In this paper we consider 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 no time-varying confounders affected by prior exposure and mediator values, identification of direct and indirect effects is achieved by a longitudinal version of Pearl's mediation formula. When there are time-varying confounders affected by prior exposure and mediator, natural direct and indirect effects are not identified. 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' regular g-formula for longitudinal data. When there are no time-varying confouders 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 accomodate both mediation and time-varying confounders.
Biostatistics | Longitudinal Data Analysis and Time Series
VanderWeele, Tyler J. and Tchetgen Tchetgen, Eric, "Mediation Analysis with Time-Varying Exposures and Mediators" (March 2014). Harvard University Biostatistics Working Paper Series. Working Paper 168.