Doubly robust estimation of the weighted average treatment effect for a target population

The weighted average treatment effect is a causal measure for the comparison of interventions in a specific target population, which may be different from the population where data are sampled from. For instance, when the goal is to introduce a new treatment to a target population, the question is what efficacy (or effectiveness) can be gained by switching patients from a standard of care (control) to this new treatment, for which the average treatment effect for the control estimand can be applied. In this paper, we propose two estimators based on augmented inverse probability weighting to estimate the weighted average treatment effect for a well-defined target population (ie, there exists a predefined target function of covariates that characterizes the population of interest, for example, a function of age to focus on elderly diabetic patients using samples from the US population). The first proposed estimator is doubly robust if the target function is known or can be correctly specified. The second proposed estimator is doubly robust if the target function has a linear dependence on the propensity score, which can be used to estimate the average treatment effect for the treated and the average treatment effect for the control. We demonstrate the properties of the proposed estimators through theoretical proof and simulation studies. We also apply our proposed methods in a comparison of glucagon-like peptide-1 receptor agonists therapy and insulin therapy among patients with type 2 diabetes, using the UK Clinical Practice Research Datalink data.