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Aging and Disease    2015, Vol. 6 Issue (3) : 196-207     DOI: 10.14336/AD.2014.0623
Original Article |
Information Theoretical Analysis of Aging as a Risk Factor for Heart Disease
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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We estimate the weight of various risk factors in heart disease, and the particular weight of age as a risk factor, individually and combined with other factors. To establish the weights we use the information theoretical measure of normalized mutual information that permits determining both individual and combined correlation of diagnostic parameters with the disease status. The present information theoretical methodology takes into account the non-linear correlations between the diagnostic parameters, as well as their non-linear changes with age. Thus it may be better suited to analyze complex biological aging systems than statistical measures that only estimate linear relations. We show that individual parameters, including age, often show little correlation with heart disease. Yet in combination, the correlation improves dramatically. For diagnostic parameters specific for heart disease the increase in the correlative capacity thanks to the combination of diagnostic parameters, is less pronounced than for the less specific parameters. Age shows the highest influence on the presence of disease among the non-specific parameters and the combination of age with other diagnostic parameters substantially improves the correlation with the disease status. Hence age is considered as a primary “metamarker” of aging-related heart disease, whose addition can improve diagnostic capabilities. In the future, this methodology may contribute to the development of a system of biomarkers for the assessment of biological/physiological age, its influence on disease status, and its modifications by therapeutic interventions.

Keywords biomarkers of aging      biomarkers of disease      system aging      normalized mutual information      in silico assessment of anti-aging interventions     
Corresponding Authors: Ilia Stambler     E-mail:
Just Accepted Date: 25 November 2014   Online First Date: 23 November 2014    Issue Date: 22 May 2015
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David Blokh
Ilia Stambler
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David Blokh,Ilia Stambler. Information Theoretical Analysis of Aging as a Risk Factor for Heart Disease[J]. A&D, 2015, 6(3): 196-207.
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Parameter 1 (X1) Parameter 2 (X2) … Parameter n (Xn) Disease
Subject 1 x(1,1) x(1,2) ... x(1,n) y(1)
Subject 2 x(2,1) x(2,2) ... x(2,n) y(2)
... ... ... ... ...
Subject m x(m,1) x(m,2) ... x(m,n) y(m)
Table 1  The presentation form of the sample dataset
Parameters Hungary Va Long Beach Cleveland
P1 age 0.01902 0.02389 0.03124
P3 cp 0.15316 0.03541 0.12281
P4 trestbps 0.01392 0.02105 0.00786
P5 chol 0.02352 0.01895 0.00564
P6 fbs 0.01749 0.00543 0.01104
P7 restecg 0.01699 0.02103 0.02505
P8 thalach 0.04772 0.00933 0.05168
P9 exang 0.14928 0.04466 0.07769
P10 oldpeak 0.15251 0.03931 0.07685
Table 2  Values of Normalized Mutual Information (C)
Parameters Hungary Va Long Beach Cleveland Sum of ranks
P1 age 4 6 5 15
P3 cp 9 7 9 25
P4 trestbps 1 5 2 8
P5 chol 5 3 1 9
P6 fbs 3 1 3 7
P7 restecg 2 4 4 10
P8 thalach 6 2 6 14
P9 exang 7 9 8 24
P10 oldpeak 8 8 7 23
Table 3  Parameter ranks
No. Clusters Parameters Sum of ranks
1 Cluster 1 P3 cp 25
2 P9 exang 24
3 P10 oldpeak 23
4 Cluster 2 P1 age 15
5 P8 thalach 14
6 Cluster 3 P7 restecg 10
7 P4 trestbps 9
8 P5 chol 8
9 P6 fbs 7
Table 4  Parameters partition
No. Parameters Values of normalizedmutual information (C)
1 P13 thal 0.1316
2 P12 ca 0.13083
3 P3 cp 0.12281
4 P9 exang 0.07769
5 P10 oldpeak 0.07685
6 P11 slope 0.07549
7 P8 thalach 0.05168
8 P2 sex 0.03164
9 P1 age 0.03124
10 P7 restecg 0.02505
11 P6 fbs 0.01104
12 P4 trestbps 0.00786
13 P5 chol 0.00564
Table 5  Influence of single parameters
No. Parameters Values of normalized mutual information (C)
1 P1, P12 ca 0.18501
2 P1, P13 thal 0.17928
3 P1, P3 cp 0.17886
4 P1, P9 exang 0.11853
5 P1, P11 slope 0.11404
6 P1, P8 thalach 0.09757
7 P1, P10 oldpeak 0.09735
8 P1, P2 sex 0.09135
9 P1, P7 restecg 0.06918
10 P1, P5 chol 0.06582
11 P1, P6 fbs 0.05269
12 P1, P4 trestbps 0.03981
Table 6  Combined influence of age (P1) with other parameters
No. Parameters Values of normalizedmutual information (C)
1 P12 ca, P13 thal 0.27686
2 P3 cp, P9 exang 0.1726
3 P10 oldpeak, P11 slope 0.1174
4 P7 restecg, P8thalach 0.07135
5 P4trestbps, P8thalach 0.06878
6 P5 chol,P8 thalach 0.06877
7 P6 fbs,P8 thalach 0.06405
8 P5 chol,P7 restecg 0.05368
9 P2 sex, P5 chol 0.05067
10 P4 trestbps,P7 restecg 0.04209
11 P6 fbs,P7 restecg 0.04082
12 P4 trestbps,P6 fbs 0.02443
13 P5 chol,P6 fbs 0.02298
14 P4 trestbps,P5 chol 0.02157
Table 7  Influence of several double combined parameters on the disease status
No. Parameters Values of normalized mutual information (C)
1 P1 age, P12 ca, P13 thal 0.3753
2 P1 age, P3 cp, P12 ca 0.36317
3 P1 age, P11 slope, P12 ca 0.3503
4 P1 age, P2 sex, P12 ca 0.28037
5 P1 age, P5 chol, P12 ca 0.2764
6 P1 age, P7 restecg, P12 ca 0.27107
7 P1 age, P7 restecg, P13 thal 0.26664
8 P1 age, P2 sex, P3 cp 0.26048
9 P1 age, P3 cp, P5 chol 0.2516
10 P1 age, P5 chol, P11 slope 0.21026
11 P1 age, P2 sex, P11 slope 0.20168
12 P1 age, P2 sex, P9 exang 0.19274
13 P1 age, P5 chol, P9 exang 0.18908
14 P1 age, P8 thalach, P11 slope 0.18687
15 P1 age, P2 sex, P5 chol 0.15166
Table 8  Influence of triple combined parameters
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