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

Abstract

Dose-response relations can be obtained from systems at any structural level of biological matter, fromthe molecular to the organismic level. There are two types of approaches for analyzing dose-responsecurves: a deterministic approach, based on the law of mass action, and a statistical approach, based on theassumed probabilities distribution of phenotypic characters. Models based on the law of mass actionhave been proposed to analyze dose-response relations across the entire range of biological systems. Thepurpose 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 reactingmolecules, and therefore are supported by the law of mass action. In consequence, the shape of thesecurves is perfectly sustained by physicochemical features. However, dose-response curves of bioassayswith quantal response are not explained by the simple collision of molecules but by phenotypicvariations among individuals and can be interpreted as individual tolerances. The expression of toleranceis the result of many genetic and environmental factors and thus can be considered a random variable. Inconsequence, 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 noreason to use deterministic equations for its analysis; on the contrary, statistical models are theappropriate tools for analyzing these dose-response relations.