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

Abstract

SUMMARY 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. 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 and their distribution varies substantially with treatment status, standard adjustment methods such as covari- ance adjustment are often inadequate. Rosenbaum & Rubin (1983, 1984) propose an alternative method for adjusting for pre-treatment variables based on the propensity score, the conditional probability of receiving the treatment given pre-treatment variables. They demonstrate that adjusting solely for the propensity score removes all bias associated with differences in the pre- treatment variables. The Rosenbaum-Rubin proposals deal exclusively with binary-valued treat- ments. In many cases of interest, however, treatments take on more than two values. Here an extension of the propensity score methodology is proposed that allows for estimation of average causal effects with multi-valued treatments. The key insight is that for estimation of average causal effects it is not necessary to divide the population into subpopulations where causal comparisons are valid, as the propensity score does; it is sufficient to divide the population into subpopulations where average potential outcomes can be estimated.