Predicting mixture toxicity with models of additivity

Researchers in numerous fields (e.g., pharmacology, entomology, toxicology, and epidemiology) have attempted to model the joint action of chemicals using simple formulas based only on knowledge of individual chemical toxicity or pharmacological effect (i.e., dose-response relationships). Collectively, these formulas are referred to as "additivity models," and they are based on concepts of additivity that include dose addition, independent action, integrated addition, and effect summation. In toxicology, additivity-based predictions are often compared to observed mixture data to assess the presence and magnitude of interactions (greater-than-additive or less-than-additive) among chemicals. These models can also be used to estimate the toxicity of a defined mixture for comparison to the observed toxicity of a related, but more complex, mixture. Alternatively, additivity models have been used to explore mechanisms of joint action. In general, the steps for investigating joint toxicity using additivity models include (1) deciding on which additivity model(s) to apply (e.g., dose addition, independent action, or both), (2) collecting dose-response data on individual chemicals and the mixture, (3) incorporating individual chemical data in an additivity model to generate predictions, and (4) comparing predicted to observed mixture responses. Many of the additivity models have a long and sometimes controversial history. This chapter provides background on several of the common additivity models, illustrates their application with examples, and discusses their advantages and limitations.