The performance of marginal structural models for estimating risk differences and relative risks using weighted univariate generalized linear models

We used Monte Carlo simulations to compare the performance of marginal structural models (MSMs) based on weighted univariate generalized linear models (GLMs) to estimate risk differences and relative risks for binary outcomes in observational studies. We considered four different sets of weights based on the propensity score: inverse probability of treatment weights with the average treatment effect as the target estimand, weights for estimating the average treatment effect in the treated, matching weights and overlap weights. We considered sample sizes ranging from 500 to 10,000 and allowed the prevalence of treatment to range from 0.1 to 0.9. We examined both the robust variance estimator when using generalized estimating equations with an independent working correlation matrix and a bootstrap variance estimator for estimating the standard error of the risk difference and the log-relative risk. The performance of these methods was compared with that of direct weighting. Both the direct weighting approach and MSMs based on weighted univariate GLMs resulted in the identical estimates of risk differences and relative risks. When sample sizes were small to moderate, the use of an MSM with a bootstrap variance estimator tended to result in the most accurate estimates of standard errors. When sample sizes were large, the direct weighting approach and an MSM with a bootstrap variance estimator tended to produce estimates of standard error with similar accuracy. When using a MSM to estimate risk differences and relative risks, in general it is preferable to use a bootstrap variance estimator than the robust variance estimator. We illustrate the application of the different methods for estimating risks differences and relative risks using an observational study on the effect on mortality of discharge prescribing of a beta-blocker in patients hospitalized with acute myocardial infarction.