Fight the [Statistical] Power: Imperfect Compliance and Treatment Effect Estimation

Experimental research designs must often allow for participants' imperfect compliance with their randomized treatment assignment. That is, some in the control group might obtain the treatment of interest, while some in the treatment group might not obtain the treatment. Instrumental variables estimation in this context sidesteps this problem, and yields an unbiased estimate of the average treatment effect on "compliers," the group of individuals whose treatment take-up is determined by their randomized treatment assignment. Although non-compliance does not bias this treatment effect estimate, it nonetheless comes at a cost in the form of a reduction in precision. Low compliance rates therefore result in many studies being underpowered, weakening the conclusions that can be drawn from them. While individual compliers cannot be directly identified, in this paper I propose a framework for assessing individuals' likelihood of compliance utilizing their baseline (i.e. pre-randomization) characteristics, and harnessing this information to improve the precision of treatment effect estimates. Using publicly available data from the Oregon Health Insurance Experiment, I empirically demonstrate the feasibility of these methods and go on to discuss the contexts in which they are most likely to be effective.