Biases in estimating the effect of cumulative exposure in log-linear models when estimated exposure levels are assigned

Exposure-response trends in occupational studies of chronic disease are often modeled via log-linear models with cumulative exposure as the metric of interest. Exposure levels for most subjects are often unknown, but can be estimated by assigning known job-specific mean exposure levels from a sample of workers to all workers. Such assignment results in (nondifferential) measurement error of the Berkson type, which does not bias the estimate of exposure effect in linear models but can result in substantial bias in log-linear models with dichotomous outcomes. This bias was explored in estimated exposure-response trends using cumulative exposure.