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Object and Aims

By considering various published studies and comments on their data this investigation gives a review of all risk factors which could be taken into account as relevant modulators of the cardiovascular risks in individual patients. Moreover, established cardiovascular risk scores were systematically evaluated.

Based on this, several mathematical models were developed to calculate resulting total risks in respect of all thinkable constellations of relevant risk factors.

By these mathematical means, the coincidence of risk factors and the relativities of risk factors and risk scores can be described. Moreover, various risk constellations can be compared with each other with regard to the resulting total risk

In cooperation with the University of Freiburg, Germany (Prof. Dr. Sigrun Chrubasik) and the cantonal hospital of Luzern, Switzerland,  the mathematical models developed were evaluated on a Swiss population survey; results were published in Swiss Medical Weekly.

 

Introduction

At the present, various scores exist for estimating the cardiac or cardiovascular risk of individuals based on their cardiovascular risk factors. The FRAMINGHAM-Score (21) is aimed to CHD (coronory heart disease)-events i.e. manifestations of angina pectoris, myocardial infarction and myocardial death. The PROCAM-Score (4, 18) points out the risk for all manifestations of myocardial infarction. The ESC-Score (8) and the HEART-Score (10), a software-based version of the ESC-Score, are different from the scores mentioned above, because these scores only calculate the risk for cardiovascular death, i.e. death caused by myocardial infarction, stroke, rupture of aorta etc.. All these scores have several limitations:

  • Only a few risk factors are considered quantitatively (age, lipid levels, blood pressure).
  • Various important risk factors are not taken into account (e.g. obesity, waist-hip-ratio, stress-factors).
  • Other important risk factors are just considered as qualitative parameters (e.g. diabetes mellitus, smoking). These risk factors are defined as existent or non-existent i.e. there are only two categories “yes” and “no”. Quantitative aspects of these risk factors like the daily number of cigarettes smoked or the blood glucose level or Hb A1c are not considered.
  • Several “newer” risk factors, which are nowadays in the focus of interest, are not considered (e.g. Lp(a)/Lipoprotein A, hs-CRP/high sensitivity-C-Reactive Protein, homocysteine, fibrinogen, microalbuminuria, chronic chlamydia pneumoniae infection).

Thus, it does not seem to be astonishing, that just about 50 or 60 percent of all patients with myocardial infarctions belong to a high risk group according to these scores, whereas 40 or 50 percent of these patients are associated with a moderate or low risk when the scores are used for risk calculations.

In view of these limitations a new algorithm has been developed with regard to all important “traditional” and “newer” risk factors. Most of these are elaborated as quantitative factors, so that special aspects related to the situation of the individual patient can be considered (e.g. blood levels of metabolic parameters, intensity of smoking). The mathematical models, presented here, describe the interactions of these factors and the relations between the various risk scores mentioned above. These models might be regarded as a first step to an universally appliable “relativity-theory” of risk faktors and risk scores.

 

Method and results

By intensive investigation of several published studies and published comments to their results, all quantitative aspects of the risk factors known at the present were compiled. Moreover, the current versions of the cholesterol based FRAMINGHAM-Score (published on the Framingham-homepage),  the PROCAM- and ESC-/HEART-Score were used and compared with each other based on various traditionally accepted risk factor constellations associated with low, moderate and high risk. Forthermore, corresponding single risk levels listed in the tables were multiplied by each other and compared with the score based results. By these means, the influences of single risk factors and their combinations were calculated systematically with regard to their quantitative values.

With regard to “old” / “traditional” risk the following risk factors or risk multiplicators were considered:

age (years)

35

36-37

38

39-40

41

42

43

44

45

46

47

48

49

50

Basal risik (%)

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

1,2

1,4

1,5

1,7

1,9

2,1

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

2,3

2,5

2,8

3,1

3,4

3,8

4,2

4,6

5,1

5,7

6,3

6,9

7,7

8,5

9,3

The basal risk values associated with age shown in this table were calculated according to the PROCAM-score for healthy male persons who are not affected with relevant risk factors (LDL-cholesterol 3,1 mmol/l, HDL-Cholesterol 1,4 mmol/l, triglycerides 1,7 mmol/l, systolic blood pressure 130 mmHg). For women, the age-associated basal risks are lower (circa a quarter) – as suggested by the Procam study group. The respective basal risk associated with age can be multiplied with additional existing “traditional” risk factors as follows:

total cholesterol (mmol/l)

< 5,2

5,2-6,2

6,2-7,3

>7,3

risk multiplicator

1

1,5

1,9

3

LDL-cholesterol (mmol/l)

