The performance of different propensity score methods for estimating marginal odds ratios

The propensity score is the probability of exposure to a specific treatment conditional on observed variables.  Conditioning on the propensity score results in unbiased estimation of the expected difference in observed responses to two treatments.  In the medical literature, propensity score methods are frequently used for estimating odds ratios.  The performance of propensity score methods for estimating marginal odds ratios has not been studied.

Investigators performed a series of Monte Carlo simulations to assess the performance of propensity score matching, stratifying on the propensity score, and covariate adjustment using the propensity score to estimate marginal odds ratios.  They assessed bias, precision, and mean-squared error (MSE) of the propensity score estimators, in addition to the proportion of bias eliminated due to conditioning on the propensity score.

When the true marginal odds ratio was one, then matching on the propensity score and covariate adjustment using the propensity score resulted in unbiased estimation of the true treatment effect, whereas stratification on the propensity score resulted in minor bias in estimating the true marginal odds ratio.  When the true marginal odds ratio ranged from two to 10, then matching on the propensity score resulted in the least bias, with a relative biases ranging from 2.3 to 13.3 per cent.  Stratifying on the propensity score resulted in moderate bias, with relative biases ranging from 15.8 to 59.2 per cent.  For both methods, relative bias was proportional to the true odds ratio.  Finally, matching on the propensity score tended to result in estimators with the lowest MSE.