Exposure-dependent misclassification of exposure in interaction analyses

The objectives of this paper are to analyze the consequences of exposure misclassification on effect estimates in interaction analysis, and to develop a mathematical equation for the potentially biased estimate. The main point is to identify situations in which misclassification of the first exposure, dependent on the second exposure but independent on outcome status, leads to overestimation or underestimation of the interaction effect. We show that misclassification theoretically can cause overestimation of the interaction effect. Nevertheless, because the categories that yield overestimation due to misclassification are fewer than the categories that yield underestimation, and misclassification in reality mostly is multidimensional (more than one category are biased simultaneously), it is more likely that the effect of misclassification is underestimation rather than overestimation. Misclassification in the categories that lead to overestimation is compensated by misclassification in the categories that lead to underestimation. The magnitude of the biased estimate depends on the prevalences of the misclassified exposure, stratified for the second exposure and the outcome-the lower the prevalence, the smaller the bias.