Propensity score stratified MAP prior and posterior inference for incorporating information across multiple potentially heterogeneous data sources.

Incorporation of external information is becoming increasingly common when designing clinical trials. Availability of multiple sources of information has inspired the development of methodologies that account for potential heterogeneity not only between the prospective trial and the pooled external data sources but also between the different external data sources themselves. Our approach proposes an intuitive way of handling such a scenario for the continuous outcomes setting by using propensity score-based stratification and then utilizing robust meta-analytic predictive priors for each stratum to incorporate the prior data to distinguish among different external data sources in each stratum. Through extensive simulations, our approach proves to be more efficient and less biased than the currently available methods. A real case study using clinical trials that study schizophrenia from multiple different sources is also included.