Carotid ultrasound screening for coronary heart disease - Journal of by yaofenji




Carotid ultrasound screening for coronary
heart disease: results based on a meta-analysis
of 18 studies and 44,861 subjects
David S Wald and Jonathan P Bestwick

                                                                                                      J Med Screen 2009;16:147–154
                                                                                                        DOI: 10.1258/jms.2009.009038

                               Background Carotid artery ultrasound is a possible screening test for future coronary heart disease
                               (CHD) events to select individuals for preventive treatment.
                               Objectives To assess the screening performance of carotid artery intima-media thickness (IMT) and
See end of article for
                               carotid plaque in the identification of individuals with CHD.
authors’ affiliations           Methods Meta-analysis of case-control and cohort studies, reporting carotid IMT or plaque in
...................            individuals with and without CHD. Screening performance (detection rates [DRs] for specified false-
Correspondence to: David       positive rates [FPRs]) was assessed from the relative Gaussian distributions of IMT among
S Wald, Wolfson Institute of   individuals with and without CHD and from the proportion of affected and unaffected individuals
Preventive Medicine, Barts     with plaque.
and The London School of
Medicine, Queen Mary
                               Results Eighteen studies, involving 2920 individuals with CHD (mean age range 46 –73 years) and
University of London,          41,941 without (aged 44 –73 years) were included in the meta-analysis. For plaque the DR was 62%
Charterhouse Square,           for an FPR of 30%; likelihood ratio (2.1 [95% CI 1.6–2.4]). For IMT, the DR was 65% for the same
London EC1M 6BQ, UK;           30% FPR (IMT cut-off !0.82 mm); likelihood ratio 2.2 (1.9– 2.5). The results were similar in case-
                               control and cohort studies.
Accepted for publication       Conclusion Neither carotid plaque nor IMT has a CHD screening performance that is sufficiently
14 August 2009
...................            discriminatory between affected and unaffected individuals to be a worthwhile screening test.

INTRODUCTION                                                         METHODS

         arotid artery ultrasound is a non-invasive imaging          Data sources were identified using a search of Medline and
         method used to measure the thickness of the wall            EMBASE databases and a manual search of the citation lists
         of carotid arteries and the presence or absence of          of the relevant publications and reviews. Keywords for the
atherosclerotic plaque. Observational studies have shown             Medline search were carotid ultrasound or carotid intima-
that increased carotid intima-media thickness (IMT) or the           media or carotid plaque and CHD or coronary artery disease
presence of plaque is associated with angiographic coronary          or ischaemic heart disease or myocardial infarction. All
heart disease (CHD) and the risk of coronary death and               studies published in English up until March 2008 were con-
myocardial infarction1,2 raising interest in using such              sidered eligible provided they reported either the carotid
measurements in screening to select individuals for the              ultrasound IMT and the presence or absence of carotid
investigation and treatment of CHD.3,4                               plaque in affected individuals with either a confirmed CHD
  Observational studies have tended to present the risk of           event (death or myocardial infarction) or symptoms of ischae-
CHD as an odds ratio for a higher versus a lower IMT                 mic chest pain (angina) supported by a confirmed coronary
result,3 which demonstrates whether or not there is an               artery stensois of ^50% on a coronary angiogram. Control
association between IMT and disease, but does not permit             subjects were unaffected individuals from the general popu-
a quantitative assessment of carotid ultrasound as a screen-         lation without a history of vascular disease or subjects under-
ing test. There is therefore uncertainty over the value of           going coronary angiography with normal coronary arteries in
carotid ultrasound in screening and whether the measure-             whom either carotid ultrasound IMT and plaque measure-
ment of IMT or plaque or a combination of the two is the             ments were reported. Studies (i) with fewer than 20 affected
more discriminatory variable in screening.                           or unaffected individuals and (ii) with controls who were
  This prompted us to carry out a meta-analysis of case-             patients with ischaemic chest pain and mild coronary artery
control and cohort studies that provided information on              disease (generally ,50% coronary stenosis on coronary
both carotid IMT and plaque in individuals with and                  angiography) were excluded. The initial search generated
without CHD, to estimate the screening performance of                463 potentially relevant studies which reduced to 74 on
these measurements in predicting CHD.                                review of the abstracts and 18 on review of the full                                                     Journal of Medical Screening   2009    Volume 16   Number 3

