Estimation of Covariate Balancing Propensity Score Based on Outcome Adaptive Lasso

In observational studies, propensity score estimation is crucial for estimating the average treatment effect (ATE). However, covariate imbalance can introduce estimation bias, and including unnecessary covariates can also negatively affect the bias and statistical efficiency of propensity score estimation. To address this issue, this paper proposes an OALIPS estimation method for covariate balancing with causal variable selection. Through a two-step framework of screening followed by estimation, the method first precisely identifies core covariates using a comprehensive propensity score objective function with an outcome-adaptive penalty term. Subsequently, propensity score estimation is performed in a reduced-dimensional space based on a covariate balancing approach, effectively avoiding the shrinkage bias problem in traditional regularized estimation. We prove the consistency of the method's variable selection, the asymptotic normality of the parameter estimates, and the consistency of the ATE estimator based on these estimates. Simulation studies show that the proposed method outperforms conventional methods, accurately identifies confounders and predictors, and remains robust under conditions of covariate imbalance and model misspecification. Subsequently, we applied this method to right heart catheterization (RHC) data, verifying its applicability in handling complex clinical data. The results indicate that, after effectively correcting for severe baseline bias, RHC significantly increases the length of hospital stay for surviving patients.