A note on correlated errors in exposure and outcome in logistic regression

In cross-sectional studies or studies based on questionnaires, errors in exposures and misclassification of health status may be related. The reason may be that some subjects tend to over- or underreport both exposure and disease. The author investigated the effects of such dependent misclassification from a threshold-model point of view, in that an assumption was made of an underlying linear relation between a continuous exposure and response, both measured with error, and where these errors are correlated. Allowance is also made for covariates measured without error. This approach enables the derivation of explicit expressions for bias in the estimated association between exposure and outcome in different situations. It is shown that, dependent on the true effect of the exposure, the effect of the errors can be both an over- and an underestimation of the true relation. In addition, a study design from which the true effect can be consistently estimated is also provided.