  Investigators are increasingly using novel methods for extending
(generalizing or transporting) causal inferences from a trial to a target
population. In many generalizability and transportability analyses, the trial
and the observational data from the target population are separately sampled,
following a non-nested trial design. In practical implementations of this
design, non-randomized individuals from the target population are often
identified by conditioning on the use of a particular treatment, while
individuals who used other candidate treatments for the same indication or
individuals who did not use any treatment are excluded. In this paper, we argue
that conditioning on treatment in the target population changes the estimand of
generalizability and transportability analyses and potentially introduces
serious bias in the estimation of causal estimands in the target population or
the subset of the target population using a specific treatment. Furthermore, we
argue that the naive application of marginalization-based or weighting-based
standardization methods does not produce estimates of any reasonable causal
estimand. We use causal graphs and counterfactual arguments to characterize the
identification problems induced by conditioning on treatment in the target
population and illustrate the problems using simulated data. We conclude by
considering the implications of our findings for applied work.
