Making censored pairs count: conditional tie weighting for win statistics with composite survival endpoints

Hierarchical composite endpoints are increasingly used in clinical trials to compare patients first on the most clinically important outcome and then, only when that comparison is tied, on lower priority outcomes.

Under right censoring, a lower priority comparison may already be observed but still cannot contribute because the higher priority genuine tie required for descent through the hierarchy is not confirmed.

Existing restricted win-statistic estimators address censoring by requiring such ties from higher priority to be observed as genuine ties.

This all-or-nothing rule preserves the restricted-time estimand, but excludes pairs with censoring-induced ties even when their lower priority comparisons contain useful information.

We propose conditional tie weighting, which replaces the unavailable higher priority genuine-tie indicator by its conditional probability given the observed pairwise data.

The resulting estimator targets the same restricted-time win probabilities while allowing partially observed pairs to contribute fractionally when their lower priority comparison is informative.

We establish identification and large-sample theory for the resulting two-sample U-statistics with estimated nuisance functions, and derive sandwich variance estimators for the win ratio, net benefit, and win odds.

Simulations show substantial efficiency gains, especially under heavier censoring and longer restriction horizons.

A reanalysis of the HF-ACTION trial illustrates how conditional tie weighting recovers information from censoring-induced ties in death-first hospitalization comparisons further apply our estimator to reanalyze a completed randomized clinical trial.