  We are interested in the estimation of average treatment effects based on
right-censored data of an observational study. We focus on causal inference of
differences between t-year absolute event risks in a situation with competing
risks. We derive doubly robust estimation equations and implement estimators
for the nuisance parameters based on working regression models for the outcome,
the censoring and the treatment distribution conditional on auxiliary baseline
covariates. We use the functional delta method to show that our estimators are
regular asymptotically linear estimators and estimate their variances based on
estimates of their influence functions. In empirical studies we assess the
robustness of the estimators and the coverage of confidence intervals. The
methods are further illustrated using data from a Danish registry study.