                               Table1 Studies included in the meta-analysis according to age of participants

                                                                                              Number                      Mean age                Description of

                                                                                              CHD                         CHD
                               First author               % men         Design                affected       Unaffected   affected   Unaffected   Coronary heart disease (CHD)      Intima-media thickness (IMT)    Plaque

Journal of Medical Screening
                               Vrtovec5                   100           Case control           30                   30    46         44           Myocardial infarction             Maximum of left and right       .1.0 mm
                                                                                                                                                                                     common carotid artery†
                               Lorenz                       49          Cohort                227                  4825   50         50           Myocardial infarction             Mean of left and right common   Not measured

                                                                                                                                                                                     carotid artery
                               Cerne7                       85          Case control          100                   70    54         52           Angina and angiographic           Maximum of right common         .2.0 mm
                                                                                                                                                    stenosis .50%                    carotid artery
                               Chambless                    43          Cohort                290            12,551       57         54           Death or myocardial infarction    Mean of multiple measurements   Not measured
                                                                                                                                                                                     from common carotid artery†

Volume 16
                               Geroulakas9                100           Case control           75                   34    58         54           Angina and angiographic           Mean of multiple measurements   Not measured
                                                                                                                                                    stenosis .50%                    from common carotid artery
                               Kablack-                     78          Case control          463                   95    59         56           Angina or myocardial infarction   Mean of multiple measurements   .1.3 mm
                                 Ziembicka10                                                                                                        and angiographic stenosis        from common carotid artery†
                               Hunt11†                      43          Cohort                399            11,976       57         54           Death or myocardial infarction    –                               .1.5 mm

Number 3
                               Alan12                       56          Case control          180                53       59         54           Angina and angiographic           Mean of left and right common   !1.3 mm
                                                                                                                                                    stenosis .50%                     carotid artery
                               Wald13                       75          Case control           55                   45    59         55           Myocardial infarction and         Mean of left and right common   .1.0 mm
                                                                                                                                                    angiographic stenosis .50%        carotid artery
                               Rosvall                      65          Cohort                113                  5050   61         57           Death or myocardial infarction    Mean of left and right common   .1.2 mm
                                                                                                                                                                                      carotid artery
                               Sun15                        56          Case control           78                   69    62         61           Angina and angiographic           Mean of multiple measurements   Not measured
                                                                                                                                                    stenosis .50%                     from common carotid artery
                               Balbirini                    80          Case control          107                   43    64         62           Angina and angiographic           Mean and maximum of left and    .2.5 mm
                                                                                                                                                    stenosis .50%                     right common carotid artery
                               Ebrahim17                    53          Case control          102                  673    66         66           Myocardial infarction             Mean of left and Right Common   !1.2 mm
                                                                                                                                                                                      carotid artery†
                               Kato                         59          Case control           72                   46    67         65           Angina and angiographic           Maximum of left and right       Not measured
                                                                                                                                                    stenosis .50%                     common carotid artery
                               Teragawa19                   63          Case control           56                   25    67         62           Angina and angiographic           Mean of multiple measurements   Not measured
                                                                                                                                                    stenosis .50%                     from common carotid artery
                               Morito                       59          Case control           75                   41    70         65           Angina and angiographic           Mean of left and right common   .1.1 mm
                                                                                                                                                    stenosis .50%                     carotid artery
                               Raso21                       59          Case control           37                   33    71         71           Angina and angiographic           Maximum of left and right       Not measured
                                                                                                                                                    stenosis .50%                     common carotid artery
                               Iglesias                     42          Cohort                194                  2073   72         70           Myocardial infarction             Maximum of left and right       Not measured
                                  del Sol22                                                                                                                                           common carotid artery
                               O’Leary23                    39          Cohort                267                  4209   73         73           Myocardial infarction             Maximum of left and right       Not measured
                                                                                                                                                                                      common carotid artery
                                   Studies also measured IMT in carotid bifurcation and internal carotid artery
                                   Studies by Chambless and Hunt were separate reports from the same ARIC cohort
                                                                                                                                                                                                                                   Wald and Bestwick
Carotid ultrasound screening for coronary heart disease                                                                                                        149

publication5 – 23 (in one cohort study the results on IMT were                                    meta-regression was used to account for possible sources of
published separately from those on plaque).                                                       heterogeneity. STATA (Version 10) was used for all analyses.

