A generalized bootstrap procedure of the standard error and confidence interval estimation for inverse probability of treatment weighting

The inverse probability of treatment weighting (IPTW) approach is commonly used in propensity score analysis to infer causal effects in regression models. Due to oversized IPTW weights and errors associated with propensity score estimation, the IPTW approach can underestimate the standard error of causal effect. To remediate this, bootstrap standard errors have been recommended to replace the IPTW standard error, but the ordinary bootstrap (OB) procedure might still result in underestimation of the standard error because of its inefficient sampling algorithm and un-stabilized weights. In this paper, we develop a generalized bootstrap (GB) procedure for estimating the standard error of the IPTW approach. Compared with the OB procedure, the GB procedure has much lower risk of underestimating the standard error and is more efficient for both point and standard error estimates. The GB procedure also has smaller risk of standard error underestimation than the ordinary bootstrap procedure with trimmed weights, with comparable efficiencies. We demonstrate the effectiveness of the GB procedure via a simulation study and a dataset from the National Educational Longitudinal Study-1988 (NELS-88).