Bounds on Treatment Effects From Studies With Imperfect Compliance

Abstract

BOUNDS ON TREATMENT EFFECTS FROM STUDIES WITH IMPERFECT COMPLIANCE Alexander Balke and Judea Pearl y Cognitive Systems Laboratory Computer Science Department University of California, Los Angeles, CA 90024 balke@cs.ucla.edu judea@cs.ucla.edu Abstract This paper establishes nonparametric formulas that can be used to bound the aver- age treatment e ect in experimental studies in which treatment assignment is random but subject compliance is imperfect. The bounds provided are the tightest possible, given the distribution of assignments, treatments, and responses. The formulas show that even with high rates of noncompliance, experimental data can yield useful and sometimes accurate information on the average e ect of a treatment on the population. 1. INTRODUCTION Consider an experimental study where random assignment has taken place but compliance is not perfect i.e., the treatment received di ers from that assigned. It is well known that under such conditions a bias may be introduced. Subjects who did not comply with the assignment may be precisely those who would have responded adversely positively to the treatment; therefore, the actual e ect of the treatment, when applied uniformly to the population, might be substantially less more e ective than the study reveals. In an attempt to avert this bias, analysts sometimes resort to parametric models which make restrictive commitments to a particular mode of interaction between compliance and response Efron and Feldman 1991. Angrist et al. 1996 have identi ed a set of assump- tions under which a nonparametric correction formula, called Instrumental Variables , is valid for certain subpopulations. Since these subpopulations cannot be identi ed from em- pirical observation alone, the need remains to devise alternative, assumption-free formulas for assessing the e ect of treatment over the population as a whole. Robins 1989 and JASA . was partially supported by Air Force grant AFOSR 90 0136, NSF grant IRI-9200918, and Northrop-Rockwell Micro grant 93-124. Alexander Balke was supported by the Fannie and John Hertz Foundation. This work bene ted from discussions with Joshua Angrist, David Chickering, Thomas Ferguson, David Galles, Guido Imbens, James Robins, and Donald Rubin. We thank Bradley Efron for providing us with the data used in Section 4.2. To appear in y The research