Several frameworks have been proposed for studying causal mediation analysis. What these frameworks have in common is that they all make assumptions for point identifications that can be violated even when treatment is randomized. When a causal effect is not point-identified, one can sometimes derive bounds, i.e. a range of possible values that are consistent with the observed data. In this work, we study causal bounds for mediation effects under both the natural effects framework and the separable effects framework. In particular, we show that when there are unmeasured confounders for the intermediate variables(s) the sharp symbolic bounds on separable (in)direct effect coincide with existing bounds for natural (in)direct effects in the analogous setting. We compare these bounds to valid bounds for the natural direct effects when only the cross-world independence assumption does not hold. Furthermore, we demonstrate the use and compare the results of the bounds on data from a trial investigating the effect of peanut consumption on the development of peanut allergy in infants through specific pathways of measured immunological biomarkers.

翻译：已有多个框架被提出用于研究因果中介分析。这些框架的共同点是，它们都基于点识别的假设，这些假设即使在处理随机化的情况下也可能被违反。当因果效应无法点识别时，有时可以推导出界限，即与观测数据一致的可能值范围。在本研究中，我们探讨了自然效应框架和可分离效应框架下中介效应的因果界限。具体而言，我们证明当中介变量存在未测量的混杂因素时，可分离（间接）效应的尖锐符号界限与类似设置下现有自然（间接）效应的界限一致。我们将这些界限与仅当跨世界独立性假设不成立时自然直接效应的有效界限进行比较。此外，我们通过一项试验数据展示了这些界限的应用并比较了结果，该试验研究了花生摄入通过特定测量的免疫生物标志物通路对婴儿花生过敏发展的影响。