On summarizing group exposures in risk assessment: is an arithmetic mean or a geometric mean more appropriate?

Since substantial bias can result from assigning some type of mean exposure to a group, risk assessments based on epidemiological data should avoid the grouping of data whenever possible. However, ungrouped data are frequently unavailable, and the question arises as to whether an arithmetic or geometric mean is the most appropriate summary measure of exposure. It is argued in this paper that one should use the type of mean for which the total risk that would result if every member of the population was exposed to the mean level is as close as possible to the actual total population risk. Using this criterion an arithmetic mean is always preferred over a geometric mean whenever the dose response is convex. In each of several data sets examined in this paper for which the dose response was not convex, an arithmetic mean was still preferred based on this criterion.