Mathematical modeling in environmental health.

Editorial In both recent and forthcoming issues of EHP, an increasing number of papers and news articles feature applications of statistical and mathematical modeling in environmental health. My comments focus on applications of mathematical models, which have become increasingly popular as tools for organizing and conducting the analysis of complex problems, partially because of easy access to sophisticated software and computational power. Risk assessment applications provide a good example where the model serves as a platform for the integration of the fate and transport, exposure, and response data central to risk estimation. Generally, the information needed to undertake model-based analysis is of three sorts (1). The first is the set of causal hypotheses that describe current understanding of how different processes and variables are interrelated. This information provides the structure of the model. Second, simulation models can incorporate independent information on the range of values of the model's parameters, because many parameters of models based on physical, chemical, or biological processes have a clear experimental interpretation. Values of these parameters are often reported in the literature of the various scientific specialties that underpin the integrated analyses common to environmental health. Finally, such structured models can incorporate data on observed patterns of behavior characteristic of the particular system under analysis. Although all this seems straightforward enough, an inherent challenge relates to the relative weight one places on the different types of information contained in these three categories. Mathematics has long been the language of engineering and the physical sciences, where basic physical laws form the foundations of analysis as well as of models studied by computational techniques. Hence, those of us who come from this tradition tend to place high value on the causal linkages implicit in model structure and parameterization. Problems in biology, on the other hand, have been a major motivation for the development of the descriptive and empiric approaches of statistical analysis. In this tradition little emphasis is placed on a priori model structure, and the goal is to summarize the observed data in an efficient and useful manner. Both mathematical and statistical modeling have become common tools in risk assessments. On the mathematical side, the tendency to emphasize structural information in model development leads to large and complex models. Beck et al. (2) have commented that " there is a natural tendency to rely on the complexity of the model as a form of insurance against the …