The propensity score is the conditional probability of treatment given the observed covariates. Matching or stratifying on the scalar propensity score tends to balance the observed covariates used to construct the score. If it suffices to adjust for the observed covariates -- if there is no unmeasured confounding -- then it suffices to adjust for the propensity score. Alas, unmeasured confounding is a central concern in every observational study. Propensity scores are sometimes used in inverse probability weighting, also known as model-based direct adjustment.
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Rosenbaum PR, Rubin DB. Propensity scores in the design of observational studies for causal effects. Biometrika. 2023 Mar 1;110(1):1-13. https://doi.org/10.1093/biomet/asac054
Brumberg K, Small DS, Rosenbaum PR. Optimal refinement of strata to balance covariates. Biometrics. 2024 Sep;80(3):ujae061. https://doi.org/10.1093/biomtc/ujae061