On variance estimation of target population created by inverse probability weighting.

Inverse probability weighting (IPW) is frequently used to reduce or minimize the observed confounding in observational studies. IPW creates a pseudo-sample by weighting each individual by the inverse of the conditional probability of receiving the treatment level that he/she has actually received. In the pseudo-sample there is no variation among the multiple individuals generated by weighting the same individual in the original sample. This would reduce the variability of the data and therefore bias the variance estimate in the target population. Conventional variance estimation methods for IPW estimators generally ignore this underestimation and tend to produce biased estimates of variance. We here propose a more reasonable method that incorporates this source of variability by using parametric bootstrapping based on intra-stratum variability estimates. This approach firstly uses propensity score stratification and intra-stratum standard deviation to approximate the variability among multiple individuals generated based on a single individual whose propensity score falls within the corresponding stratum. The parametric bootstrapping is then used to incorporate the target variability by re-generating outcomes after adding a random error term to the original data. The performance of the proposed method is compared with three existing methods including the naïve model-based variance estimator, the nonparametric bootstrap variance estimator, and the robust variance estimator in the simulation section. An example of patients with sarcopenia is used to illustrate the implementation of the proposed approach. According to the results, the proposed approach has desirable statistical properties and can be easily implemented using the provided R code.