  Survival outcomes are common in comparative effectiveness studies and require
unique handling because they are usually incompletely observed due to
right-censoring. A ``once for all'' approach for causal inference with survival
outcomes constructs pseudo-observations and allows standard methods such as
propensity score weighting to proceed as if the outcomes are completely
observed. We propose a general class of model-free causal estimands with
survival outcomes on user-specified target populations. We develop
corresponding propensity score weighting estimators based on the
pseudo-observations and establish their asymptotic properties. In particular,
utilizing the functional delta-method and the von Mises expansion, we derive a
new closed-form variance of the weighting estimator that takes into account the
uncertainty due to both pseudo-observation calculation and propensity score
estimation. This allows valid and computationally efficient inference without
resampling. We also prove the optimal efficiency property of the overlap
weights within the class of balancing weights for survival outcomes. The
proposed methods are applicable to both binary and multiple treatments.
Extensive simulations are conducted to explore the operating characteristics of
the proposed method versus other commonly used alternatives. We apply the
proposed method to compare the causal effects of three popular treatment
approaches for prostate cancer patients.
