Synthesized difference in differences

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.