Many investigators write as if non-differential exposure misclassification inevitably leads to a reduction in the strength of an estimated exposure-disease association. Unfortunately, non-differentiality alone is insufficient to guarantee bias towards the null. Furthermore, because bias refers to the average estimate across study repetitions rather than the result of a single study, bias towards the null is insufficient to guarantee that an observed estimate will be an underestimate. Thus, as noted before, exposure misclassification can spuriously increase the observed strength of an association even when the misclassification process is non-differential and the bias it produced is towards the null. We present additional results on this topic, including a simulation study of how often an observed relative risk is an overestimate of the true relative risk when the bias is towards the null. The frequency of overestimation depends on many factors: the value of the true relative risk, exposure prevalence, baseline (unexposed) risk, misclassification rates, and other factors that influence bias and random error. Non-differentiality of exposure misclassification does not justify claims that the observed estimate must be an underestimate; further conditions must hold to get bias towards the null, and even when they do hold the observed estimate may by chance be an overestimate.
