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. 2020 May;62(3):532-549.
doi: 10.1002/bimj.201800263. Epub 2019 Feb 19.

Time-dependent mediators in survival analysis: Modeling direct and indirect effects with the additive hazards model

Odd O Aalen  1 , Mats J Stensrud  1   2 , Vanessa Didelez  3   4 , Rhian Daniel  5 , Kjetil Røysland  1 , Susanne Strohmaier  6   7
Affiliations

Time-dependent mediators in survival analysis: Modeling direct and indirect effects with the additive hazards model

Odd O Aalen et al. Biom J. 2020 May.

Abstract

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 nonparametric 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 generalize and formalize the method of dynamic path analysis (Fosen, Ferkingstad, Borgan, & Aalen, 2006; Strohmaier et al., 2015). An application to data from a clinical trial on blood pressure medication is given.

Keywords: additive hazards; causal inference; extended graphical approach; mediation; survival analysis.

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References

REFERENCES

    1. Aalen, O. O., Borgan, Ø., & Gjessing, H. K. (2008). Survival and event history analysis: A process point of view. Berlin: Springer.
    1. Aalen, O. O., Cook, R. J., & Røysland, K. (2015). Does Cox analysis of a randomized survival study yield a causal treatment effect? Lifetime Data Analysis, 21, 579-593.
    1. Aalen, O. O., Gran, J. M., Røysland, K., Stensrud, M. J., & Strohmaier, S. (2018). Feedback and mediation in causal inference illustrated by stochastic process models. Scandinavian Journal of Statistics, 45, 62-86.
    1. Aalen, O., Røysland, K., Gran, J., Kouyos, R., & Lange, T. (2016). Can we believe the DAGs? A comment on the relationship between causal DAGs and mechanisms. Statistical Methods in Medical Research, 25, 2294-2314.
    1. Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173.

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