When Better is Worse: A Paradox of the Win Ratio and Net Treatment Benefit

Win ratio and related net benefit summaries analyze prioritized composite endpoints via hierarchical pairwise comparisons. It is tempting to expect monotonicity: If treatment improves each component endpoint, then the hierarchical summary should favor treatment. We show this intuition can fail even in the simplest setting with two binary endpoints. Using an exact 2-by-2 frequency table, treatment has higher marginal success probabilities on both endpoints, yet the win ratio is below one, and the net treatment benefit is negative. The reversal occurs because the secondary endpoint is consulted only within primary-tie strata, inducing a reweighting that can emphasize strata where treatment performs worse. We decompose the net treatment benefit to isolate the tie-stratum contributions driving the reversal and propose minimal reporting diagnostics to improve interpretability.