Exposure-dependent misclassification of exposure in interaction analyses

The objectives of this paper are to analyze the consequences of exposure mi sclassification on effect estimates in interaction analysis, and to develop a mathematical equation for the potentially biased estimate. The main poin t is to identify situations in which misclassification of the first exposur e, dependent on the second exposure hut independent on outcome status, lead s to overestimation or underestimation of the interaction effect. We show t hat misclassification theoretically can cause overestimation of the interac tion effect. Nevertheless, because the categories that yield overestimation due to misclassification are fewer than the categories that yield underest imation, and misclassification in reality mostly is multidimensional (more than one category are biased simultaneously), it is more likely that the ef fect of misclassification is underestimation rather than overestimation. Mi sclassification in the categories that lead to overestimation is compensate d by misclassification in the categories that lead to underestimation. The magnitude of the biased estimate depends on the prevalences of the misclass ified exposure, stratified for the second exposure and the outcome-the lowe r the prevalence, the smaller the bias.