Sharp symbolic nonparametric bounds for measures of benefit in observational and imperfect randomized studies with ordinal outcomes
本文推导了有序结局下获益概率、无伤害概率和相对治疗效果三个不可识别指标的非参数界，并将其从完美随机试验扩展到存在未测量混杂的观察性研究和依从性不完美的随机试验。
Abstract The probability of benefit can be a valuable and meaningful measure of treatment effect. Particularly for an ordinal outcome, it can have an intuitive interpretation. 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.