Use of propensity scores in non-linear response models

"Under the assumption of no unmeasured confounders, a large literature exists on methods that can be used to estimating average treatment effects (ATE) from observational data and that spans regression models, propensity score adjustments using stratification, weighting or regression and even the combination of both as in doubly-robust estimators. However, comparison of these alternative methods is sparse in the context of data generated via non-linear models where treatment effects are heterogeneous, such as is in the case of healthcare cost data. In this paper, we compare the performance of alternative regression and propensity score-based estimators in estimating average treatment effects on outcomes that are generated via non-linear models. Using simulations, we find that in moderate size samples (n= 5000), balancing on estimated propensity scores balances the covariate means across treatment arms but fails to balance higher-order moments and covariances amongst covariates, raising concern about its use in non-linear outcomes generating mechanisms. We also find that besides inverse-probability weighting (IPW) with propensity scores, no one estimator is consistent under all data