Propensity Score Analysis

Underlying Theory

Formally, the propensity score is defined as the conditional probability of receiving treatment given a set of observed covariates. For simplicity, treatment will be assumed to be a binary variable (i.e., treatment or control). The majority of propensity score research addresses this binary treatment case; however, the propensity score method has been extended to treatments with multiple doses. The propensity score is a one-number summary of the multivariate information in the covariates that are related to treatment assignment. More specifically, the propensity score is a balancing score in the sense that matching on the propensity score creates pairs or subclasses within which the distribution of observed covariates is the same, on average, for both treated and control groups. In other words, the covariate distributions are “balanced” between the treated and control groups within these subclasses. Under two key assumptionsstrongly ignorable treatment assignment and stable unit treatment value assumption (SUTVA)an unbiased estimate of the average treatment effect at a specific propensity score value is given by the difference between the treated and [Page 1116]control means for all units with that value of the propensity score. Averaging these differences across all propensity score values in the population yields an average overall treatment effect. The strongly ignorable treatment assumption implies that each unit has a nonzero probability of receiving treatment and that all relevant covariates have been included in the propensity score model so that treatment assignment is unconfounded with the covariates (sometimes referred to as “unconfoundedness” or “no hidden bias” or “selection on observables”). The SUTVA assumption implies that there is only one version of each treatment for each unit and that the treatment assignment of one unit does not affect the outcome of any other units (“no interference between units”).

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