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Aging and Disease    2014, Vol. 5 Issue (4) : 218-225     DOI: 10.14336/AD.2014.0500218
Estimation of Heterogeneity in Diagnostic Parameters of Age-related Diseases
David Blokh1, Ilia Stambler2, *
1C.D. Technologies Ltd., Israel
2Department of Science, Technology and Society, Bar Ilan University, Ramat Gan, Israel
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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 parameter heterogeneity      Friedman test      Newman-Keuls method      normalized Shannon entropy      diabetes      heart disease      age related disease      aging      system complexity     
Corresponding Authors: Ilia Stambler   
Issue Date: 04 November 2014
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David Blokh
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David Blokh,Ilia Stambler. Estimation of Heterogeneity in Diagnostic Parameters of Age-related Diseases[J]. Aging and Disease, 2014, 5(4): 218-225.
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Plasma glucose concentration1299788103105141958914271
2-Hour serum insulin270140548214212838946476
Diastolic blood pressure86665880645866668248
Body mass index35.123.224.819.441.525.419.628.124.720.4
Table 1.  Sample parameter values for 10 healthy subjects, from the diabetes dataset, aged 21–25
Plasma glucose concentration85267943101
2-Hour serum insulin10825971634
Diastolic blood pressure1062.5842.56691
Body mass index94611072853
Sum of ranks372312.5203025.51323279
Table 2.  Ranked entries of each row of the data array, from the diabetes dataset
Object numberClusterSubjectSum of ranks
1Cluster 1137
2Cluster 2530
8Cluster 3713
Table 3.  Partition of a set of objects, from the diabetes dataset
Number of elements in a cluster1246720
Number of clusters632111
Table 4.  Partition according to clusters, for 53 healthy women aged 21–25, from the diabetes dataset
Number of elements in a cluster1239
Number of clusters5121
Table 5.  Partition according to clusters, for 22 healthy women aged 26–29, from the diabetes dataset
Number of elements in a cluster1234689
Number of clusters2321111
Table 6.  Partition according to clusters, for 41 healthy women aged 30–39, from the diabetes dataset
Number of elements in a cluster1511
Number of clusters111
Table 7.  Partition according to clusters, for 17 healthy subjects aged less than 50 years, from the heart disease dataset
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