Evaluating quantitative formulas for dose-response assessment of chemical mixtures

Risk assessment formulas are often distinguished from dose-response models by being rough but necessary. The evaluation of these rough formulas is described here, using the example of mixture risk assessment. Two conditions make the dose-response part of mixture risk assessment difficult, lack of data on mixture dose-response relationships, and the need to address risk from combinations of chemicals because of public demands and statutory requirements. Consequently, the U.S. Environmental Protection Agency has developed methods for carrying out quantitative dose-response assessment for chemical mixtures that require information only on the toxicity of single chemicals and of chemical pair interactions. These formulas are based on plausible ideas and default parameters but minimal supporting data on whole mixtures. Because of this lack of mixture data, the usual evaluation of accuracy (predicted vs. observed) cannot be performed. Two approaches to the evaluation of such formulas are to consider fundamental biological concepts that support the quantitative formulas (e.g., toxicologic similarity) and to determine how well the proposed method performs under simplifying constraints (e.g., as the toxicologic interactions disappear). These ideas are illustrated using dose addition and two weight-of-evidence formulas for incorporating toxicologic interactions.