Asymptotic properties of resampling-based processes for the average treatment effect in observational studies with competing risks

In observational studies with time-to-event outcomes, the g-formula can be used to estimate a treatment effect in the presence of confounding factors. However, the asymptotic distribution of the corresponding stochastic process is complicated and thus not suitable for deriving confidence intervals or time-simultaneous confidence bands for the average treatment effect. A common remedy are resampling-based approximations, with Efron's nonparametric bootstrap being the standard tool in practice. We investigate the large sample properties of three different resampling approaches and prove their asymptotic validity in a setting with time-to-event data subject to competing risks.