  The availability of electronic health records (EHR) has opened opportunities
to supplement increasingly expensive and difficult to carry out randomized
controlled trials (RCT) with evidence from readily available real world data.
In this paper, we use EHR data to construct synthetic control arms for
treatment-only single arm trials. We propose a novel nonparametric Bayesian
common atoms mixture model that allows us to find equivalent population strata
in the EHR and the treatment arm and then resample the EHR data to create
equivalent patient populations under both the single arm trial and the
resampled EHR. Resampling is implemented via a density-free importance sampling
scheme. Using the synthetic control arm, inference for the treatment effect can
then be carried out using any method available for RCTs. Alternatively the
proposed nonparametric Bayesian model allows straightforward model-based
inference. In simulation experiments, the proposed method exhibits higher power
than alternative methods in detecting treatment effects, specifically for
non-linear response functions. We apply the method to supplement single arm
treatment-only glioblastoma studies with a synthetic control arm based on
historical trials.
