Dose addition and the isobole method as approaches for predicting the cumulative effect of non-interacting chemicals: A critical evaluation

Abstract

The prediction of the effect of cumulative exposure to similarly acting chemicals is commonly done by dose addition, such as in the relative potency factor approach. This can only be done under the assumption of zero interaction between the chemicals. The related, but not equivalent, isobole method is the most common criterion to judge whether interactions between similarly acting chemicals have taken place in a mixture experiment. Many who apply this latter method assume that it is applicable to any combination of substances, regardless of the shape of the dose-response curves of the individual substances or their underlying mechanism of action. Proponents commonly refer to the work of Berenbaum, who claimed to have proven the general applicability of the isobole method based on zero interaction. In this article, we argue that his argumentation is not generally valid. We further demonstrate that the isobole method, just like dose addition, has limited applicability. Using a physiologically based mathematical model, we provide a theoretical example of a combination of chemicals with zero interaction where the isobole method would result in the decision that they do interact. We discuss the implications for research focusing on detecting or defining interactions, and for the prediction of effects from combined exposures assuming zero interaction.

Keywords::

• Antagonism
• cumulative risk
• mechanistic model
• mixture
• relative potency factors
• synergy

Acknowledgments

This research was sponsored by the EU 6th Framework Program Integrated Project SAFE FOODS (EU Contract Food-CT-2004-506446).

Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.