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Comparison of adjusted and unadjusted marginal probabilities for estimating binomial parameters in observational studies

In this study, we demonstrate how generalized propensity score estimators (Imbens’ weighted estimator, the propensity score weighted estimator and the generalized doubly robust estimator) can be used to calculate the adjusted marginal probabilities for estimating the three common binomial parameters: the risk difference (RD), the relative risk (RR), and the odds ratio (OR). We further conduct a simulation study to compare the estimated RD, RR, and OR using the adjusted and the unadjusted marginal probabilities in terms of the bias and mean-squared error (MSE). Although there is no clear winner in terms of the MSE for estimating RD, RR, and OR, simulation results surprisingly show thatthe unadjusted marginal probabilities produce the smallest bias compared with the adjusted marginal probabilities in most of the estimates. Hence, in conclusion, we recommend using the unadjusted marginal probabilities to estimate RD, RR, and OR, in practice.