  When considering the effect a treatment will cause in a population of
interest, we often look to evidence from randomized controlled trials. In
settings where multiple trials on a treatment are available, we may wish to
synthesize the trials' participant data to obtain causally interpretable
estimates of the average treatment effect in a specific target population.
Traditional meta-analytic approaches to synthesizing data from multiple studies
estimate the average effect among the studies. The resulting estimate is often
not causally interpretable in any population, much less a particular population
of interest, due to heterogeneity in the effect of treatment across studies.
Inspired by traditional two-stage meta-analytic methods, as well as methods for
extending inferences from a single study, we propose a two-stage approach to
extending inferences from a collection of randomized controlled trials that can
be used to obtain causally interpretable estimates of treatment effects in a
target population when there is between-study heterogeneity in conditional
average treatment effects. We first introduce a collection of assumptions under
which the target population's average treatment effect is identifiable when
conditional average treatment effects are heterogeneous across studies. We then
introduce an estimator that utilizes weighting in two stages, taking a weighted
average of study-specific estimates of the treatment effect in the target
population. The performance of our proposed approach is assessed through
simulation studies and an application to a collection of trials studying an
online therapy treatment for symptoms of pediatric traumatic brain injury.
