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Statistical Theory and Methods

  1. Richard C. Hertzberg

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vae059

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Hertzberg, R. C. 2006. Extrapolation. Encyclopedia of Environmetrics. 2.

Author Information

  1. United States Environmental Protection Agency, GA, USA

Publication History

  1. Published Online: 15 SEP 2006


Quantitative extrapolation refers to a process where inferences about data-poor scenarios are developed from studies of data-rich scenarios. For dose–response relationships in environmental risk assessment, several different kinds of extrapolation are used in order to accommodate the variety of available information and risk assessment goals. Examples of such extrapolation include estimating human health risk at low doses from rodent toxicology data at high doses, or estimating ecosystem response at a given ambient pollution concentration from laboratory studies of individual animal or plant species at similar concentrations. The examples discussed in this article are for human health risk assessment but most of the principles apply to ecological risk assessment as well. These examples include low-dose extrapolation of cancer response (extending a fitted function below the range of the data), simple scaling methods (e.g. allometric interspecies extrapolation), biomathematical models (e.g. physiologically-based pharmacokinetic models), and quantitative formulas for estimating mixture response (e.g. modifying dose addition to account for synergism).