Beyond weighting: Propensity score modeling for causal inference

Propensity score weighting is a common method in causal inference methods. However, this approach faces two well-known challenges: (i) high variance due to small probability values in the denominator, and (ii) sensitivity to model specification errors when estimating propensity scores in observational studies. In this article, we establish that the expected potential outcomes, conditional on the propensity score, can be identified as a function of the propensity score. Based on this identification result, we utilize spline regression to estimate the function. Treatment effect estimation and inference are derived from the asymptotic normality of the spline regression. Our approach preserves the low bias of inverse probability weighting (IPW), benefiting from the flexibility of nonparametric models, while achieving significantly lower variance due to its model-based stability. Furthermore, we extend this method to regression-based adjustment for improved efficiency in causal inference. Extensive simulations show that our approach achieves lower variance than IPW-based methods while maintaining low bias and robustness to propensity score misspecification. A real-data application further demonstrates its reliability in inference.