Synthesized Difference in Differences

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. Difference in Differences (DD) eliminates confounding from observational data by comparing outcomes before and after treatment administration. However, the algorithm requires a parallel slopes assumption that may not apply in practice when confounding shifts across time. In this paper, we 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.