Semi-parametric model approach to causal mediation analysis for longitudinal data

There has been a lack of causal mediation analysis implementation on complicated longitudinal data. Most existing work focuses on extensions of parametric models that have been well developed for causal mediation analysis. To better handle more complex data patterns, our approach takes advantage of the flexibility of penalized splines and performs the causal mediation analysis under the structural equation model framework. We also provide the formula for identifying the natural direct and indirect effects based on our semi-parametric models, whose inference is carried out by the delta method and Monte Carlo approximation. Our approach is first evaluated by conducting simulation studies, where the two methods for inference are compared. Finally, we apply the method to data from a longitudinal cohort study to examine the effect of a training programme for healthcare providers on improving their patients' type 2 diabetes condition.