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We consider how to merge a limited amount of data from a randomized controlled trial (RCT) into a much larger set of data from an observational data base (ODB), to estimate an average causal treatment effect. Our methods are based on stratification. The strata are defined in terms of effect moderators as well as propensity scores estimated in the ODB. Data from the RCT are placed into the strata they would have occupied, had they been in the ODB instead. We assume that treatment differences are comparable in the two data sources. Our first “spiked‐in” method simply inserts the RCT data into their corresponding ODB strata. We also consider a data‐driven convex combination of the ODB and RCT treatment effect estimates within each stratum. Using the delta method and simulations, we identify a bias problem with the spiked‐in estimator that is ameliorated by the convex combination estimator. We apply our …