Simple similar action and independent joint action - two similar models for the joint effects of toxicants applied as mixtures

Abstract

Two commonly referenced modes of joint action, simple similar joint action (SSA) and independent joint action (IJA), in their simplest forms, are assumed to describe very different types of action by toxicants. SSA is assumed to describe toxicants that act similarly and at the same sites of action, and IJA to describe toxicants that act differently or at different sites of action. It is demonstrated in this paper that maintaining both models and their common variations is not practical for the development of larger and more inclusive models. It is shown that the ranges of responses that can be described by common simple variations of both models are very similar. It is also argued that the two models in their simplest forms are not alternative hypotheses since they are expressions about different variables. Moreover, since toxicants often cannot be uniquely described as acting similarly, dissimilarly or at only one site of action, it is argued that only one of the above models and its expanded forms should be used to describe the results of experiments with a diversity of toxicants. Variations of the probit response model are believed to be more desirable because they resemble a model used to make predictions about the effects of complex mixtures, namely the toxic units model.