Study Designs for Extending Causal Inferences From a Randomized Trial to a Target Population

Abstract

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 targetpopulation, 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 counterfactual 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 counterfactual 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.

Regression-based estimation of heterogeneous treatment effects when extending inferences from a randomized trial to a target population

“…We refer to the functions p(X), e a (X), and g a (X) as "nuisance functions" because they are useful in identifying and estimating CATEs, but, in our setup, are not of scientific interest per se. Because φ(O) involves the observed data O and nuisance functions that are identifiable from the observed data under the nested trial design [18], we conclude that CATEs conditional on X are identifiable. In fact, φ(O) is the (uncentered) influence function of the functional that identifies the average treatment effect in the target population under a nonparametric model for the observed data that obeys conditions (1) through (5); see reference [6] for details.…”

“…Study design: We consider a nested trial design [18], where the trial is embedded within a cohort sampled from the target population of substantive interest. The nesting can be achieved by designing a prospective cohort study of individuals from the target population and inviting some of the cohort members to participate in the trial, while collecting information on baseline covariates on all cohort members, including those who do not participate in the trial.…”

“…Here, we build on recent advances in estimating CATEs in observational studies [11][12][13][14][15][16][17] and efficient and robust methods for generalizability and transportability analyses [6,7] to propose general methods for estimating the target population CATEs when a trial is embedded in a sample from the target population (i.e., in nested trial designs [18]). The methods allow the examination of CATEs given a small set of effect modifiers, while conditioning on a rich set of covariates that is sufficient to render the trial and target population exchangeable.…”

Learning about treatment effects in a new target population under transportability assumptions for relative effect measures

“…Study design: Consider a non-nested study design where the investigators have data from a randomized trial that compared the treatments of interest and a separately obtained sample from a target population in which experimentation is not feasible [7]. This design can be used to learn about treatment effects in a target population that meets the eligibility criteria of the trial (in generalizability analyses) as well as broader target populations (in transportability analyses) [8].…”

“…Throughout, we use f (•) to generically denote densities. In what follows all densities and expectations are with respect to the sampling scheme underlying the non-nested trial design [7].…”