STATISTICAL ANALYSIS                                                                              RESULTS
The published studies included in the meta-analysis gener-                                        Table 1 summarizes the characteristics of the 18 studies used
ally reported the arithmetic mean IMT values and standard                                         in the meta-analysis that provided information on carotid
deviation. For each study, the IMT and standard deviation                                         IMT or plaque or both in a total of 2920 CHD-affected indi-
values were log 10 transformed because of the positive                                            viduals and 41,941 unaffected individuals, listed in order of
skew of the IMT distributions, using published formulae                                           increasing age of participants (65% were men). Table 2
for the mean and standard deviation of the log-Gaussian                                           shows the reported IMT results in each study and the pro-
distribution24 (see Statistical Appendix). Probability plots of                                   portion of participants with plaque in affected and unaf-
log-transformed data, from two studies that reported                                              fected individuals. Web Table 2 (
individuals data points, showed a reasonably good fit to a                                         uk/epm/publications/webtables) gives the corresponding
Gaussian distribution.9,13                                                                        log IMT values for each study and the summary weighted
   A summary mean (and standard deviation) IMT was                                                estimates for all studies combined.
calculated for affected and unaffected individuals, weighted                                         Figure 1 shows forest plots of carotid IMT (and 95% CI) in
by 1/standard error2 in affected and unaffected individuals,                                      affected (upper plot) and unaffected individuals (lower plot)
respectively, using a random effects model. Screening                                             for each study, ranked according to age of participant and
performance was estimated from the relative Gaussian distri-                                      for all studies combined. Median IMT values are shown
butions of IMT in affected and unaffected individuals for all                                     (the antilog of the individual and pooled weighted mean
studies combined. IMT is a quantitative variable, so detection                                    log IMT values. The median IMT in affected (mean age, 62
rates (DRs) were estimated at specified false-positive rates                                       years) was 0.92 mm (95% CI 0.83 –1.01) and that in unaf-
(FPRs) and the corresponding IMT cut-offs were determined.                                        fected (mean age, 58 years) was 0.76 mm (0.68 –0.84).
Plaque is a qualitative variable (either present or absent), so a                                 Median IMT in affected individuals was similar in the 12
summary DR (the proportion of unaffected individuals with                                         case-control studies (0.93 mm [0.83– 1.05]) and in the six
plaque) and a summary FPR (the proportion of unaffected                                           cohort studies (0.89 mm [0.73 –1.08]). In unaffected indi-
individuals with plaque) were calculated for all studies,                                         viduals they were also similar, 0.74 mm (0.68 –0.81) and
weighted by 1/standard error2 using a random effects                                              0.8 mm (0.66–0.97), respectively.
model. Heterogeneity was assessed by Cochranes Q-test for                                            Figure 2 shows forest plots of the proportion of CHD-
log mean IMT and plaque in cases and controls and                                                 affected individuals with plaque (the DR) and unaffected

Table 2 Intima-media thickness and plaque in studies of coronary heart disease (affected) and unaffected individuals

                                       Affected                                                                       Unaffected

                                                            IMT (mm)                                % with                          IMT (mm)                 % with
First author                           Number               Mean                  SD                plaque            Number        Mean          SD         plaque

