Causal mediation analysis in the multilevel intervention and multicomponent mediator case

Mediation analysis is an important tool in social and medical sciences as it helps to understand why an intervention works. The commonly used approach, given by Baron and Kenny, requires the strong assumption sequential ignorability' to yield causal interpretation. Ten Have and his colleagues proposed a rank preserving model to relax this assumption. However, the rank preserving model is restricted to the case with binary intervention and single mediator and needs another strong assumption rank preserving'. We propose a new model that can relax this assumption and can handle both multilevel intervention and multicomponent mediators. As an estimating-equation-based method, our model can handle both correlated data with the generalized estimating equation and missing data with inverse probability weighting. Finally, our method can also be used in many other research settings, using mathematical models similar to mediation analysis, such as treatment compliance and post-randomized treatment component analysis. For the causal mediation model proposed, we first show identifiability for the parameters in the model. We then propose a semiparametric method for estimating the model parameters and derive asymptotic results for the estimators proposed. Simulation shows good performance for the proposed estimators in finite sample sizes. Finally, we apply the method proposed to two real world clinical studies: the college student drinking study, and the Improving mood promoting access to collaborative treatment for late life depression' study.