The heterogeneity of parameters is a ubiquitous biological phenomenon, with critical implications for biological systems functioning in normal and diseased states. We developed a method to estimate the level of objects set heterogeneity with reference to particular parameters and applied it to type II diabetes and heart disease, as examples of age-related systemic dysfunctions. The Friedman test was used to establish the existence of heterogeneity. The Newman-Keuls multiple comparison method was used to determine clusters. The normalized Shannon entropy was used to provide the quantitative evaluation of heterogeneity. There was obtained an estimate for the heterogeneity of the diagnostic parameters in healthy subjects, as well as in heart disease and type II diabetes patients, which was strongly related to their age. With aging, as with the diseases, the level of heterogeneity (entropy) was reduced, indicating a formal analogy between these phenomena. The similarity of the patterns in aging and disease suggested a kind of "early aging" of the diseased subjects, or alternatively a "disease-like" aging process, with reference to these particular parameters. The proposed method and its validation on the chronic age-related disease samples may support a way toward a formal mathematical relation between aging and chronic diseases and a formal definition of aging and disease, as determined by particular heterogeneity (entropy) changes.
Keywords: Friedman test; Newman-Keuls method; age related disease; aging; diabetes; heart disease; normalized Shannon entropy; parameter heterogeneity; system complexity.