  We consider estimating the conditional average treatment effect for everyone
by eliminating confounding and selection bias. Unfortunately, randomized
clinical trials (RCTs) eliminate confounding but impose strict exclusion
criteria that prevent sampling of the entire clinical population. Observational
datasets are more inclusive but suffer from confounding. We therefore analyze
RCT and observational data simultaneously in order to extract the strengths of
each. Our solution builds upon Difference in Differences (DD), an algorithm
that eliminates confounding from observational data by comparing outcomes
before and after treatment administration. DD requires a parallel slopes
assumption that may not apply in practice when confounding shifts across time.
We instead propose Synthesized Difference in Differences (SDD) that infers the
correct (possibly non-parallel) slopes by linearly adjusting a conditional
version of DD using additional RCT data. The algorithm achieves state of the
art performance across multiple synthetic and real datasets even when the RCT
excludes the majority of patients.
