
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 FRAMINGHAMScore (21) is aimed to CHD (coronory
heart disease)events i.e. manifestations of angina pectoris, myocardial infarction and myocardial death. The PROCAMScore (4, 18) points out the risk for all manifestations of myocardial infarction. The ESCScore
(8) and the HEARTScore (10), a softwarebased version of the ESCScore, 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, waisthipratio, stressfactors).
 Other important risk factors are just considered as qualitative parameters (e.g. diabetes mellitus, smoking). These risk factors are defined as existent or
nonexistent 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, hsCRP/high sensitivityCReactive 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 “relativitytheory” 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 FRAMINGHAMScore (published on the Framinghamhomepage), the PROCAM and ESC/HEARTScore 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

3637

38

3940

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 PROCAMscore for healthy male persons
who are not affected with relevant risk factors (LDLcholesterol 3,1 mmol/l, HDLCholesterol 1,4 mmol/l, triglycerides 1,7 mmol/l, systolic
blood pressure 130 mmHg). For women, the ageassociated 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

5,26,2

6,27,3

>7,3

risk multiplicator

1

1,5

1,9

3

LDLcholesterol (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

HDLcholesterol (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

cholesterolHDLratio

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

6,06,5

6,57,0

7,09,0

9,011,0

11,013,0

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

BodyMassIndex (BMI)

< 25

2528

> 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 cholesterolbased risk total cholesterol or LDLcholesterol and HDLcholesterol or CholesterolHDLratio 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
Waisttohipratio / WHR  men

< 0.859

0,8600,909

0,9100,949

0,9500,999

1,0001,039

> 1,04

risk multiplicator

1

1,6

2,3

2,9

3,6

5

Waisttohipratio/ WHR  women

< 0,720

0,7200,759

0,7600,799

0,8000,839

0,8400,879

> 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 Creactive proteine (hsCRP) (mg/l)

< 0,7

0,71,1

1,21,9

2,03,8

3,915,0

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 PROCAMstudy lipoproteine (a) should just be considered when the blood level of LDLcholesterol 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 ESCScore:
 Age: 40 – 60 years  Blood pressure: 130 – 180 mmHg systolic, 80 – 95 mmHg diastolic  Total cholesterol: 6,4 – 9,0 mmol/l  LDLcholesterol: 3,8 – 5,2 mmol/l
 HDLcholesterol: 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/HEARTScore. 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 scorebases 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


hsCRP





2







occasional smoker



1,4



chainsmoker



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 LDLcholesterol  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. INTERHEARTStudy) are taken into account subsidiarily when no data based on prospective studies
yet exist.
According to the PROCAMScore (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 PROCAMScore, 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 PROCAMScore; 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 3065 years. The corresponding risk levels for women
are 0,25fold 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 FRAMINGHAMScore 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 (xaxis: PROCAM risk, yaxis: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 FRAMINGHAMrisk levels corresponding to PROCAMriks.
In low risk constellations according to PROCAM, the average corresponding FRAMIMGHAMrisk is about 3,5fold higher, in moderate
risk constellations about 2,5fold, in high risk constellations about 2,0fold or lower. When PROCAMrisks are higher than 30 %, there
remain no significant differences to the corresponding FRAMINGHAMrisk levels in practice.
Morever, calculated PROCAMrisks can be transformed into the ESC/HEARTScore 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 (xaxis) and ESC risk (yaxis) for high risk countries
PROCAM risk (xaxis) and ESC risk (yaxis) for low risk countries
Based on the PROCAMrisk value P, the corresponding ESC/HEARTscore risk level E can be approximately calculated by linear functions:
E = m x P
For high riskcountries:
 m = 0,2826 (minimum factor)  m = 0,3846 (average factor)  m = 0,5652 (maximum factor).
For low riskcountries:
 m = 0,1136 (minimum factor)  m = 0,2045 (average factor)  m = 0,2955 (maximum factor).
In high riskcountries the risk levels for cardiovascular death are approximately 0,3 – 0,5fold lower, in low riskcountries nearly 0,1 – 0,3fold 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 computerbased 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 PROCAMalgorithm 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 PROCAMScore.
PROCAMrisks can be transformed into corresponding risk levels based on the FRAMINGHAM and ESC/HEARTScore 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 INTERHEARTstudy,
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
(casecontrol 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 casecontrolling INTERHEARTstudy 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 timeprognosis.
When total risk levels are comparatively estimated based on PROCAM, FRAMINGHAM and ESC/HEARTScore, separate risk estimations for all manifestations of CHD
(FRAMINGHAM), myocardial infarction (PROCAM) and cardiovascular death (ESC/HEARTScore) 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 casecontrol 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 DustryVerlag, 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
DustryVerlag, 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. DustryVerlag, 2006 (in German)
Piper, J.: Calculation of cardiovascular risks in primary prevention Congress for research in rehabilitation
Charité, Berlin (22.23. June, 2007)
ChrubasikHausmann,
S., Chrubasik, C. (†), Piper, J., SchulteMönting,
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/smw201514180/
Piper,
J.: Universal estimation of cardiovascular
risk in multirisk constellations  a “relativity
theory” for global risk calculation.
Medical Research Archives (MRA), 2016
http://www.journals.kei.org/index.php/mra/article/view/475/269
Copyright: Joerg Piper, Bad Bertrich, Germany, 2010
