Worst-Case Win Ratios Under Partially Specified Outcome Hierarchies
Abstract
Win statistics require a prespecified outcome hierarchy. Clinical teams sometimes agree only on the highest priority outcome, leaving the order of lower priority outcomes unresolved, and clinically meaningful thresholds may be specified as ranges. Separate sensitivity analyses describe how the results change. A single inference for the full set of planned analyses is generally absent. We define the estimand as the smallest net benefit among the comparison rules allowed by the protocol or statistical analysis plan. Each rule uses the usual two-sample U-statistic. Large-sample results are developed for a finite list of rules and for a continuous threshold range. Inversion of an intersection-union test gives a one-sided lower confidence bound, with no multiplicity adjustment for the single claim that every individual net benefit is positive. Simulations show valid one-sided coverage and illustrate the gap between a favorable result for one selected hierarchy and a favorable result across all prespecified hierarchies. An application to ACTG 175 shows how the ordering of laboratory outcomes can affect the strength of the conclusion. A further example identifies an unfavorable threshold that is missed by a sparse grid.
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BibTeX
@misc{li2026worstcase,
title = {{Worst-Case Win Ratios Under Partially Specified Outcome Hierarchies}},
author = {Kexuan Li and Xue Fan and Lingli Yang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29857},
eprint = {2608.29857},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29857},
}
RIS
TY - UNPB
TI - Worst-Case Win Ratios Under Partially Specified Outcome Hierarchies
AU - Kexuan Li
AU - Xue Fan
AU - Lingli Yang
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29857
UR - https://arxiv.org/abs/2608.29857
AB - Win statistics require a prespecified outcome hierarchy. Clinical teams sometimes agree only on the highest priority outcome, leaving the order of lower priority outcomes unresolved, and clinically meaningful thresholds may be specified as ranges. Separate sensitivity analyses describe how the results change. A single inference for the full set of planned analyses is generally absent. We define the estimand as the smallest net benefit among the comparison rules allowed by the protocol or statistical analysis plan. Each rule uses the usual two-sample U-statistic. Large-sample results are developed for a finite list of rules and for a continuous threshold range. Inversion of an intersection-union test gives a one-sided lower confidence bound, with no multiplicity adjustment for the single claim that every individual net benefit is positive. Simulations show valid one-sided coverage and illustrate the gap between a favorable result for one selected hierarchy and a favorable result across all prespecified hierarchies. An application to ACTG 175 shows how the ordering of laboratory outcomes can affect the strength of the conclusion. A further example identifies an unfavorable threshold that is missed by a sparse grid.
ER -