A general approach to the isobolographic method - Panov, Vladimir (Brazilian Journal of Biometrics, 2025)
Strict definitions and formal mathematical constructions are given to represent the main concepts of the isobolographic method as mathematical objects. In particular, a strict definition of zero interaction notion is introduced. The peculiarity of this definition is that this notion appears to depend on the dose-response function of a particular acting agent, whereas it is commonly believed that it is completely determined only by the whole set of acting agents. It is shown that without additional assumptions about the type of dose-response functions, a type of joint action of agents can be different and even opposite depending on the dose-response function of which the notion of zero interaction is considered. The only case when the concept of zero interaction is unambiguously defined and does not depend on the chosen dose-response function is the case of scale equivalence of dose-response functions of all acting agents. A theorem on the representation of the zero-interaction manifold in the case of arbitrary single-factor dose-response functions is proved. Examples of analyzing the joint action of factors using isoboles for a two-factor linear model with a cross term and a quadratic model are considered.