Longitudinal mediation analysis with multilevel and latent growth models: a separable effects causal approach.

Background: Causal mediation analysis is widespread in applied medical research, especially in longitudinal settings. However, estimating natural mediational effects in such contexts is often difficult because of the presence of post-treatment confounding. Moreover, many models frequently used in applied research, like multilevel and latent growth models, present an additional difficulty, i.e. the presence of latent variables. In this paper, we propose a causal interpretation of these two classes of models based on a novel type of causal effects called separable, which overcome some of the issues of natural effects.

Methods: We formally derive conditions for the identifiability of separable mediational effects and their analytical expressions based on the g-formula. We carry out a simulation study to investigate how moderate and severe model misspecification, as well as violation of the identfiability assumptions, affect estimates. We also present an application to real data.

Results: The results show how model misspecification impacts the estimates of mediational effects, particularly in the case of severe misspecification, and that the bias worsens over time. The violation of assumptions affects separable effect estimates in a very different way for the mixed effect and the latent growth models.

Conclusion: Our approach allows us to give multilevel and latent growth models an appealing causal interpretation based on separable effects. The simulation study shows that model misspecification can heavily impact effect estimates, highlighting the importance of careful model choice.