  Instrumental variable (IV) analyses are becoming common in health services
research and epidemiology. IV analyses can be used both to analyze randomized
trials with noncompliance and as a form of natural experiment. In these
analyses, investigators often adopt a monotonicity assumption, which implies
that the relevant effect only applies to a subset of the study population known
as compliers. Since the estimated effect is not the average treatment effect of
the study population, it is important to compare the characteristics of
compliers and non-compliers. Profiling compliers and non-compliers is necessary
to understand what subpopulation the researcher is making inferences about, and
an important first step in evaluating the external validity (or lack thereof)
of the IV estimate for compliers. Here, we discuss the assumptions necessary
for profiling, which are weaker than the assumptions necessary for identifying
the local average treatment effect if the instrument is randomly assigned. We
then outline a simple and general method to characterize compliers and
noncompliers using baseline covariates. Next, we extend current methods by
deriving standard errors for these estimates. We demonstrate these methods
using an IV known as tendency to operate (TTO) from health services research.

Methodology