Exposure misclassification: bias in category specific Poisson regression coefficients

In epidemiologic studies of the association between exposure and disease, misclassification of exposure is common and known to induce bias in the effect estimates. The nature of the bias is difficult to foretell. For this purpose, we present a simple method to assess the bias in Poisson regression coefficients for a categorical exposure variable subject to misclassification. We derive expressions for the category specific coefficients from the regression on the error-prone exposure (naive coefficients) in terms of the coefficients from the regression on the true exposure (true coefficients). These expressions are similar for crude and adjusted models, if we assume that the covariates are measured without error and that it is independence between the misclassification probabilities and covariate values. We find that the bias in the naive coefficient for one category of the exposure variable depends on all true category specific coefficients weighted by misclassification probabilities. On the other hand, misclassification of an exposure variable does not induce bias in the estimates of the coefficients of the (perfectly measured) covariates. Similarities with linear regression models are pointed out. For selected scenarios of true exposure-disease associations and selected patterns of misclassification, we illustrate the inconsistency in naive Poisson regression coefficients and show that it can be difficult to intuitively characterize the nature of the bias. Both the magnitude and the direction of the bias may vary between categories of an exposure variable.