The analysis of dose-response curve from bioassays with quantal response: Deterministic or statistical approaches?

Dose-response relations can be obtained from systems at any structural level of biological matter, from the molecular to the organismic level. There are two types of approaches for analyzing dose-response curves: a deterministic approach, based on the law of mass action, and a statistical approach, based on the assumed probabilities distribution of phenotypic characters. Models based on the law of mass action have been proposed to analyze dose-response relations across the entire range of biological systems. The purpose of this paper is to discuss the principles that determine the dose-response relations. Dose-response curves of simple systems are the result of chemical interactions between reacting molecules, and therefore are supported by the law of mass action. In consequence, the shape of these curves is perfectly sustained by physicochemical features. However, dose-response curves of bioassays with quantal response are not explained by the simple collision of molecules but by phenotypic variations among individuals and can be interpreted as individual tolerances. The expression of tolerance is the result of many genetic and environmental factors and thus can be considered a random variable. In consequence, the shape of its associated dose-response curve has no physicochemical bearings; instead, they are originated from random biological variations. Due to the randomness of tolerance there is no reason to use deterministic equations for its analysis; on the contrary, statistical models are the appropriate tools for analyzing these dose-response relations.