Vrtovec5                                30                  0.80                  0.19              63                    30        0.57          0.11       20
Lorenz6                                227                  0.78Ã                 0.13              –                   4825        0.69Ã         0.12       –
Cerne7                                 100                  1.00                  0.30              50                    70        0.70          0.20         8.6
Hunt11†                                399                  –                     –                 58                11,976        –             –          34
Chambless8†                            290                  0.70                  0.16              –                 12,551        0.63          0.16       –
Geroulakas9                             75                  0.91                  0.18              –                     40        0.71          0.16       –
Alan12                                 180                  0.82                  0.10              37                    53        0.57          0.10       11
Wald13                                  55                  0.91                  0.28              75                    45        0.75          0.18       18
Kablack-Ziembicka10‡                   463                  1.32                  0.28              –                     95        1.01          0.19       –
Rosvall14                              113                  0.84                  0.15§             65                  5050        0.77          0.15§      43
Sun15                                   78                  1.10Ã                 0.40              –                     69        0.90Ã         0.20       –
Balbirini16                            107                  0.89                  0.13              71                    43        0.71          0.18       44
Ebrahim17                              102                  0.84                  0.17              79                   673        0.79          0.18       54
Teragawa19                              56                  1.09                  0.37              –                     25        0.79          0.20       –
Kato18                                  25                  0.99                  0.19              –                     84        0.84          0.16       –
Morito20‡                               75                  0.90                  0.36              –                     41        0.77          0.20       –
Raso21                                  37                  1.10                  0.24              –                     33        0.84          0.23       –
Iglesias del Sol22                     194                  1.17                  0.29              –                   2073        1.03          0.22       –
O’Leary23                              267                  1.10Ã                 0.19              –                   4209        1.01Ã         0.19       –
IMT, intima-media thickness; SD, standard deviation
  Median in place of mean
  Data from ARIC study; IMT reported by Chambless,8 plaque reported by Hunt11
  Kablack-Ziembicka10 and Morito20 specified a plaque cut-off but did not report prevalence in affected and unaffected individuals
  Standard deviation of cases and controls (figures not given separately)
Where SD missing the SD was calculated directly from the proportion of subjects in categories of IMT (see Methods)                                                                                   Journal of Medical Screening      2009    Volume 16   Number 3
150                                                                                                                  Wald and Bestwick

Figure 1 Forest plots of carotid IMT (and 95% CI) in affected (upper plot) and unaffected individuals (lower plot) for each study, ranked
according to age of participant and for all studies combined

individuals with plaque (FPR) in each study together with the          any one study. Meta-regression was used to examine age
weighted summary estimates for all studies combined. The               and other sources of variation between studies such as
overall summary screening performance yielded a DR of                  differences in the methods used to measure IMT (the
62% (95% CI 50–75) for an FPR of 30% (18–39%). There                   mean of multiple IMT measurements was used in 11
were only two cohort studies that reported plaque, limiting            studies and the maximum IMT in 7) and the definition of
the extent to which differences between case-control and               plaque (,2 mm in 8 studies and .2 mm in 2), differences
cohort studies could be examined. The proportion in affected           in study design (case control in 12 studies and cohort in
individuals in case-control studies was 63% (47–77%) and               6), CHD outcome used (death or myocardial infarction in
in cohort studies was 60% (54–66%) and in unaffected indi-             7 studies and angina supported by an angiographic stenosis
viduals, 24% (8–46%) and 38% (30–48%), respectively.                   of .50% in 11) and the proportion of men and women in
   There was heterogeneity in the proportion of affected               each study. With the exception of age, there were no statisti-
and unaffected individuals with plaque (P , 0.001) and in              cally significant effects observed in meta-regression analyses
the median IMT in affected and unaffected individuals                  of IMT or plaque on any of these variables.
between studies (P , 0.001), justifying the use of a                      IMT increased with age by 1.4% per year (95% CI 0.7 –
random effects model in the analysis. Sensitivity analyses             2.1, P , 0.001). In unaffected individuals the increase was
were conducted to examine the influence of individual                   greater than in affected (1.7% versus 1.1%); however, this
studies on the pooled estimates. Each study was removed                difference was not statistically significant (P ¼ 0.372). The
in turn and the analysis repeated on all but the removed               presence of plaque increased by about 1.5 percentage
study. The overall results were not materially affected by             points per year (0.3–2.8, P ¼ 0.018). Again, the increase

Journal of Medical Screening   2009     Volume 16    Number 3                                             
Carotid ultrasound screening for coronary heart disease                                                                            151

Figure 2 Forest plots of the proportion of CHD affected individuals with plaque (detection rate) and unaffected individuals with plaque
(false-positive rate) in each study ranked according to age of participant, together with the weighted summary estimates for all studies
combined. CHD, Coronary heart disease

