Consider a study in which the effect of a binary exposure on an outcome operates partly through a binary mediator but measurement of the mediator is nondifferentially misclassified. Suppose that an investigator wishes to estimate the direct and indirect effects of the exposure on the outcome. In this paper, the authors describe a mathematical correspondence between the empirical expressions for the natural direct effect and the effect of exposure among the unexposed standardized by a binary confounder. They then exploit this correspondence to prove that the direction of the bias due to nondifferential measurement error in estimating the natural direct and indirect effects is to overestimate the natural direct effect and underestimate the natural indirect effect.
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