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

Mark van der Laan, Alan Hubbard and Nicholas Jewell
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Mark van der Laan: Division of Biostatistics, School of Public Health, University of California, Berkeley
Alan Hubbard: Division of Biostatistics, School of Public Health, University of California, Berkeley
Nicholas Jewell: Division of Biostatistics, School of Public Health, University of California, Berkeley

No 1157, U.C. Berkeley Division of Biostatistics Working Paper Series from Berkeley Electronic Press

Abstract: 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.

Keywords: Instrumental variable; counterfactual; causal treatment effect; non-compliance; generalized quantile-quantile function; binary outcome (search for similar items in EconPapers)
Date: 2004-09-02
Note: oai:bepress.com:ucbbiostat-1157
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