Survival and Mediation Analysis with Correlated Frailty

Many studies have focused on mediation effects, but fewer have focused on these in a time-to-event analysis and even fewer have focused on these effects in a survival model with frailty effects. The purpose of this study was to show unique modeling of correlated frailty effects with mediation and to demonstrate their use through simulations as well as on a real data application. We focused on a technique introduced by (Lange et al., 2012), which involves a procedure based on Marginal Structural Models (MSM) that directly parameterize the natural direct and indirect effects of interest. Using their method of specifying the MSM structure along with a correlated frailty model allowed us to incorporate the unexplained heterogeneity still unaccounted for by these models. We were able to ascertain direct and indirect mediating effects in the simulations. In the real dataset, we were also able to demonstrate stronger frailty effect in the correlated frailty model accounting for mediation.