On the relation between g-formula and inverse probability weighting estimators for generalizing trial results

Abstract

When generalizing inferences from a randomized trial to a target population, two classes of estimators are used: g-formula estimators that depend on modeling the conditional outcome mean among trial participants and inverse probability (IP) weighting estimators that depend on modeling the probability of participation in the trial. In this article, we take a closer look at the relation between these two classes of estimators. We propose IP weighting estimators that combine models for the probability of trial participation and the probability of treatment among trial participants. We show that, when all models are estimated using nonparametric frequency methods, these estimators are finite-sample equivalent to the g-formula estimator. We argue for the use of augmented IP weighting (doubly robust) generalizability estimators when nonparametric estimation is infeasible due to the curse of dimensionality, and examine the finite-sample behavior of different estimators using parametric models in a simulation study.