Computing and using rural versus urban measures in statistical applications

We discuss various measures of urban-versus-rural character, particularly when used for adjustment of epidemiologic or environmental data. For example, because urban-versus-rural differences may conceal more subtle effects, such a measure may be used to adjust for urban-versus-rural differences in county mortality rates, so that underlying geographic or demographic patterns may be revealed. Urban-versus-rural measures frequently have been defined as categorical variables given by ranges of (i) total population; (ii) population density; and (iii) percent urban population. When regions are counties in the United States, such measures are easily obtained, but their relation to one's concept of urban-versus-rural character is often weak, as illustrated with several examples. A class of alternative measures is proposed. These measures are functions of the individual populations of places (usually minor civil divisions) in the county: (1) population of the largest place; (2) root sum of squared populations of three largest places; and (3) root sum of squared populations of all places. Two members of this class already have shown promise in statistical analyses of lung cancer mortality rates, namely (1) and (2). Using U.S. county data, we demonstrate that (3) adds only very marginal information to the measure, and that (2), which we call urbanicity, is useful for purposes of adjustment in studies of ecological exploration.