Mediation with a single mediator M, exposure A, outcome Y, and confounders Z.
Let The controlled direct effect expresses the exposure effect that would be realised if the mediator were controlled, i.e., set to a specific level for everyone. Controlled direct effects are relevant quantities when interest lies in the evaluation of an intervention that can shift or fix the mediator across the population. However, the controlled direct effect does not usually lead to the splitting of the total effect in to direct and indirect effect. That is, the total effect minus the controlled direct effect may not have the interpretation of indirect effect in situations where the direct effect is different at different levels of the mediator. Hence, we introduce below two additional quantities that can split the total effect in to direct and indirect effect. They are the natural direct and natural indirect effects.The average natural direct and indirect effects, given a pre-exposure covariates Z, are defined as [The indirect effect 