  We are interested in estimating the effect of a treatment applied to
individuals at multiple sites, where data is stored locally for each site. Due
to privacy constraints, individual-level data cannot be shared across sites;
the sites may also have heterogeneous populations and treatment assignment
mechanisms. Motivated by these considerations, we develop federated methods to
draw inference on the average treatment effects of combined data across sites.
Our methods first compute summary statistics locally using propensity scores
and then aggregate these statistics across sites to obtain point and variance
estimators of average treatment effects. We show that these estimators are
consistent and asymptotically normal. To achieve these asymptotic properties,
we find that the aggregation schemes need to account for the heterogeneity in
treatment assignments and in outcomes across sites. We demonstrate the validity
of our federated methods through a comparative study of two large medical
claims databases.
