Bootstrap vs asymptotic variance estimation when using propensity score weighting with continuous and binary outcomes

We used Monte Carlo simulations to compare the performance of asymptotic variance estimators to that of the bootstrap when estimating standard errors of differences in means, risk differences, and relative risks using propensity score weighting. We considered four different sets of weights: conventional inverse probability of treatment weights with the average treatment effect (ATE) as the target estimand, weights for estimating the average treatment effect in the treated (ATT), matching weights, and overlap weights. We considered sample sizes ranging from 250 to 10 000 and allowed the prevalence of treatment to range from 0.1 to 0.9. We found that, when using ATE weights and sample sizes were ≤ 1000, then the use of the bootstrap resulted in estimates of SE that were more accurate than the asymptotic estimates. A similar finding was observed when using ATT weights and sample sizes were ≤ 1000 and the prevalence of treatment was moderate to high. When using matching weights and overlap weights, both the asymptotic estimator and the bootstrap resulted in accurate estimates of SE across all sample sizes and prevalences of treatment. Even when using the bootstrap with ATE weights, empirical coverage rates of confidence intervals were suboptimal when sample sizes were low to moderate and the prevalence of treatment was either very low or very high. A similar finding was observed when using the bootstrap with ATT weights when sample sizes were low to moderate and the prevalence of treatment was very high.