A comparative analysis of different adjustment sets using propensity score based estimators

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Propensity score based estimators are commonly employed in observational studies to address baseline confounders, without explicitly modeling their association with the outcome. In this paper, to fully leverage these estimators, we consider a series of regression models for improving estimation efficiency. The proposed estimators rely solely on a properly modeled propensity score and do not require the correct specification of outcome models. In addition, we consider a comparative analysis by applying the proposed estimators to four different adjustment sets, each consisting of background covariates. The theoretical results imply that incorporating predictive covariates into both propensity score and regression model demonstrates the lowest asymptotic variance. However, including instrumental variables in the propensity score may decrease the estimation efficiency of the proposed estimators. To evaluate the performance of the proposed estimators, we conduct simulation studies and provide a real data example.