Embedded cluster modelling: a novel quantitative structure-activity relationship method for generating elliptic models of biological activity

The aim of this study was to devise a statistical method for deriving prediction models (PMs) from embedded data sets. These are toxicological or pharmacological data sets in which the chemicals are divided into two classes (toxic/non-toxic or active/inactive), and in which one class of chemicals (typically, the toxic or active one) is found to cluster along one or more variables (e.g. physicochemical descriptors), forming an "embedded cluster" surrounded by the "diffuse cluster" of chemicals in the other class (typically, the non-toxic or inactive one). The statistical significance of embedded clusters can be assessed by the method of cluster significance analysis (CSA), but this does not provide a means of discriminating between embedded and diffuse chemicals. In this study, we have therefore developed a method called "embedded cluster modelling" (ECM). If ECM is applied to two or more variables, the output of the method is an elliptic boundary in two or more dimensions. The equation of the resulting ellipse can be used to define a PM, since toxic (or active) chemicals are predicted to lie inside the elliptic boundary, whereas non-toxic (or inactive) chemicals are predicted to lie outside the elliptic boundary. The combined use of CSA and ECM is illustrated by their application to an eye irritation data set. The resulting PM can be used to classify certain types of chemicals as eye irritants or non-irritants.