"Assessing the Effect of an Influenza Vaccine in an Encouragement
Design"

Keisuke Hirano, Guido W. Imbens, Donald Rubin, and Xiao-Hua Zhou

ABSTRACT

Many randomized experiments suffer from noncompliance.  Some of these
experiments, so-called encouragement designs, can be expected to have
especially large amounts of noncompliance, because encouragement to
take the treatment rather than the treatment is randomly assigned to
individuals.

We present an extended framework for the Bayesian analysis of data
from such designs with a binary treatment, background covariates, and
the existence of individuals who can be classified as compliers,
never-takers, and always-takers.  This framework is illustrated in a
medical example concerning the effects of inoculation for influenza.

In this example, analyses using ``weakly identified'' models suggest
that positive estimates of the intention-to-treat effect may not be
due to the treatment itself, but rather to the encouragement to take
the treatment: the intention-to-treat effect for always-takers --
those who would be inoculated whether or not encouraged -- is
estimated to be approximately as large as the intention-to-treat
effect for the compliers -- those whose inoculation status agrees
with their (randomized) encouragement status.

Thus, our methods suggest that global intention-to-treat estimates,
although often regarded as conservative, can be scientifically
uninformative and even misleading when taken as summarizing the
evidence in the data for the effects of treatments.