Retrospective causal inference with multiple effect variables
针对多个结果变量同时存在的情况，提出基于后验因果效应的回顾性因果推断方法，用于更准确地追溯原因，适用于因果归因、医疗诊断等场景。
Summary As highlighted in Dawid (2000) and Pearl & Mackenzie (2018), deducing the causes of given effects is a more challenging problem than evaluating the effects of causes in causal inference. Lu et al. (2023) proposed an approach for deducing causes of a single effect variable based on posterior causal effects. In many applications, there are multiple effect variables, and they can be used simultaneously to more accurately deduce the causes. To retrospectively deduce causes from multiple effects, we propose multivariate posterior total, intervention and direct causal effects conditional on the observed evidence. We describe the assumptions of no confounding and monotonicity, under which we prove identifiability of the multivariate posterior causal effects and provide their identification equations. The proposed approach can be applied for causal attributions, medical diagnosis, blame and responsibility in various studies with multiple effect or outcome variables. Two examples are used to illustrate the proposed approach.