Causal mediation analysis for difference-in-difference design and panel data

Objectives: Advantages of panel data, i.e., difference in difference (DID) design data, are a large sample size and easy availability. Therefore, panel data are widely used in epidemiology and in all social science fields. The literature on causal inference in panel data settings or DID designs has been expanding, although existing studies often focus on the exposed group (or treated group), limiting the development of mediation analysis methods. Methods: In this study, we present a methodology for conducting causal mediation analysis in a DID design and panel data setting that encompasses the entire population including both exposed and unexposed groups, by proposing a general common trend assumption which has a form of exchangeability. We provide formal counterfactual definitions for controlled direct effect and natural direct and indirect effect in panel data setting and DID design, including the identification and required assumptions. We also demonstrate that, under the assumptions of linearity and additivity, controlled direct effects can be estimated by contrasting marginal and conditional DID estimators whereas natural indirect effects can be estimated by calculating the product of the exposure-mediator DID estimator and the mediator-outcome DID estimator. A panel regression-based approach is also proposed. Results: The proposed method is then used to investigate mechanisms of the effects of the Covid-19 pandemic on the mental health status of the population. The results revealed that mobility restrictions mediated approximately 45 % of the causal effect of Covid-19 on mental health status. Conclusions: The proposed approach offers a framework for mediation analysis in DID and panel data settings, addressing limitations of existing studies by including both exposed and unexposed groups.