was greater in unaffected individuals (2 versus 1 percentage          identifying patients with CHD. At an FPR of 30% (the
point), but the difference was not statistically significant           summary value using plaque) the DR for plaque was 62%
(P ¼ 0.359). There was no effect of age on the variance for           and for IMT it was 65% (IMT cut-off !0.82 mm). Both
either measure.                                                       ultrasound variables therefore yield a likelihood ratio of
   Figure 3 shows relative frequency distributions of IMT in          about 2; indicating about a two-fold increase in risk in
affected and unaffected individuals (mean age 59 years).              those with a screen-positive result, compared with an
The DRs are shown for a range of FPRs, together with the              untested population.
IMT cut-offs (mm) that specify these FPRs; DRs of 19%,                  This is the first meta-analysis to provide a quantitative
30% and 47% for FPRs of 5%, 10% and 20%, respectively.                assessment on the value of carotid ultrasound as a screening
   Table 3 gives the screening performance (DR, FPR and the           test for CHD. Previous observational studies and
corresponding likelihood ratios) using plaque and IMT for all         meta-analysis of such studies have focused attention on
studies combined. The IMT-based DR is estimated for the               the association between plaque or IMT and CHD.4 These
summary FPR observed with plaque (30%) to allow a                     generally presented results as a relative risk of CHD for a
direct comparison between IMT and plaque. The screening               very high IMT (say the top fifth of the distribution) com-
performance for the two ultrasound variables was similar.             pared with a very low IMT (the bottom fifth of the
                                                                      distribution).This comparison is useful for demonstrating
                                                                      whether an association is present but not for assessing its
                                                                      value as a screening test, because the groups being compared
The results of this meta-analysis show that carotid IMT and           are mutually exclusive and most people in the middle of the
carotid plaque each have similar screening performance in             distribution, where most cases tend to occur, are not                                                      Journal of Medical Screening   2009     Volume 16     Number 3
152                                                                                                                            Wald and Bestwick

Figure 3 Relative frequency distributions of IMT in affected and unaffected individuals (mean age 59), together with the detection rates and IMT
cut-offs specified by a 5%, 10% and 20% false-positive rate. IMT, intima-media thickness

Table 3 Comparison of screening performance between
                                                                                    considered in the analysis.25 When IMT is examined using
intima-media thickness and plaque from meta-analysis of 18
studies                                                                             overlapping distributions, as in our analysis, the probability
                                                                                    of a positive test result is estimated relative to the whole
                                                  Cut-off (mm)   Likelihood ratio   sample population rather than only those in the tails of
               FPR (%)          DR (%)            (IMT only)     (95% CI)           the distribution. This permits an assessment of the DR for
                                                                                    specified FPRs. It also allows comparison of IMT with
Plaque         30               62                –              2.1 (1.6 – 3.4)    plaque and with other risk factors which are used as screen-
IMT            30               65                0.82           2.2 (1.9 – 2.5)
                                                                                    ing tests for cardiovascular disease. For example, at age 55
IMT, intima-media thickness; DR, detection rate                                     and an FPR of 5%, the DR for IMT in our meta-analysis

Journal of Medical Screening                2009         Volume 16   Number 3                                       
Carotid ultrasound screening for coronary heart disease                                                                                      153

was about 19%, compared with previously published esti-           tests of comparable discrimination (possibly CT calcium
mates of 15% using serum cholesterol,25 13% for diastolic         score31 or measures of arterial stiffness32), then there may be
blood pressure,26 13% for serum homocysteine27 and                a case for screening younger people (about age 45) to select
about 10% for C-reactive protein.28                               individuals for preventive treatment. Further work is needed
   There was a suggestion from the results of our                 to assess this and the screening performance of other such
meta-analysis that screening performance may decline              tests, alone and in combination with carotid ultrasound, to
with increasing age. While we lacked the power to confirm          determine if this would be worthwhile.
this pattern, we cannot exclude the possibility that screening
may be better at younger ages. For plaque, for example, the
estimated DR at age 45 was 41% for an FPR of 12% (likeli-         ...............
                                                                  Authors’ affiliations
hood ratio 3.3) and at age 65 the DR was 72% for an FPR of        David S Wald, MD, MRCP, Consultant Cardiologist and Senior
43% (likelihood ratio 1.6). While a three-fold concentration      Lecturer, Wolfson Institute of Preventive Medicine, Barts and The
in risk in a 45-year old person with a positive carotid ultra-    London School of Medicine, Queen Mary University of London,
sound result may be seen as a worthwhile means of target-         Charterhouse Square, London EC1M 6BQ, UK
                                                                  Jonathan P Bestwick, MSc, Statistician, Wolfson Institute of
ing preventive treatment, the background risk in this age         Preventive Medicine, Barts and The London School of Medicine,
group is relatively low (about 1 in 1000). The effect of          Queen Mary University of London, Charterhouse Square, London
screening would be to identify a group with a risk of 1 in        EC1M 6BQ, UK
300 (3.3/1000) and this would be at the cost of missing
over half of all cases of CHD (DR about 41%). Whatever
the preventive remedy offered, screening is unlikely to be
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     an independent predictor of the presence and severity of coronary artery                               s2 ¼ exp (2m þ 2s2 ) À exp (2m þ s2 ):                                            ð2Þ
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21   Raso F, van Popele NM, Schalekamp DH, van der Cammen TJ.
     Intima-media thickness of the common carotid arteries is related to              Treating equations (1) and (2) as simultaneous equations and solving
     coronary aterosclerosis and left ventricular hypertrophy in older adults.        for m and s gives
     Angiology 2002;53:569 –74
22   Iglesias del Sol A, Bots ML, Grobbee DE, Hofman A, Witteman JCM.                                                        1   m þ s2
     Carotid intima-media thickness at different sites: relation to incident                                            m ¼ À ln                                                              ð3Þ
     myocardial infarction. Eur Heart J 2002;23:934 –40
                                                                                                                             2      m 4