3,1

3,6

4,1

4,7

5,2

5,7

6,2

risik multiplicator

1

1,3

1,8

2,3

3

3,8

5

HDL-cholesterol (mmol/l)

1,4

1,3

1,2

1,0

0,9

0,8

0,6

risik multiplikator

1

1,3

1,4

1,6

1,9

2,1

2,4

cholesterol-HDL-ratio

3,5

4

4,5

5

5,5

6

6,5

7

7,5

8

8,5

risik multiplikator

1

1,3

1,45

1,65

2,3

2,65

3,3

4

5,3

6

9,3

triglycerides (mmol/l)

1,1

2,3

3,4

4,5

risik multiplikator

1

1,2

1,4

1,6

systolic blood pressure  (mm Hg)

130

140

150

160

170

180

190

200

210

220

risk multiplicator

1

1,2

1,3

1,4

1,5

1,6

2

2,2

2,3

2,5

diastolic blood pressure (mmHg)

80

85

90

95

100

105

110

risik multiplicator

0,7

1

1,4

1,8

2,2

3

4

smoking (number of cigaretts per day)

< 10

20

30

40

> 50

risk multiplicator for myocardial infarction

1,5

2

2,5

3

4

risk multiplicator for cancer

4

7

20

30

40

HbA1c

6,0-6,5

6,5-7,0

7,0-9,0

9,0-11,0

11,0-13,0

risk multiplicator for macroangiopathy (CHD)

1

1,25

1,9

2,5

3,1

risk multiplicator for mikroangiopathy (kidney, retina)

1

2

6

13

25

Body-Mass-Index (BMI)

< 25

25-28

> 28

>30

>32

risk multiplikator

1

1,5

2

3

4

familial clustering / aggregation

no

yes

risk multiplicator

1

1,5



Annotations:
For calculations of the cholesterol-based risk total cholesterol or LDL-cholesterol and HDL-cholesterol or Cholesterol-HDL-ratio should be used.
In patients with hypertension the risk multiplicators for systolic or diastolic blood pressure should be used.

With regard to “newer” risk the following risk factors can be considered

Waist-to-hip-ratio / WHR - men

< 0.859

0,860-0,909

0,910-0,949

0,950-0,999

1,000-1,039

> 1,04

risk multiplicator

1

1,6

2,3

2,9

3,6

5

Waist-to-hip-ratio/ WHR - women

< 0,720

0,720-0,759

0,760-0,799

0,800-0,839

0,840-0,879

> 0,88

risk multiplicator

1

1,6

2,3

2,9

3,6

5

waist circumference - men (cm)

> 94

> 102

waist circumference - women (cm)

> 80

> 88

risk multiplicator

1,5 - 2,5

3 - 8

lipoproteine (a) (mg/l)

< 200

>200

risk multiplicator

1

2

high sensitivity C-reactive proteine (hs-CRP) (mg/l)

< 0,7

0,7-1,1

1,2-1,9

2,0-3,8

3,9-15,0

risk multiplicator

1

1,2

1,4

1,7

2,2

homocysteine (micromol/l)

< 10

12 bis 13

15

17 bis 18

> 20

risk multiplicator

1

1,5

2

3

4

fibrinogen (factor I)

normal blood level

increased blood level

risk multiplicator

1

1,5

chronic chlamydia pneumoniae infection

no

yes

risk multiplicator

1

2,6

psychosocial stress

low

much

risk multiplicator

1

2,7



Annotations:
For calculations of risk associated with abdominal fat deposition the WHR or waist circumference should be used. In cases with obesity the multiplicators for BMI (cf. tab. 1), WHR or waist circumference should be used.
According to the PROCAM-study lipoproteine (a) should just be considered when the blood level of LDL-cholesterol is higher than 3,37 mmol/l.


According to the INTERHEART Study three “bonus factors” (= “protective factors”) can be considered as follows:

bonus factors

fruits / vegetables

sportive activity

moderate alcohol

risk multiplikator

0,7

0,85

0,9


The following traditionally accepted risk constellations and ranges were used for elaborating the mathematical tools and their adjustment to the PROCAM-, FRAMINGHAM- and ESC-Score:

 - Age: 40 – 60 years
 - Blood pressure: 130 – 180 mmHg systolic, 80 – 95 mmHg diastolic
 - Total cholesterol: 6,4 – 9,0 mmol/l
 - LDL-cholesterol: 3,8 – 5,2 mmol/l
 - HDL-cholesterol: 0,7 – 1,4 mmol/l
 - Triglyceride: 1,7 – 2,9 mmol/l

 - Optional additional risks: smoking, diabetes mellitus, familial clustering.

