Recent developments in causal mediation analysis have offered new notions of direct and indirect effects, that formalize more traditional and informal notions of mediation analysis emanating primarily from the social sciences. The pure or natural direct effect of Robins-Greenland-Pearl quantifies the causal effect of an exposure that is not mediated by a variable on the causal pathway to the outcome, and combines with the natural indirect effect to produce the total causal effect of the exposure. Sufficient conditions for identification of natural direct effects were previously given, that assume certain independencies about potential outcomes, and a rich literature on estimation of natural direct effects has since developed. A common situation in epidemiology is that the mediator is subject to measurement error, in which case, existing techniques for estimating natural direct and indirect effects could be biased and the resulting inferences could be incorrect if measurement error were ignored. In this paper, the authors consider classical measurement error of a continuous mediator. The authors propose a three-stage least-squares regression technique for estimating natural direct effects on the additive scale, that is robust to classical measurement error of the mediator under certain assumptions about the structure of confounding. The robustness property implies that no additional data such as a validation sample, nor replicate measurements of the error prone mediator are needed to recover valid mediation inferences. An important appeal of the three-stage approach is that it is easy to implement using standard software. A simulation study is provided illustrating the finite sample performance of the proposed approach as compared to the prevailing mediation technique, and the new methodology is also shown to apply under a specific form of differential additive measurement error, and to extend to multiplicative effects under a log-linear regression framework.
Tchetgen Tchetgen, Eric J. and Lin, Sheng Hsuan, "Robust Estimation of Pure/Natural Direct Effects with Mediator Measurement Error" (September 2012). COBRA Preprint Series. Working Paper 96.