What are propensity scores? Why are they used?

Propensity scores are calculations of the likelihood of a subject being in a particular treatment group, conditional on that subject's values on those independent variables thought to influence group membership. They are used to statistically adjust for differences between nonrandomized groups, typically for studies comparing different treatments.

To calculate a propensity score, you first identify the variables that influence treatment group membership, including demographics, disease severity, and characteristics of the treatment system (e.g., physician specialty, hospital, etc.). These variables are entered into a model (typically logistic) estimating the likelihood of treatment group membership. This model yields a score for each subject; the score is the estimated likelihood of being in one group versus the other, conditional on a weighted score of that subject's values on the set of independent variables used to create the propensity score.

Once calculated there are different ways you can use propensity scores. You can include each subject's propensity score in your multivariable model as an independent variable. Or you can use this score to individually match subjects with different treatment assignments but an equal likelihood of being in a particular group and assess the outcome using a matched analysis (Section 11.1). Alternatively you can assess the likelihood of outcome within quintiles of the propensity score.