In contrast to evaluating treatment effects, causal attribution analysis focuses on identifying the key factors responsible for an observed outcome. For two binary exposure variables and a binary outcome variable, researchers need to assess not only the likelihood that an observed outcome was caused by a particular exposure, but also the likelihood that it resulted from the interaction between the two exposures. For example, in the case of a male worker who smoked, was exposed to asbestos, and developed lung cancer, researchers aim to explore whether the cancer resulted from smoking, asbestos exposure, or their interaction. Even in randomized controlled trials, widely regarded as the gold standard for causal inference, identifying and evaluating retrospective causal interactions between two exposures remains challenging. In this paper, we define posterior probabilities to characterize the interactive causes of an observed outcome. We establish the identifiability of posterior probabilities by using a secondary outcome variable that may appear after the primary outcome. We apply the proposed method to the classic case of smoking and asbestos exposure. Our results indicate that for lung cancer patients who smoked and were exposed to asbestos, the disease is primarily attributable to the synergistic effect between smoking and asbestos exposure.

翻译：与评估处理效应不同，因果归因分析侧重于识别导致观察结果的关键因素。对于两个二元暴露变量和一个二元结果变量，研究者不仅需要评估观察结果由特定暴露引起的可能性，还需要评估其由两种暴露间交互作用导致的可能性。例如，针对一名吸烟、接触石棉并罹患肺癌的男性工人，研究者旨在探究肺癌是由吸烟、石棉暴露还是二者交互作用所致。即使在随机对照试验——这一被广泛视为因果推断金标准的研究设计中，识别和评估两种暴露间的回顾性因果交互作用仍具挑战性。本文通过定义后验概率来刻画观察结果的交互性原因。我们利用可能在主要结果之后出现的次要结果变量，建立了后验概率的可识别性。我们将所提方法应用于经典的吸烟与石棉暴露案例。研究结果表明，对于吸烟且接触石棉的肺癌患者，其疾病主要归因于吸烟与石棉暴露之间的协同效应。