Additive interaction in the presence of a mismeasured outcome.

Misclassification and measurement error are very common in studies of effects of exposures and are often ignored. The problem of exposure misclassification for interaction measures in the context of both multiplicative interaction (1–4) and additive interaction (5) has been discussed previously. Other investigators have discussed problems of outcome misclassification for a single exposure (6, 7). However, little is known about how interaction measures perform when the outcome is misclassified. In the present letter, we consider additive interactions with a mismeasured outcome. All the proofs are given in Web Appendix 1, available at http://aje.oxfordjournals.org/. Let X1 and X2 denote 2 binary exposures and let D denote a binary outcome. Let px1x2 1⁄4 PðD 1⁄4 1jX1 1⁄4 x1;X2 1⁄4 x2Þ. The measure of interaction for risks on the linear additive scale is as follows: