The probability of benefit is a valuable and important measure of treatment effect, which has advantages over the average treatment effect. Particularly for an ordinal outcome, it has a better interpretation and can make apparent different aspects of the treatment impact. Unfortunately, this measure, and variations of it, are not identifiable even in randomized trials with perfect compliance. There is, for this reason, a long literature on nonparametric bounds for unidentifiable measures of benefit. These have primarily focused on perfect randomized trial settings and one or two specific estimands. We expand these bounds to observational settings with unmeasured confounders and imperfect randomized trials for all three estimands considered in the literature: the probability of benefit, the probability of no harm, and the relative treatment effect.

翻译：获益概率是衡量处理效应的重要指标，相较于平均处理效应具有显著优势。尤其对于序数结局而言，该指标不仅具备更优的可解释性，还能揭示治疗影响的不同维度。遗憾的是，即使在依从性完美的随机试验中，这一指标及其衍生形式也无法被识别。鉴于此，学界已形成关于不可识别获益指标非参数界的长期研究传统，但现有成果主要聚焦于完美随机试验场景及一两种特定估计量。我们将这些界扩展到存在未测量混杂因素的观察性研究及非完美随机试验中，涵盖文献中讨论的全部三种估计量：获益概率、无伤害概率与相对处理效应。