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Title: Causal mediation with longitudinal mediator and survival outcome Authors:  Vanessa Didelez - Leibniz Institute for Prevention Research and Epidemiology - BIPS, University of Bremen (Germany) [presenting]
Abstract: Notions of direct and indirect causal effects are based on nested counterfactuals, i.e. on the outcome $Y$ under the hypothetical situation that treatment $X$ was set to $x$, while a mediator $M$ was set to $M(x')$ for a different $x'$. These may have problems of interpretation and identifiability when the outcome of interest is a survival or time-to-event and the mediator a set of longitudinal measurements, as the mediator may not exist for as long in one world compared to another world due to different survival. This is known as the cross-world nature of nested counterfactuals. We will discuss the problem and propose an alternative approach that does not suffer from those shortcomings and makes no cross-world assumptions. The new suggestion follows an extended graphical approach where mechanisms need to be specified that separate the treatment node formalized based on an augmented DAG. We will demonstrate under what assumptions identification of such alternative mediated effects is possible, resulting in the familiar mediation g-formula. Relations to path-specific effects and edge-interventions will be discussed. The proposed new approach is founded in decision theory and while it constitutes an interesting alternative to the prevailing structural equation models, it can be shown that for the particular case of combining linear structural equations for the mediator with an additive hazard model, the familiar linear effect decomposition can be recovered.