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Mediation analysis is a valuable approach to examine pathways in epidemiological research. Prospective cohort studies are often conducted to study biological mechanisms and often collect longitudinal measurements on each participant. Mediation formulae for longitudinal data have been developed. Here, we formalize the natural direct and indirect effects using a causal framework with potential outcomes that allows for an interaction between the exposure and the mediator. To allow different types of longitudinal measures of the mediator and outcome, we assume two generalized mixed-effects models for both the mediator and the outcome. The model for the mediator has subject-specific random intercepts and random exposure slopes for each cluster, and the outcome model has random intercepts and random slopes for the exposure, the mediator, and their interaction. We also expand our approach to …