Can Bayesian Network empower propensity score estimation from Real World Data?

A new method, based on Bayesian Networks, to estimate propensity scores is proposed with the purpose to draw causal inference from real world data on the average treatment effect in case of a binary outcome and discrete covariates. The proposed method ensures maximum likelihood properties to the estimated propensity score, i.e. asymptotic efficiency, thus outperforming other available approach. Two point estimators via inverse probability weighting are then proposed, and their main distributional properties are derived for constructing confidence interval and for testing the hypotheses of absence of the treatment effect. Empirical evidence of the substantial improvements offered by the proposed methodology versus standard logistic modelling of propensity score is provided in simulation settings that mimic the characteristics of a real dataset of prostate cancer patients from Milan San Raffaele Hospital.