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

Objectives 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. Methods simulations were conducted under the assumptions that (i) exposure level is assigned to all workers based on the job-specific means from a sample of workers, (ii) exposure level and duration are log-normal, (iii) the true exposure-response model is log-linear for cumulative exposure, (iv) the disease is rare, and (v) the variance of job-specific exposure level increases with its job-specific mean. Results Assignment of job-specific mean exposure levels from a sample of workers causes an upward bias in the estimated exposure-response trend when there is little variance in the duration of exposure but causes a downward bias when duration has a large variance. This bias can be substantial (eg, 30-50%). Conclusions Berkson errors in exposure result in little bias in estimating exposure-response trends when the standard deviation of duration is approximately equal to its mean, which is common in many occupational studies. No bias occurs when the variance of exposure level is constant across jobs, but such conditions are probably uncommon.