23   O’Leary DH, Polak JF, Krnmal RA, Manolio TA, Burke GL, Wolfson SK.
     Carotid-artery intima and media thickness as a risk factor for myocardial        and
     infarction and stroke in older adults. N Engl J Med 1999;340:14 –22                                                     sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
24   Aitcheson J, Brown JAC. The Lognormal Distribution. USA: Cambridge
                                                                                                                                     m þ s2
     University Press, 1969                                                                                               s ¼ ln                          :                                   ð4Þ
25   Wald NJ, Hackshaw AK, Frost CD. When can a risk factor be used as a                                                                   m2
     worthwhile screening test? BM J 1999;319:1562 – 5
26   Law M, Wald N, Morris J. Lowering blood pressure to prevent myocardial           To convert a natural logarithm scale to a log10 scale, equations (3) and
     infarction and strokes: a new preventive strategy. Health Technol Assess         (4) are divided by ln(10).
     2003;7(No. 31):29 –38                                                                The following example, using data from the paper by Vrtovec et al. 5
27   Wald DS, Law MR, Morris J. The dose-response relation between serum              illustrates the method used for this transformation. The mean IMT was
     homocysteine and cardiovascular disease: implications for treatment and          reported as m ¼ 0.80 mm and standard deviation s ¼ 0.19 mm in
     screening. Eur J Cardiovasc PrevRehabil 2004;11:250 – 3                          affected individuals. From equation (3), the mean on the log10 scale
28   Shah T, Casas JP, Cooper JA, et al. Critical approasial of CRP measurement
                                                                                      is given as
     for the prediction of coronary heart disease events: new data and
     systematic review of 31 prospective cohorts. Int J Epidemiol
     2009;38:217 –31                                                                             À1=2 ln (m2 þ s2 =m4 ) À1=2 ln (0:802 þ 0:192=0:804 )
                                                                                            m¼                         ¼
29   Law M, Morris JK, Wald NJ. Screening for abdominal aortic aneurysms.                               lnð10Þ                      lnð10Þ
     J Med Screen 1994;1:110 –6
                                                                                             ¼ À0:1088
30   Egger M, Davey Smith G, Schneider M, Minder C. Bias in meta-analysis
     detected by a simple, graphical test. BMJ 1997;315:629 –34
31   Arad Y, Goodman KJ, Roth M, Newsteain D, Gurci AD. Coronary                      and from equation (4) the standard deviation on the log10 scale is
     calcification, coronary disease risk factors, C-Reative Protein, and              given as
     atherolsclerotic cardiovascular disease events: the St Francis Heart Study.                                             ffi
                                                                                             pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
     J Am Coll Cardiol 2005;46:158 –65                                                        ln (m2 þ s2 =m2 )                  ln (0:802 þ 0:192=0:802 )
32   Liao D, Arnett D, Tyroler HA, et al. Arterial stiffness and the development of     s¼                                     ¼                                                      ¼ 0:1017:
     hypertension. Hypertension 1999;34:201 –6
                                                                                                     lnð10Þ                                      lnð10Þ

Journal of Medical Screening           2009       Volume 16        Number 3                                                                          

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