The use of geometric and arithmetic mean exposures in occupational epidemiology

In constructing quantitative measures of exposure for the study of chronic occupational disease, researchers have generally used a cumulative exposure calculated as the sum of the products of period-specific exposure concentrations and the time each individual spent in each exposure category. There has been some disagreement and lack of clarity about the use of the geometric or arithmetic mean of exposure for this calculation. This paper explores the difference in the use of the two measures and defines a relative bias introduced with the geometric vs. the arithmetic mean. The magnitude of the bias is calculated in two linear models of possible exposure-response relationships. The theoretical basis for the choice of one mean over the other is then explored. It is suggested that when adopting a linear exposure response model, the arithmetic mean is the more appropriate measure. In other models, such as a linear-log (outcome is proportional to the logarithm of exposure) model, the geometric mean would be more appropriate.