The propensity score is a balancing score: conditional on the propensity score, treated and untreated subjects have the same distribution of observed baseline characteristics. Four methods of using the propensity score have been described in the literature: stratification on the propensity score, propensity-score matching, inverse probability of treatment weighting using the propensity score, and covariate adjustment using the propensity score. However, the relative ability of these methods to reduce systematic differences between treated and untreated subjects has not been examined. We used an empirical case study and Monte Carlo simulations to examine the relative ability of the four methods to balance baseline covariates between treated and untreated subjects. We used standardized differences in the propensity-score matched sample and in the weighted sample. For stratification on the propensity score, within-quintile standardized differences were computed comparing the distribution of baseline covariates between treated and untreated subjects within the same quintile of the propensity score. These quintile-specific standardized differences were then averaged across the quintiles. For covariate adjustment, we used the weighted conditional standardized absolute difference to compare balance between treated and untreated subjects. In both the empirical case study and in the Monte Carlo simulations, we found that matching on the propensity score and weighting using the inverse probability of treatment eliminated a greater degree of the systematic differences between treated and untreated subjects compared to the other two methods. In the Monte Carlo simulations, propensity-score matching tended to have either comparable or marginally superior performance compared to propensity-score weighting.
- Propensity score,
- propensity-score matching,
- covariate adjustment with the propensity score,
- inverse probability of treatment weighting,
- stratification on the propensity score,
Available at: http://works.bepress.com/peter_austin/5/