  Randomized Controlled Trials (RCTs) represent a gold standard when developing
policy guidelines. However, RCTs are often narrow, and lack data on broader
populations of interest. Causal effects in these populations are often
estimated using observational datasets, which may suffer from unobserved
confounding and selection bias. Given a set of observational estimates (e.g.
from multiple studies), we propose a meta-algorithm that attempts to reject
observational estimates that are biased. We do so using validation effects,
causal effects that can be inferred from both RCT and observational data. After
rejecting estimators that do not pass this test, we generate conservative
confidence intervals on the extrapolated causal effects for subgroups not
observed in the RCT. Under the assumption that at least one observational
estimator is asymptotically normal and consistent for both the validation and
extrapolated effects, we provide guarantees on the coverage probability of the
intervals output by our algorithm. To facilitate hypothesis testing in settings
where causal effect transportation across datasets is necessary, we give
conditions under which a doubly-robust estimator of group average treatment
effects is asymptotically normal, even when flexible machine learning methods
are used for estimation of nuisance parameters. We illustrate the properties of
our approach on semi-synthetic and real world datasets, and show that it
compares favorably to standard meta-analysis techniques.
