Using Propensity Scores to Adjust for Group Differences: Examples Comparing Alternative Surgical Methods

Comparing the effectiveness of two treatments on nonrandomized groups is difficult because there are almost always baseline differences between the groups. Propensity scores (Rosenbaum and Rubin, Biometrika 1983) are a valuable but underutilized approach for adjusting for group differences. When two groups are being compared, the propensity score can be calculated as the predicted probability of group membership from a logistic regression. It represents the 'propensity' for an observation to be in one group or the other. By adjusting for the value of the propensity score in a linear model, one effectively adjusts for any group differences attributable to the variables used to create the propensity score. In addition, the values of the propensity scores can serve as a diagnostic tool to evaluate the comparability of the groups in a quantitative way. In this paper, three practical examples are presented. In each example, propensity scores are used to adjust for differences between nonrandomized groups. Propensity scores were created using SAS System PROC LOGISTIC or PROC CATMOD. For two examples, a linear model estimated using PROC GLM was used to compare groups; in the third example, Poisson regression was performed using PROC GENMOD. This paper will be of interest to individuals familiar with basic regression and ANOVA regardless of their level of SAS experience.