A. Balke et J. Pearl, BOUNDS ON TREATMENT EFFECTS FROM STUDIES WITH IMPERFECT COMPLIANCE, Journal of the American Statistical Association, 92(439), 1997, pp. 1171-1176
This article establishes nonparametric formulas that can be used to bo
und the average treatment effect in experimental studies in which trea
tment assignment is random but subject compliance is imperfect. The bo
unds provided are the tightest possible, given the distribution of ass
ignments, treatments, and responses. The formulas show that even with
high rates of noncompliance, experimental data can yield useful and so
metimes accurate information on the average effect of a treatment on t
he population.