Analysis of interaction for mixtures of agents using the linear isobole

The linear isobole that is commonly used as a reference for the study of interaction is derived from the interaction of an agent with itself. It is shown that the general use of the linear isobole in the study of the combined effects of mixtures of agents implies interaction between the agents whether the dose-effect curves of the agents are the same or not. It is difficult to generalize the interaction between two doses of the same agent to the interaction between two doses of different agents with different action mechanisms without the use of a mechanistic model. Predictions using non-interaction defined as independent action are generally different from those using linear isobole. A simple mechanistic framework based on the concept of common intermediate lesions is introduced in this paper to relate these two methods used for the analysis of synergism and antagonism. In this framework of lesion development, two agents that have no common intermediate lesion in their action will be non-interactive (referred to as independent action). When the two agents share a common intermediate, it is shown that the combined effect will follow the linear isobole (referred to as common action). This simple framework of analysis is applicable to the general study of interaction between two agents with different types of dose-effect curves.