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

Methods for extending -- generalizing or transporting -- inferences from a randomized trial to a target population involve conditioning on a large set of covariates that is sufficient for rendering the randomized and non-randomized groups exchangeable. Yet, decision-makers are often interested in examining treatment effects in subgroups of the target population defined in terms of only a few discrete covariates. Here, we propose methods for estimating subgroup-specific potential outcome means and average treatment effects in generalizability and transportability analyses, using outcome model-based (g-formula), weighting, and augmented weighting estimators. We consider estimating subgroup-specific average treatment effects in the target population and its non-randomized subset, and provide methods that are appropriate both for nested and non-nested trial designs. As an illustration, we apply the methods to data from the Coronary Artery Surgery Study to compare the effect of surgery plus medical therapy versus medical therapy alone for chronic coronary artery disease in subgroups defined by history of myocardial infarction.