Causal reasoning in difference graphs

Abstract: Understanding causal mechanisms across different populations is essential for designing effective public health interventions. Recently, difference graphs have been introduced as a tool to visually represent causal variations between two distinct populations. While there has been progress in inferring these graphs from data through causal discovery methods, there remains a gap in systematically leveraging their potential to enhance causal reasoning. This paper addresses that gap by establishing conditions for identifying causal changes and effects using difference graphs. It specifically focuses on identifying total causal changes and total effects in a nonparametric setting, as well as direct causal changes and direct effects in a linear setting. In doing so, it provides a novel approach to causal reasoning that holds potential for various public health applications.