An interpretation of the properties of the propensity score in the regression framework

The propensity score is the probability of receiving the treatment given a set of baseline covariates. The two properties of the propensity score has been illustrated under the potential outcome framework. First, it is a balancing score. Once conditional on the propensity score, observed confounders are balanced between the treatment and control groups. Second, when the treatment status is independent of the potential outcomes conditional on the observed confounders (the ignorability assumption), this conditional independence still holds when conditional on the propensity score. In this article, we illustrate the properties of the propensity score in the regression framework and present an alternative interpretation of the role of the propensity score in controlling for confounding bias.