  We focus on the problem of generalizing a causal effect estimated on a
randomized controlled trial (RCT) to a target population described by a set of
covariates from observational data. Available methods such as inverse
propensity sampling weighting are not designed to handle missing values, which
are however common in both data sources. In addition to coupling the
assumptions for causal effect identifiability and for the missing values
mechanism and to defining appropriate estimation strategies, one difficulty is
to consider the specific structure of the data with two sources and treatment
and outcome only available in the RCT. We propose three multiple imputation
strategies to handle missing values when generalizing treatment effects, each
handling the multi-source structure of the problem differently (separate
imputation, joint imputation with fixed effect, joint imputation ignoring
source information). As an alternative to multiple imputation, we also propose
a direct estimation approach that treats incomplete covariates as semi-discrete
variables. The multiple imputation strategies and the latter alternative rely
on different sets of assumptions concerning the impact of missing values on
identifiability. We discuss these assumptions and assess the methods through an
extensive simulation study. This work is motivated by the analysis of a large
registry of over 20,000 major trauma patients and an RCT studying the effect of
tranexamic acid administration on mortality in major trauma patients admitted
to ICU. The analysis illustrates how the missing values handling can impact the
conclusion about the effect generalized from the RCT to the target population.
