The role of the propensity score in estimating dose-response functions

Estimation of average treatment effects in observational studies often requires adjustment for differences in pre-treatment variables. If the number of pre-treatment variables is large, standard covariance adjustment methods are often inadequate. Rosenbaum & Rubin (1983) propose an alternative method for adjusting for pre-treatment variables for the binary treatment case based on the so-called propensity score. Here an extension of the propensity score methodology is proposed that allows for estimation of average casual effects with multi-valued treatments.