Mediation analysis with time varying exposures and mediators
We consider causal mediation analysis when exposures and mediators vary over time. We give non‐parametric identification results, discuss parametric implementation and also provide a weighting approach to direct and indirect effects based on combining the results of two marginal structural models. We also discuss how our results give rise to a causal interpretation of the effect estimates produced from longitudinal structural equation models. When there are time varying confounders affected by prior exposure and a mediator, natural direct and indirect effects are not identified. However, we define a randomized interventional analogue of natural direct and indirect effects that are identified in this setting. The formula that identifies these effects we refer to as the ‘mediational g‐formula’. When there is no mediation, the mediational g‐formula reduces to Robins's regular g‐formula for longitudinal data. When there are no time varying confounders affected by prior exposure and mediator values, then the mediational g‐formula reduces to a longitudinal version of Pearl's mediation formula. However, the mediational g‐formula itself can accommodate both mediation and time varying confounders and constitutes a general approach to mediation analysis with time varying exposures and mediators.
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