When Measurement Errors Correlate with Truth

Most of the literature on the effect of nondifferential misclassification and errors in variables either addresses binary exposure variables or discusses continuous variables in the classical error model, where the error is assumed to be uncorrelated with the true value. In both of these situations, an imperfectly measured exposure always attenuates the relation, at least in the univariate setting. Furthermore, measuring a confounder with error independent of the exposure, even while measuring the exposure of interest perfectly, leads to partial control of the confounding. For many variables measured in epidemiology, particularly those based on self-report, however, errors are often correlated with the true value, and these rules may not apply. Epidemiologists need to be wary of deviations from the classical error model, since poor measurement might occasionally explain a positive finding even when the error does not differ by disease status.