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Observational data are often readily available or less costly to obtain than conducting a randomized controlled trial. With observational data, investigators may statistically evaluate the relationship between a treatment or therapy and outcomes. However, inherent in observational data is the potential for confounding arising from the nonrandom assignment of treatment. In this statistical grand rounds, we describe the use of propensity score methods (ie, using the probability of receiving treatment given covariates) to reduce bias due to measured confounders in anesthesia and perioperative medicine research. We provide a description of the theory and background appropriate for the anesthesia researcher and describe statistical assumptions that should be assessed in the course of a research study using the propensity score. We further describe 2 propensity score methods for evaluating the association of treatment or therapy with outcomes, propensity score matching and inverse probability of treatment weighting, and compare to covariate-adjusted regression analysis. We distinguish several estimators of treatment effect available with propensity score methods, including the average treatment effect, the average treatment effect for the treated, and average treatment effect for the controls or untreated, and compare to the conditional treatment effect in covariate-adjusted regression. We highlight the relative advantages of the various methods and estimators, describe analysis assumptions and how to critically evaluate them, and demonstrate methods in an analysis of thoracic epidural analgesia and new-onset atrial arrhythmias after pulmonary resection.