Prognostic models and the propensity score.

Subjects in observational studies of exposure effects have not been randomized to exposure groups and may therefore differ systematically with regard to variables related to exposure and/or outcome. To obtain unbiased estimates and tests of exposure effects one needs to adjust for these variables. A common method is adjustment via a parametric model incorporating all known prognostic variables. Rosenbaum and Rubin propose adjustment by the conditional exposure probability given a set of covariates which they call the propensity score. They show that, at any value of the propensity score, covariates are on average balanced between exposure groups. Thus matching on the propensity score leads to unbiased estimators and tests of exposure effect. However, the validity of the method depends on knowing the exposure probability. This quantity is usually not known in observational studies and needs to be estimated.