  We discuss causal mediation analyses for survival data and propose a new
approach based on the additive hazards model. The emphasis is on a dynamic
point of view, that is, understanding how the direct and indirect effects
develop over time. Hence, importantly, we allow for a time varying mediator. To
define direct and indirect effects in such a longitudinal survival setting we
take an interventional approach (Didelez (2018)) where treatment is separated
into one aspect affecting the mediator and a different aspect affecting
survival. In general, this leads to a version of the non-parametric g-formula
(Robins (1986)). In the present paper, we demonstrate that combining the
g-formula with the additive hazards model and a sequential linear model for the
mediator process results in simple and interpretable expressions for direct and
indirect effects in terms of relative survival as well as cumulative hazards.
Our results generalise and formalise the method of dynamic path analysis (Fosen
et al. (2006), Strohmaier et al. (2015)). An application to data from a
clinical trial on blood pressure medication is given.
