Conditioning on the propensity score can result in biased estimation of common measures of treatment effect: a Monte Carlo study.Stat Med. 2007 Feb 20; 26(4):754-68.SM
Propensity score methods are increasingly being used to estimate causal treatment effects in the medical literature. Conditioning on the propensity score results in unbiased estimation of the expected difference in observed responses to two treatments. The degree to which conditioning on the propensity score introduces bias into the estimation of the conditional odds ratio or conditional hazard ratio, which are frequently used as measures of treatment effect in observational studies, has not been extensively studied. We conducted Monte Carlo simulations to determine the degree to which propensity score matching, stratification on the quintiles of the propensity score, and covariate adjustment using the propensity score result in biased estimation of conditional odds ratios, hazard ratios, and rate ratios. We found that conditioning on the propensity score resulted in biased estimation of the true conditional odds ratio and the true conditional hazard ratio. In all scenarios examined, treatment effects were biased towards the null treatment effect. However, conditioning on the propensity score did not result in biased estimation of the true conditional rate ratio. In contrast, conventional regression methods allowed unbiased estimation of the true conditional treatment effect when all variables associated with the outcome were included in the regression model. The observed bias in propensity score methods is due to the fact that regression models allow one to estimate conditional treatment effects, whereas propensity score methods allow one to estimate marginal treatment effects. In several settings with non-linear treatment effects, marginal and conditional treatment effects do not coincide.