Based on these risk factors and risk ranges, several exemplary cases were created with various risk factor combinations. For all these cases comparative risk calculations were carried out, using the PROCAM-, FRAMINGHAM- and ESC-/HEART-Score. Moreover, the otherwise published corresponding risk multiplicators, listed in the tables, were multiplied by each other to compare the results of simple risk multiplications with the results of score-bases risk calculations.

Based on these comparative calculations, an algorithm was elaboratedted to estimate the resulting total risk also in cases with a lot of existing risk factors.

All mathematical tools were developed based on traditional risk factors and their accepted scores. In respect to these risk factors the evidence of these tools should be comparable with the evidence of the risk scores, the mathematical calculations are based on.

For several risk factors, the following fixed numeric values of defined risks were published by several authors:

 

Procam

Framingham

Interheart

Rifai & Ridker

Clearfield

smoking

1,7

3

2,87

 

 

diabetes mellitus

1,5

1,5

2,37

 

 

familial clustering

1,5

 

 

 

 

hypertension

 

 

1,91

 

 

dyslipidemia

 

 

3,25

 

 

abdominal fat deposition

 

 

1,19

 

 

stress

 

 

2,67

 

 

sportive activity

 

 

0,86

 

 

alcohol (moderate)

 

 

0,91

 

 

fruits and vegetables

 

 

0,7

 

 

lipoproteine (a)

 

 

 

1,4

 

homocystein

 

 

 

1,8

 

hs-CRP

 

 

 

 

2

 

 

 

 

 

 

occasional smoker

 

 

1,4

 

 

chain-smoker

 

 

9

 

 

smoking and metabolic syndrome

 

 

69

 

 

According to the findings of the respective authors, all these risk factors can be regarded as being independent of each other. Based on the hypothesis that the “newer” risk factors might combine themselves to their resulting risk in a similar manner as the “traditional” risk factors , all mathematical tools which were elaborated based on traditional risk constellations might also be used for risk estimations in cases affected with new risk factors.

The following risk factors were not separately considered to avoid potential overestimations:

 - Apolipoprotein A 1 and B because of their correlation to the HDL- and LDL-cholesterol
 - Left ventricular hypertrophy because of its correlation to hypertension
 - Type A- person because of the correlation to psychosocial stress.

When prospective studies exist, which describe the numeric influences of cardiovascular risk factors (e.g. PROCAM- and FRAMINGHAM -study), the results of these studies were first considered. On the other hand, several new risk and bonus factors are not yet investigated by prospective studies. In these cases the results of published case control studies (e.g. INTERHEART-Study) are taken into account subsidiarily when no data based on prospective studies yet exist.

According to the PROCAM-Score (4,18) patients should devided into three categories of individual risk:

 - Low risk: total risk lower than 10%
 - Moderate risk: total risk between 10% and 20%
 - High risk: total risk higher than 20%.

When “traditional” risk factor values presented in the tables are multiplied by each other, the results of multiplication are approximately identical with the corresponding total risk according to the PROCAM-Score, when the product is lower than 30 %.

In other cases, when the existing risk faktors are multiplied to their product x, the total risk f(x) can be estimated by a hyperbolic tangens function as follows: f(x) = 100 tanh (0,008x) [%] .

This formula is adjusted to the PROCAM-Score; it describes the corresponding regression graph and defines the rik for myocardial infarction based on a period of 10 years, calculated for male individuals aged from 30-65 years. The corresponding risk levels for women are 0,25-fold lower according to the suggestions of the PROCAM Study group. The higher the number of risk factors or the product of risk factor multiplications, the lower is the contribution of the single risk factor to the resulting total risk.

The results of these calculations can be transformed into the FRAMINGHAM-Score to estimate the higher risk levels for all manifestations of coronary heart disease.

Based on the Procam risk value P, the corresponding FRAMINGHAM risk level FR can be approximately calculated by a conversion factor F:

According to my own findings, the FRAMINGHAM risk range corresponding with a well defined PROCAM risk can be described and estimated based on the following graphs (x-axis: PROCAM risk, y-axis:conversing factor):

 

Graph A (exponent n = 0,8) and graph B (exponent n = 0,5) correspond with the minimal (A) and maximal (B) conversing factor; both graphs are suitable for estimating the range of FRAMINGHAM-risk levels corresponding to PROCAM-riks.

