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APPENDIX B A Model Illustrating Synergism The practical significance of synergism might be considered in a simple mathematical function based on exposure and magnitude of effect. Nearly all the data available on interactions come from observations based on high experimental or therapeutic doses. Drinking water standards are predicated on low-dose exposures, conditions under which the synergism data might not be duplicated. Although empirical data are lacking, some formal statistical models of the impact of joint exposure suggest that, as the dose (and the consequent effect) is reduced, the contribution of interaction to total toxicity or action is disproportionately attenuated. A simple mathematical model should help to make clear how this might happen. This model is intended solely to be illustrative. The subcommittee does not advocate the unquestioned use of this model, nor does it suggest that it necessarily reflects the type of response to exposure to a mixture. Suppose that the magnitudes of toxicity can be described by Equation T= Bo + B1X! + B2x2 + BI2XLX2, (1) where T is average toxicity, Bo is background, BY is relative effect of agent 1, B2 is relative effect of agent 2, By is "interaction" effect, and x~ and x2 are concentrations of agents 1 and 2, respectively. Consider the following two exposure patterns: High: x~ = 5, x2 = 10 Low: x~ = 0.5, x2 = 1.0. 175
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176 DRINKING WATER AND HEALTH Assume that Be = 10, BY = 7, B2 = 5, and BE = 0.3. Then, the total effect at a high dose with an interaction would be 110 and without an interaction would be 95. At a lower dose, total toxicity with an interaction would be 18.65 and without an interaction would be 18.5. Thus, at high doses, the interaction makes an important contribution (about 15%) to the toxicity. At low doses, the interaction contribution is only 0.8%.
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