Abstract
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 target population, due to heterogeneity in the effect of treatment across studies. Inspired by traditional two-stage meta-analytic methods and 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. We assess the performance of our proposed approach through simulation studies and two applications: A multi-center randomized clinical trial studying a Hepatitis-C treatment and a collection of studies on a therapy treatment for symptoms of pediatric traumatic brain injury.