# Study designs for extending causal inferences from a randomized trial to a target population

## TL;DR

This paper analyzes various study designs for extending causal inferences from randomized trials to broader target populations, focusing on identification methods and sampling assumptions.

## Contribution

It compares nested and non-nested trial designs, detailing how sampling knowledge affects causal inference and identification strategies.

## Key findings

- Identification depends on knowledge of sampling probabilities.
- Nested and non-nested designs have different identification conditions.
- Implications for estimating trial participation probabilities are discussed.

## 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 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.