Analytic results on the bias due to nondifferential misclassification of a binary mediator

Abstract

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.

Figure 1.

Relations among a binary exposure A, an outcome Y, and a binary mediator M. M′ is a nondifferentially misclassified measure of M.

Figure 2.

The effect of a binary exposure A on an outcome Y, confounded by C. C′ is a nondifferentially misclassified measure of C.

Figure 3.

Bias of the observed adjusted natural direct effect (NDE) as a function of sensitivity and specificity for two different hypothetical scenarios. The first scenario (top) has a true NDE of 1.75, a true natural indirect effect (NIE) of 1.75, and a total effect (TE) of 3.5. The second scenario (bottom) has a true NDE of 3.25, a true NIE of −0.75, and a TE of 2.5. The single solid line represents the true NDE and the double solid line the TE. The dashed line represents the observed adjusted NDE as a function of sensitivity when specificity is fixed at 0.9. The dotted line represents the observed adjusted NDE as a function of specificity when sensitivity is fixed at 0.9.