We present two methods for bounding the probabilities of benefit and harm under unmeasured confounding. The first method computes the (upper or lower) bound of either probability as a function of the observed data distribution and two intuitive sensitivity parameters which, then, can be presented to the analyst as a 2-D plot to assist her in decision making. The second method assumes the existence of a measured nondifferential proxy (i.e., direct effect) of the unmeasured confounder. Using this proxy, tighter bounds than the existing ones can be derived from just the observed data distribution.

翻译：我们提出了两种在未测量混杂因素存在下界定获益与害处概率的方法。第一种方法将两种概率的（上界或下界）计算为观测数据分布和两个直观敏感性参数的函数，进而可向分析师呈现为二维图形以辅助其决策。第二种方法假设存在未测量混杂因素的一个已测量无差异代理变量（即直接效应）。利用该代理变量，仅基于观测数据分布即可推导出比现有方法更紧的界限。