In low risk constellations according to PROCAM, the average corresponding FRAMIMGHAM-risk is about 3,5-fold higher, in moderate risk constellations about 2,5-fold, in high risk constellations about 2,0-fold or lower. When PROCAM-risks are higher than 30 %, there remain no significant differences to the corresponding FRAMINGHAM-risk levels in practice.

Morever, calculated PROCAM-risks can be transformed into the ESC-/HEART-Score to estimate the corresponding lower risks for cardiovascular death, excluding surviviors. These calculations can be carried out separately for countries with high and low risk:

PROCAM risk (x-axis) and ESC risk (y-axis) for high risk countries


PROCAM risk (x-axis) and ESC risk (y-axis) for low risk countries
 

Based on the PROCAM-risk value P, the corresponding ESC-/HEART-score risk level E can be approximately calculated by linear functions:

E = m x P

For high risk-countries:

 - m = 0,2826 (minimum factor)
 - m = 0,3846 (average factor)
 - m = 0,5652 (maximum factor).

For low risk-countries:

 - m = 0,1136 (minimum factor)
 - m = 0,2045 (average factor)
 - m = 0,2955 (maximum factor).

In high risk-countries the risk levels for cardiovascular death are approximately 0,3 – 0,5-fold lower, in low risk-countries nearly 0,1 – 0,3-fold lower than the corresponding risk levels for myocardial infarction.

 

Conclusions for risk calculations in practice

Firstly the risk can be calculated on the basis of age, increased lipid levels and hypertension. These calculations can be carried out by multiplying the risk values compiled in the presented tables or by using the established risk scores including existing computer-based programs.

In cases of smoking and diabetes the etablished scores can be used when calculations based on constant or fixed risk values seem to be adequate. For other calculations with regard to the individual blood levels of HB A1c or the number of smoked cigarettes the tabular listed data should be preferred.

Additional risks resulting from obesity or increased abdominal fat deposition can be estimated by using the values listed in the tables. Moreover, risks resulting from familial clustering can be calculated using the PROCAM-algorithm or the fixed multiplicators according to the tables.

In this way, the total effects of “traditional” risk factors can be evaluated.

On the other hand, influences of the “newer” risk factors can be calculated in a separate step based on their specific multiplicators. These factors can probably be multiplied with each other, too. This way, further individuals with significant risk should be recognized which could not be identified by the conventional risk scores.

When the resulting products of risk factor multiplications are higher than 30%, the regression graph according to the  hyperbolic tangens function can be used to estimate realistic total risk levels adjusted to the PROCAM-Score.

PROCAM-risks can be transformed into corresponding risk levels based on the FRAMINGHAM- and ESC-/HEART-Score as described above. These transformations might probably be carried out in all potential risk factor constellations, also in cases with multiple newer risk factors.

For general risk calculations based on average risk levels independently of individual cases fixed published multiplicators can also be used.

In this way, many existing risk constellations can be calculated which are not taken into account by the established scores.

 

Discussion

Several studies, especially the INTERHEART-study, have demonstrated that myocardial infarctions result from a cluster of various risk factors. The usual risk scores, developed many years ago, based on prospective studies, are not suitable for calculating the cardiovascular risk in all cases with relevant risk constellations. Thus, about 50 % of all patients with myocardial infarction belong to populations with a moderate or low risk according to these scores. In such cases other risk factors are probably dominant, which are not taken into account by the established scores.

Therefore, the methods presented were elaborated to calculate the total risk of individual patients by using specific numeric modulators with regard to all relevant “traditional” and “newer” risk factors.

These methods were evaluated based on traditional risks which are considered by the established risk scores, too, based on the results of prospective studies. Thus, the elaborated algorithms and the current scores could be compared. Nevertheless, the presented formulas and regression graphs should probably be utilizable for universal calculations in all potential risk constellations, also including “new” risk factors which are not yet investigated by prospective studies.

With respect to method, it should be said, that it is not unproblematic to create mathematical calculations based both on prospective and case -control studies. Both types of studies have their characteristic potential bias, especially selection bias (prospective studies) and memory bias (case-control study).

On the other hand, there is no other way at present to establish mathematical models for global risk estimations with regard to all known risk factors, because only a few risk factors are investigated by prospective studies, as yet. Moreover, it could be considered that the results of the case-controlling INTERHEART-study are not drastically different from the corresponding results of prospective studies shown, when those risk factors are taken into account which are investigated both by prospective and case control studies.

