# Defining causal meditation with a longitudinal mediator and a survival outcome

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## Abstract

In the context of causal mediation analysis, prevailing notions of direct and indirect effects are based on nested counterfactuals. These can be problematic regarding interpretation and identifiability especially when the mediator is a time-dependent process and the outcome is survival or, more generally, a time-to-event outcome. We propose and discuss an alternative definition of mediated effects that does not suffer from these problems, and is more transparent than the current alternatives. Our proposal is based on the extended graphical approach of Robins and Richardson (in: Shrout (ed) Causality and psychopathology: finding the determinants of disorders and their cures, Oxford University Press, Oxford, 2011), where treatment is decomposed into different components, or aspects, along different causal paths corresponding to real world mechanisms. This is an interesting alternative motivation for *any* causal mediation setting, but especially for survival outcomes. We give assumptions allowing identifiability of such alternative mediated effects leading to the familiar mediation g-formula (Robins in Math Model 7:1393, 1986); this implies that a number of available methods of estimation can be applied.

## Keywords

Causal inference Mediation analysis Graphical models Causal graphs Path specific effects## Notes

### Acknowledgements

I would like to thank Odd Aalen, Rhian Daniel, Ilya Sphitser, Mats Stensrud, Susanne Strohmaier, and Stijn Vansteelandt for helpful discussions.

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