In this paper, we develop models of bias in estimates of exposure-disease associations for epidemiological studies that use group- and individual-based exposure assessments. In a study that uses a group-based exposure assessment, individuals are grouped according to shared attributes, such as job title or work area, and assigned an exposure score, usually the mean of some concentration measurements made on samples drawn from the group. We considered bias in the estimation of exposure effects in the context of both linear and logistic regression disease models, and the classical measurement error in the exposure model. To understand group-based exposure assessment, we introduced a quasi-Berkson error structure that can be justified with a moderate number of exposure measurements from each group. In the quasi-Berkson error structure, the true value is equal to the observed one plus error, and the error is not independent of the observed value. The bias in estimates with individual-based assessment depends on all variance components in the exposure model and is smaller when the between-group and between-subject variances are large. In group-based exposure assessment, group means can be assumed to be either fixed or random effects. Regardless of this assumption, the behavior of estimates is similar: the estimates of regression coefficients were less attenuated with a large sample size used to estimate group means, when between-subject variability was small and the spread between group means was large. However, if groups are considered to be random effects, bias is present, even with large number of measurements from each group. This does not occur when group effects are treated as fixed. We illustrate these models in analyses of the associations between exposure to magnetic fields and cancer mortality among electric utility workers and respiratory symptoms due to carbon black.