  The simultaneous availability of experimental and observational data to
estimate a treatment effect is both an opportunity and a statistical challenge:
Combining the information gathered from both data is a promising avenue to
build upon the internal validity of randomized controlled trials (RCTs) and a
greater external validity of observational data, but it raises methodological
issues, especially due to different sampling designs inducing distributional
shifts. We focus on the aim of transporting a causal effect estimated on an RCT
onto a target population described by a set of covariates. Available methods
such as inverse propensity weighting are not designed to handle missing values,
which are however common in both data. In addition to coupling the assumptions
for causal identifiability and for the missing values mechanism and to defining
appropriate strategies, one has to consider the specific structure of the data
with two sources and treatment and outcome only available in the RCT. We study
different approaches and their underlying assumptions on the data generating
processes and distribution of missing values and suggest several adapted
methods, in particular multiple imputation strategies. These methods are
assessed in an extensive simulation study and practical guidelines are provided
for different scenarios. This work is motivated by the analysis of a large
registry of over 20,000 major trauma patients and a multi-centered RCT studying
the effect of tranexamic acid administration on mortality. The analysis
illustrates how the missing values handling can impact the conclusion about the
effect transported from the RCT to the target population.
