Priority-Standardized Net Benefit: A Stage-Normalized Estimand for Hierarchical Composite Endpoints

David McCoy; John Leopold; Shirley Galbiati; Minhthien Vu; Bonnie Zhang

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arXiv · 2607.22950

Priority-Standardized Net Benefit: A Stage-Normalized Estimand for Hierarchical Composite Endpoints

David McCoy·John Leopold·Shirley Galbiati·Minhthien Vu·Bonnie Zhang

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Abstract

Hierarchical composite endpoints analyzed with win statistics are increasingly used when outcomes differ in clinical importance and hard events are too rare to support a single-component primary endpoint. Their appeal is that the analysis respects a prespecified priority order; their less-stated vulnerability is that standard win summaries aggregate layer-specific information using reach probabilities, the fraction of treated-control pairs still tied at each layer. When upper layers are rare or highly tied, a frequently reached last layer can dominate the composite even if it is lowest priority and more vulnerable to bias or missingness, such as an open-label patient-reported outcome. We propose the Priority-Standardized Net Benefit (PSNB), an estimand that decomposes a hierarchical comparison into stage-conditional net benefits and recombines them with a prespecified priority/credibility charter rather than data-determined reach weights. We identify the methodological gap as across-layer aggregation, not within-layer comparison, and show that fixed weighted win-loss statistics remain mechanically reach-weighted; we develop an influence-function-based estimator and large-sample inference, with a ratio-scale companion (the Priority-Standardized Win Ratio); and we give design tools (a layer influence cap, tipping-point analysis, and charter-envelope sensitivity analysis) usable before unblinding. Simulations confirm nominal type I error, show PSNB is approximately invariant to large changes in reach when stage-conditional effects are held fixed, and show that late-layer bias and missingness sensitivity is governed by the charter rather than the reach distribution. At a sample size where the Win Ratio has about 90% power under broad benefit, PSNB with the baseline charters keeps pace, while power under final-layer-dominated benefit depends on the permitted last-layer weight.

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BibTeX RIS

David McCoy, John Leopold, Shirley Galbiati, Minhthien Vu, Bonnie Zhang. 2026-07-24. Priority-Standardized Net Benefit: A Stage-Normalized Estimand for Hierarchical Composite Endpoints. https://arxiv.org/abs/2607.22950

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