Mediation analysis serves as a crucial tool to obtain causal inference based on directed acyclic graphs, which has been widely employed in the areas of biomedical science, social science, epidemiology and psychology. Decomposition of total effect provides a deep insight to fully understand the casual contribution from each path and interaction term. Since the four-way decomposition method was proposed to identify the mediated interaction effect in counterfactual framework, the idea had been extended to a more sophisticated scenario with non-sequential multiple mediators. However, the method exhibits limitations as the causal structure contains direct causal edges between mediators, such as inappropriate modeling of dependence and non-identifiability. We develop the notion of natural counterfactual interaction effect and find that the decomposition of total effect can be consistently realized with our proposed notion. Furthermore, natural counterfactual interaction effect overcomes the drawbacks and possesses a clear and significant interpretation, which may largely improve the capacity of researchers to analyze highly complex causal structures.
Probability of Root Cause: A Counterfactual Definition and Its Identification
City University of Hong Kong（香港城市大学）；The Chinese University of Hong Kong（香港中文大学）；Beijing Technology and Business University（北京工商大学）；Renmin University of China（中国人民大学）
What is a good matching of probability measures? A counterfactual lens on transport maps
Institut Elie Cartan de Lorraine, Université de Lorraine（伊莱·卡坦研究所（洛林）、洛林大学）；Université Paris-Saclay, CNRS, Inria, Laboratoire de mathématiques d’Orsay（巴黎-萨克雷大学、国家科学研究中心、法国国家信息与自动化技术研究院、奥赛数学实验室）
Causal treatment effect decompositions with time-to-event outcomes under competing events
University of Turku（图尔库大学）；Finnish Institute for Health and Welfare（芬兰健康福利研究所）；University of Eastern Finland（东芬兰大学）；Karolinska Institutet（卡罗林斯卡学院）；Imperial College London（伦敦帝国理工学院）；Karolinska University Hospital（卡罗林斯卡大学医院）
