Abstract
In epidemiological studies we often want to learn about the direct effect of an exposure on an outcome, i.e. the effect that is not relayed by a specific intermediate variable. In the literature, there are two common definitions of direct effects; controlled and natural. When the intermediate variable and the outcome have common causes, neither the controlled nor the natural direct effect is identified. Cai et al. (Biometrics 2007; 64(3):695-701) derived bounds for the controlled direct effect under a set of hierarchical assumptions. In this paper we derive bounds on the natural direct effect under the same assumptions.
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