There is increasing interest in combining information from experimental studies, including randomized and single-group trials, with information from external experimental or observational data sources. Such efforts are usually motivated by the desire to compare treatments evaluated in different studies -- for instance, through the introduction of external treatment groups -- or to estimate treatment effects with greater precision. Proposals to combine experimental studies with external data were made at least as early as the 1970s, but in recent years have come under increasing consideration by regulatory agencies involved in drug and device evaluation, particularly with the increasing availability of rich observational data. In this paper, we describe basic templates of study designs and data structures for combining information from experimental studies with external data, and use the potential (counterfactual) outcomes framework to elaborate identification strategies for potential outcome means and average treatment effects in these designs. In formalizing designs and identification strategies for combining information from experimental studies with external data, we hope to provide a conceptual foundation to support the systematic use and evaluation of such efforts.
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