Non-differential misclassification of exposure always leads to an underestimate of risk: an incorrect conclusion.

In most epidemiological surveys, there will be some errors of measurement or classification of exposure. For example, for a binary exposure variable, some exposed subjects may be classified as non-exposed, and some nonexposed subjects may be classified as exposed. Non-differential misclassification of exposure is present if, irrespective of disease, all exposed and non-exposed subjects have the same probability of being misclassified (these two probabilities may be different, one must be not zero). It is now commonplace to find statements in epidemiological textbooks, journal articles, and teaching materials to the effect that nondifferential misclassification of exposure always leads to an underestimate of risk. Rothman, for example, states that "such misclassification can introduce a bias, but the bias is always in the direction of underestimating the effect",' and Checkoway et al state "nondifferential misclassification of exposure will bias the effect estimate toward the null value".2 This contradicts our expectation that studies may overestimate as well as underestimate effects, and we therefore tested these ideas by computer simulations relevant to study settings. Each simulation (trial or study) involved a population comprising 5000 exposed and 5000 non-exposed subjects. Exposed subjects each had the same probability r, of becoming diseased within a short time period; for nonexposed subjects the probability was r2 (rate ratio = relative risk = rl/r2). Also, exposed subjects each had the probability P, of being misclassified; for non-exposed subjects the probability was P2. The simulation was performed by a computer program in which a random process was used to classify the outcome of each probability. Two point estimates of relative risk were provided by each simulation: the apparent (or observed) relative risk based on disease events in populations for which misclassification is present, and the actual relative risk based on disease events in the populations if all subjects were correctly classified. Both these estimates were compared, in turn, with the underlying (or true) relative risk set within the computer program. For each set of initial values for the four parameters rl, r2, P, and P2, 5000 independent simulations were carried out (table 1). Columns 1-7 summarise the input data and columns 8-10 summarise the results or output. The first three sets of simulations investigate the effects of misclassification in exposed or non-exposed subjects only, as opposed to being present with equal probability in both groups. Sets 4-6 show the effects of increasing the probability of misclassification, although disease risk remains constant. Sets 7-9 show the effects of increasing the probability of disease, although misclassification probability remains constant. Column 8 shows that if misclassification had not been present, the simulated studies would have overestimated the relative risk about as often as they underestimated it. Column 9 shows the percentage of simulated studies, with misclassification present, which provided an apparent relative risk > 1.5. These results indicate that studies affected by non-differential misclassification of exposure will underestimate risks more often than they overestimate risks and that this effect becomes more pronounced as the extent of misclassification is increased (sets 4-6) or when the baseline risk of disease is increased (sets 7-9). Interpretation is assisted by examination of