A recipe for population-based doubly robust estimation via weighting, regression, calibration, and standardization

A large class of doubly robust estimators can be viewed as regression standardization augmented by a bias correction based on inverse probability of treatment weights. These estimators are often justified as solutions to augmented inverse probability weighted (AIPW) estimating equations. When regression standardization is based on a canonical-link generalized linear model fit via maximum likelihood estimation to an inverse probability of treatment weighted sample (IPTW-GLM), double robustness holds without any explicit bias correction. These estimators have usually targeted causal effects within a population represented by the study sample. Here, we present a unification and extension of these doubly robust estimators in terms of constructing a weighted pseudosample that represents a flexible target population with randomized exposures. This allows the bias correction to be understood and operationalized as calibrating the outcome model to match the group means within the balanced pseudosample, illuminating the connection between IPTW-GLM and other AIPW estimators. It also allows the straightforward construction of estimators that are doubly robust for target populations other than the study sample, which is useful when data come from studies where enrollment depends on exposure (e.g., observational cohort studies).