Interventional Effect Models for Multiple Mediators
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In settings that involve multiple mediators, approaches focusing on fine-grained decompositions of natural (in)direct effects are only valid under strong assumptions. In particular, the assumptions are known to be violated when - as often - the structural dependence between the multiple mediators is unknown. In contrast, interventional (in)direct effects, introduced by VanderWeele et al. (2014), can be identified under much weaker conditions than natural (in)direct effects, but have the drawback of not adding up to the total effect. Vansteelandt and Daniel (2017) adapted their proposal to achieve an exact decomposition of the total effect, and generalized the interventional effects to the multiple mediator setting. In this article, we introduce interventional effect models that allow for simultaneous and parsimonious modeling of the interventional effects when there are multiple mediators. The parameters in the effect models encode the effects of a treatment on an outcome that are mediated by distinct mediators, even when the directions of the causal effects between the mediators are unknown, or when the mediators share hidden common causes. The mediators and outcome can be continuous or noncontinuous. Estimation proceeds via Monte Carlo integration and only requires specifying a joint distribution of the mediators and an outcome model.
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