Generalization of independent response model for toxic mixtures

Interaction between toxic compounds has long been known to researchers. Attempts to model this interaction have been based on two basic paradigms--termed additivity and independence (1, 2). Previous models based on these assumptions focused on measuring the interaction between the compounds and then classifying the type of interaction as synergism, antagonism, additivity or independence (3, 4). The aim of this work is to present a generalization of the independent action hypothesis that is quantitatively capable of describing deviations regardless of the underlying single component dose response models. The mathematical framework of copulas is employed. This approach is then tested against data sets with both human health and ecological risk applications.