Spline linear mixed-effects models for causal mediation analysis with longitudinal data

Often, causal mediation analysis is of interest when both the mediator and the final outcome are repeatedly measured, but limited work has been done for this situation (as opposed to where only the mediator is repeatedly measured). Available methods are primarily based on parametric models and tend to be sensitive to model assumptions. This article presents semiparametric, continuous-time models to provide a flexible and robust approach to causal mediation analysis for longitudinal data, which allows these data to be unbalanced or irregular. Specifically, the method uses spline linear mixed-effects models for the mediator and for the final outcome, with a two-step approach to model-fitting in which a predicted mediator is used as a covariate in the final outcome model. The models allow flexible functions for both the mean and individual response functions for each outcome. We derive estimated natural direct and indirect effects as a function of time using an extended mediation formula and sequential ignorability assumption. In simulation studies, we compare properties of estimated direct and indirect effects, and a delta method estimate of the standard error of the latter, under alternative approaches for predicting the mediator. The approach is illustrated using harmonised data from two cohort studies to examine attention as a mediator of the effect of prenatal tobacco exposure on externalising behaviour in children.