When using the presented tables and mathematical models physicians could calculate the total risks of their individual patients in a simple manner within a few minutes, based on their anamnestic and diagnostic parameters with regard to all new aspects of risks associated with the results of the current cardiovascular research.

Via realistic risk estimations potential over- and undertreatment in patients with cardiovascular risks could be avoided, so that strategies of cardiovascular prevention could be aimed at those individuals who might benefit in a significant manner and improve their long time-prognosis.

When total risk levels are comparatively estimated based on PROCAM-, FRAMINGHAM- and ESC-/HEART-Score, separate risk estimations for all manifestations of CHD (FRAMINGHAM), myocardial infarction (PROCAM) and cardiovascular death (ESC-/HEART-Score) can be carried out. By these means, the prognostic weights of various risk constallations can be evaluated and compared with special regard to their specific potential complications. Moreover, these scores can be compared with each other on a mathematical basis.

The relations between the various risk scores, demonstrated in the elaborated regression graphs and their corresponding mathematical functions are congruent with pathophysiological and epidemiological facts. Based on a definite period, e.g. 10 years, in each population the number of individuals with all clinical manifestations of CHD is higher than the number of patients with myocardial infarctions, and the number of patients with myocardial infarctions is higher than the number of cardiovascular deaths. Moreover, the higher the total individual risk level, the lower the numeric differences are of all CHD manifestations, myocardial infarctions and cases with cardiovascular death based on a period of several years. Therefore, different results of risk calculations dependent on these risk scores should not be regarded as inconsistent. 

In is desirable that future scientific projects, especially new prospective studies are aimed to the “newer” risk factors mentioned above, so that the established scores might be expanded including all relevant “newer” modulators. In this way, the relevance of these scores should be improved. By prospective studies, which should consider a maximal number of defined risk factors, some numeric risk values which can be presented only based on case-control studies nowadays, could be corrected in the future, if necessary. Also, the evidence of the mathematical models, described above, should be checked this way by multivariate analysis.

Epidemiological researchers might use the presented mathematical tools for comparative risk analyses based on the data of large populations. In this way, the elaborated modulating factors and formulas might be adjusted or modified in the future.

Thus, epidemiological research might clarify in the future, if the presented mathematical algorithms indeed describe a law of nature which is valid in all cases of cardiovascular risk factors and their combinations.

 

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Publications:

Piper, J.: Calculation of cardiovascular risks in primary prevention
Part 1: Potentials and limitations of the estabilshed risk scores
Präv.-Rehab. 18, No 1/2006, 1 – 7
Dustry-Verlag, 2006 (in German)

Piper, J.: Calculation of cardiovascular risks in primary prevention
Part 2: New aspects for global estimations of individual risks
Präv.-Rehab. 18, No 1/2006, 8 – 21
Dustry-Verlag, 2006 (in German)

Piper, J.: Calculation of cardiovascular risks in primary prevention
Teil 3: Mathematial models about the relativity of risk factors and risk scores.
Präv.-Rehab. 18, No 1/2006, 22 – 28.
Dustry-Verlag, 2006 (in German)

Piper, J.: Calculation of cardiovascular risks in primary prevention
Congress for research in rehabilitation
Charité, Berlin (22.-23. June, 2007)

Chrubasik-Hausmann, S., Chrubasik, C. (†), Piper, J., Schulte-Mönting, J,, Erne, P.:
Impact of Risk Factors on Cardiovascular Risk: a Perspective on Risk Estimation in a Swiss Population.
Swiss Med Wkly, 2015
http://www.smw.ch/content/smw-2015-14180/

Piper, J.: Universal estimation of cardiovascular risk in multi-risk constellations - a “relativity theory” for global risk calculation.
Medical Research Archives (MRA), 2016
http://www.journals.ke-i.org/index.php/mra/article/view/475/269

Copyright: Joerg Piper, Bad Bertrich, Germany, 2010

 

[Introduction]
[Luminance Contrast]
[Relief Phase Contrast]
[Aperture Reduction Phase Contrast]
[Aperture Reduction Darkfield]
[Digital Phase Contrast]
[Digital Photomicrography and Analysis]
[Cytometry in Reflexion Contrast]
[Capillaroscopy]
[Video-Endoscopy]
[Calculation of Cardiovascular Risk]
[Behavioral Risk Management]
[Efficiency in Rehabilitation]
[Diagnostics in Rehabilitation]
[Complementary Medicine]
[Publications]
[Curriculum vitae]
[University of Oradea]
[U.N.E. Brussels]
[Journals of optics and microscopy]
[Optical Society of America]