  We examine study designs for extending (generalizing or transporting) causal
inferences from a randomized trial to a target population. Specifically, we
consider nested trial designs, where randomized individuals are nested within a
sample from the target population, and non-nested trial designs, including
composite dataset designs, where a randomized trial is combined with a
separately obtained sample of non-randomized individuals from the target
population. We show that the causal quantities that can be identified in each
study design depend on what is known about the probability of sampling
non-randomized individuals. For each study design, we examine identification of
potential outcome means via the g-formula and inverse probability weighting.
Last, we explore the implications of the sampling properties underlying the
designs for the identification and estimation of the probability of trial
participation.
