Biometrika Advance Access originally published online on January 21, 2009
Biometrika 2009 96(1):19-36; doi:10.1093/biomet/asn056
Articles |
Efficient nonparametric estimation of causal effects in randomized trials with noncompliance
Division of Biostatistics, University of Florida College of Medicine, Gainesville, Florida 32610, U.S.A. jcheng{at}biostat.ufl.edu
Department of Statistics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.A. dsmall{at}wharton.upenn.edu
Department of Statistics, Rutgers University, Piscataway, New Jersey 08854, U.S.A. ztan{at}stat.rutgers.edu
Division of Biostatistics, University of Pennsylvania School of Medicine, Philadelphia, Pennsylvania 19104, U.S.A. ttenhave{at}mail.med.upenn.edu
Received for publication 1 June 2006. Revision received 1 May 2008.
Causal approaches based on the potential outcome framework provide a useful tool for addressing noncompliance problems in randomized trials. We propose a new estimator of causal treatment effects in randomized clinical trials with noncompliance. We use the empirical likelihood approach to construct a profile random sieve likelihood and take into account the mixture structure in outcome distributions, so that our estimator is robust to parametric distribution assumptions and provides substantial finite-sample efficiency gains over the standard instrumental variable estimator. Our estimator is asymptotically equivalent to the standard instrumental variable estimator, and it can be applied to outcome variables with a continuous, ordinal or binary scale. We apply our method to data from a randomized trial of an intervention to improve the treatment of depression among depressed elderly patients in primary care practices.
Key Words: Causal effect • Efficient nonparametric estimation • Empirical likelihood • Instrumental variable • Noncompliance • Randomized trial
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