Using the odds against the null hypothesis to evaluate study outcomes when exposure is misclassified

Non-differential misclassification of exposure variables is common in environmental epidemiology. In a 2 x 2 table a range of 0%-50% misclassified observations is considered. 50% misclassification eliminates any possible observed difference between cases and non-cases. Such misclassification biases the odds ratio toward the null. It also affects study power (1-β), although the usual power calculations do not take misclassification into account. When a statistically significant result is found, it is usual to ignore the study's reduced power to detect the decreased odds ratio attributable to misclassification. The importance of this reduced power is illustrated by considering 50% misclassification where the power to detect a difference is zero and any statistically significant result has to be an α error. More generally, the probability that a “statistically significant” result is an α error increases from 0.05 to 1.0 as the extent of misclassification goes from 0% to 50%. If one considers a study as analogous to a diagnostic test that is intended to distinguish between the null hypothesis and the alternate hypothesis (H1) (analogous to disease absent and disease present, respectively), study power becomes sensitivity and α error becomes the false positive rate. The posterior odds in favor of H1 (which is closely related to positive predictive value) is proportional to (1-β)/α. This relationship can be used to estimate sample size increases and/or the smaller α level that are needed to maintain unchanged posterior odds in the face of increasing misclassification.