A comparison of marginal odds ratio estimators.

Uses of the propensity score to obtain estimates of causal effect have been investigated thoroughly under assumptions of linearity and additivity of exposure effect. When the outcome variable is binary relationships such as collapsibility, valid for the linear model, do not always hold. This article examines uses of the propensity score when both exposure and outcome are binary variables and the parameter of interest is the marginal odds ratio. We review stratification and matching by the propensity score when calculating the Mantel-Haenszel estimator and show that it is consistent for neither the marginal nor conditional odds ratio. We also investigate a marginal odds ratio estimator based on doubly robust estimators and summarize its performance relative to other recently proposed estimators under various conditions, including low exposure prevalence and model misspecification. Finally, we apply all estimators to a case study estimating the effect of Medicare plan type on the quality of care received by African-American breast cancer patients.