  The use of causal mediation analysis to evaluate the pathways by which an
exposure affects an outcome is widespread in the social and biomedical
sciences. Recent advances in this area have established formal conditions for
identification and estimation of natural direct and indirect effects. However,
these conditions typically involve stringent no unmeasured confounding
assumptions and that the mediator has been measured without error. These
assumptions may fail to hold in practice where mediation methods are often
applied. The goal of this paper is two-fold. First, we show that the natural
indirect effect can in fact be identified in the presence of unmeasured
exposure-outcome confounding provided there is no additive interaction between
the mediator and unmeasured confounder(s). Second, we introduce a new estimator
of the natural indirect effect that is robust to both classical measurement
error of the mediator and unmeasured confounding of both exposure-outcome and
mediator-outcome relations under certain no interaction assumptions. We provide
formal proofs and a simulation study to demonstrate our results.
