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

TL;DR

This paper introduces a new method for causal mediation analysis in survival data using the additive hazards model, allowing for time-varying mediators and dynamic effects over time.

Contribution

It combines the g-formula with the additive hazards model to derive simple, interpretable expressions for direct and indirect effects in longitudinal survival settings.

Findings

Derived explicit formulas for effects in terms of relative survival and hazards.

Generalized dynamic path analysis to survival data with time-varying mediators.

Applied method to clinical trial data on blood pressure medication.

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 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.