  With increasing data availability, causal effects can be evaluated across
different data sets, both randomized controlled trials (RCTs) and observational
studies. RCTs isolate the effect of the treatment from that of unwanted
(confounding) co-occurring effects but they may suffer from
unrepresentativeness, and thus lack external validity. On the other hand, large
observational samples are often more representative of the target population
but can conflate confounding effects with the treatment of interest. In this
paper, we review the growing literature on methods for causal inference on
combined RCTs and observational studies, striving for the best of both worlds.
We first discuss identification and estimation methods that improve
generalizability of RCTs using the representativeness of observational data.
Classical estimators include weighting, difference between conditional outcome
models, and doubly robust estimators. We then discuss methods that combine RCTs
and observational data to either ensure uncounfoundedness of the observational
analysis or to improve (conditional) average treatment effect estimation. We
also connect and contrast works developed in both the potential outcomes
literature and the structural causal model literature. Finally, we compare the
main methods using a simulation study and real world data to analyze the effect
of tranexamic acid on the mortality rate in major trauma patients. A review of
available codes and new implementations is also provided.
