Testing for causal effect for binary data when propensity scores are estimated through Bayesian Networks

This paper proposes a new statistical approach for assessing treatment effect using Bayesian Networks (BNs). The goal is to draw causal inferences from observational data with a binary outcome and discrete covariates. The BNs are here used to estimate the propensity score, which enables flexible modeling and ensures maximum likelihood properties. When the propensity score is estimated by BNs, two point estimators are considered—Hájek and Horvitz–Thompson—based on inverse probability weighting, and their main distributional properties are derived for constructing confidence intervals and testing hypotheses about the absence of the treatment effect. Empirical evidence is presented to show the good behavior of the proposed methodology through a simulation study mimicking the characteristics of a real dataset of prostate cancer patients from Milan San Raffaele Hospital.