimator; Quantile; Instrumental variable; Data analysis; Non-compliance; Treatment efficiency; Estimation; Finite sample; Relative risk; Statistical method; Causal treatment effect; Generalized quantile-quantile function; Randomized design; Simulation; Binary outcome; Model specification; Treatment effect
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/j.1467-9868.2007.00598.x

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.