Identification strategies for combining an experimental study with external data

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, by constructing external comparator groups for some index study -- 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 within clinical practice and by regulatory agencies involved in drug and device evaluation, particularly with the increasing availability of trial and observational data. In this paper, we describe basic study templates that combine 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. We argue that these identification strategies inherit ideas relevant to the study of causation in single-source studies and the related literature on combining information (e.g., generalizability and transportability methods), but merit consideration as a separate class of causal problems because they differ in terms of their scientific motivations, definitions of the target population, sampling, data structures, and identifiability conditions. In formalizing identification strategies for the analyses described herein, we hope to provide a conceptual foundation to support the systematic use and evaluation of such efforts.