Closed-form variance estimator for weighted propensity score estimators with survival outcome

Propensity score (PS) methods are widely used in observational studies for evaluating marginal treatment effects. PS-weighting is a popular PS-based method that allows for estimating both the average treatment effect on the overall population (ATE) and the average treatment effect on the treated population (ATT). Previous research has shown that the variance of the treatment effect is accurately estimated only if the variance estimator takes into account the fact that the propensity score is itself estimated from the available data in a first step of the analysis. In 2016, Austin showed that the bootstrap-based variance estimator was the only existing estimator resulting in approximately correct estimates of standard errors when evaluating a survival outcome and a Cox model was used to estimate a marginal hazard ratio (HR). This author stressed the need to develop a closed-form variance estimator of the marginal HR accounting for the estimation of the PS. In the present research, we developed such variance estimators both for the ATE and ATT. We evaluated their performance with an extensive simulation study and compared them to bootstrap-based variance estimators and to naive variance estimators that do not account for the estimation step. We found that the performance of the proposed variance estimators was similar to that of the bootstrap-based estimators. The proposed variance estimators provide an alternative to the bootstrap estimator, particularly interesting in situations in which time-consumption and/or reproducibility are an important issue. An implementation has been developed for the R software and is freely available (package hrIPW).