Robust propensity score estimation via loss function calibration.

Propensity score estimation is often used as a preliminary step to estimate the average treatment effect with observational data. Nevertheless, misspecification of propensity score models undermines the validity of effect estimates in subsequent analyses. Prediction-based machine learning algorithms are increasingly used to estimate propensity scores to allow for more complex relationships between covariates. However, these approaches may not necessarily achieve covariates balancing. We propose a calibration-based method to better incorporate covariate balance properties in a general modeling framework. Specifically, we calibrate the loss function by adding a covariate imbalance penalty to standard parametric (e.g. logistic regressions) or machine learning models (e.g. neural networks). Our approach may mitigate the impact of model misspecification by explicitly taking into account the covariate balance in the propensity score estimation process. The empirical results show that the proposed method is robust to propensity score model misspecification. The integration of loss function calibration improves the balance of covariates and reduces the root-mean-square error of causal effect estimates. When the propensity score model is misspecified, the neural-network-based model yields the best estimator with less bias and smaller variance as compared to other methods considered.