Estimating Interventional Mediation Effects for Longitudinal Data via Generalised Additive Models

We propose a framework for estimating interventional causal effects in mediation analysis with time-varying variables and post-treatment confounders. In such settings, traditional natural direct and indirect effects are not identified, motivating the use of interventional effects defined through stochastic interventions on the mediator. Our approach combines generalised additive models (GAMs) with Monte Carlo integration to approximate the stochastic g-formula, allowing for flexible estimation of time-varying causal effects under minimal parametric assumptions. A comprehensive simulation study demonstrates accurate recovery of pointwise direct and indirect effects across a range of sample sizes, noise levels, and number of measurements over time.