  When treatment effect modifiers influence the decision to participate in a
randomized trial, the average treatment effect in the population represented by
the randomized individuals will differ from the effect in other populations. In
this tutorial, we consider methods for extending causal inferences about
time-fixed treatments from a trial to a new target population of
non-participants, using data from a completed randomized trial and baseline
covariate data from a sample from the target population. We examine methods
based on modeling the expectation of the outcome, the probability of
participation, or both (doubly robust). We compare the methods in a simulation
study and show how they can be implemented in software. We apply the methods to
a randomized trial nested within a cohort of trial-eligible patients to compare
coronary artery surgery plus medical therapy versus medical therapy alone for
patients with chronic coronary artery disease. We conclude by discussing issues
that arise when using the methods in applied analyses.
