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Biometrika Advance Access published online on January 21, 2009
Biometrika, doi:10.1093/biomet/asn056
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© 2009 Biometrika Trust

Article

Efficient nonparametric estimation of causal effects in randomized trials with noncompliance

Jing Cheng

Division of Biostatistics, University of Florida College of Medicine, Gainesville, Florida 32610, U.S.A. jcheng{at}biostat.ufl.edu

Dylan S. Small

Department of Statistics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.A. dsmall{at}wharton.upenn.edu

Zhiqiang Tan

Department of Statistics, Rutgers University, Piscataway, New Jersey 08854, U.S.A. ztan{at}stat.rutgers.edu

Thomas R. Ten Have

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.
  Abstract

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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