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Recently, several new approaches have been proposed for estimating propensity scores by achieving balance in the covariates. The philosophy is that by achieving balance, the bias in the estimated causal treatment effect due to measured covariates can be reduced. 1 In this study, we focus on two approaches in this class: the generalized boosted model 2 and the covariate balancing propensity score. 3 For both approaches, the estimation depends on the covariates that we aim to balance. The traditional belief is that we should obtain balance on all the available covariates in a study. 4 However, will including covariates that are not real confounders increase the variance of the causal estimator? Should we also include covariates that are related only to the treatment assignment?

To investigate which set of covariates should be included in the balancing condition, we conduct a simulation study following Brookhart …