WHO MONICA Project e-publications, No. 20

Estimation of contribution of changes in classical risk factors to trends in coronary-event rates across the WHO MONICA Project populations: methodological appendix to a paper published in the Lancet

February 2000

Kari Kuulasmaa1, Annette Dobson2, Hugh Tunstall-Pedoe3, Stephen Fortmann4, Susana Sans5, Hanna Tolonen1, Alun Evans6, Marco Ferrario7, Jaakko Tuomilehto1 for the WHO MONICA Project8

1 Department of Epidemiology and Health Promotion, National Public Health Institute (KTL), Helsinki, Finland
2 Department of Statistics, University of Newcastle, New South Wales, Australia
3 Cardiovascular Epidemiology Unit, (MONICA Quality Control Centre for Event Registration), University of Dundee, Ninewells Hospital and Medical School, Dundee, Scotland, U.K.
4 Stanford Center for Research in Disease Prevention, Stanford University, USA
5 Institute of Health Studies, Department of Health and Social Security, Barcelona, Spain
6 Department of Epidemiology and Public Health, The Queen's University of Belfast, UK
7 Faculty of Medicine, University of Milan - Bicocca at Monza, Italy
8 Annex: Sites and key personnel of the WHO MONICA Project


© Copyright World Health Organization (WHO) and the WHO MONICA Project investigators 2000. All rights reserved.

Contents

1. Introduction

This document is the methodological appendix to the paper titled "Estimating the contribution of changes in classical risk factors to the trends in coronary event rates in 38 WHO MONICA Project populations" published in the Lancet in 2000 [1]. It covers three topics:

2. Regression analysis

2.1 The regression model

The association between the trends in event rates and trends in risk scores (or in levels of individual risk factors) was calculated using the linear regression model:

reg1.gif (1030 bytes)

where yi's, i = 1,….n, are the trends in event rates in the n populations, xi's are the trends in risk scores, and eps.gif (862 bytes)'s are independent random variables with normal distributions norms.gif (1034 bytes) where the Wi's are quality weights of the populations. Instead of yi and xi we observe

x.gif (976 bytes)

and

y.gif (972 bytes)

where mu.gif (871 bytes) and nu.gif (862 bytes) are independent random variables with distributions normp.gif (982 bytes) and normth.gif (987 bytes) respectively. We consider the terms phi.gif (880 bytes) and theta.gif (886 bytes) to be known, having the values of the variances of the trend estimates. The regression model now becomes:

reg2.gif (1150 bytes)

which can be written as

reg3.gif (1045 bytes)

where the epspr.gif (869 bytes)'s are independent random variables with normal distributions normta.gif (1145 bytes), where tau2.gif (1101 bytes).

The parameters were estimated using an iterative reweighting procedure [2]. The estimation procedure weights the populations properly, but does not correct beta.gif (870 bytes) for the regression dilution caused by the errors mu.gif (871 bytes) in the explanatory variables.

2.2 Percentage of variation explained by the model

To characterize the contribution of the three components of variation for the observed trends in event rates (i.e the Yi's), we define four sums of squares:

For the proportion of the variation in trends in event rates explained by the trends in risk scores, the traditional statistic R2 = SM/TV is misleading because it treats the known variances of the trend estimates as unexplained variation. For example, if the "true" trends in event rates were fully explained by the "true" trends in risk scores, SM/TV would be less than one because of the statistical error in the trend estimates. A more justifiable measure for the proportion of variation explained by the model is SM/(SM+SE), which is the proportion of the variance explained by the model after excluding the contribution of the known variances of trend estimates from the denominator [3].

The correction of the regression dilution bias of the coefficient beta.gif (870 bytes) would not affect the total residual variation, but it would increase the tau1.gif (874 bytes)'s on the expense of Sigma.gif (853 bytes)(c.f. the error term of the regression model in Section 2.1). Therefore correction of the regression bias would also be expected to increase SM/(SM+SE).

3. Age-standardization

In this section we derive the weights for age-standardizing trends in risk factors in the regression analysis.

For both sexes in each population, the trend in risk scores was estimated separately for each age group, and then age-standardized using a weighted mean of the age group-specific trends:

X = (u1X1 + .... + ukXk)/u,

(1)

where

To make the  age-standardized trends in risk factors and event rates comparable, the trends in event rates should ideally be age-standardized in the same way as the trends in risk factor levels [4]. In practice, however, it is preferrable to estimate the trends in event rates from the age-standardized annual rates, because the numbers of events in the young age groups are very small, making the estimation of the trends in the younger age groups unreliable. The age-standardized event rate, for any given year, is:

r = (w1r1 + .... + wkrk)/w,

(2)

where

Let Z1, .... , Zk denote the trends in age group-specific event rates and let Z denote the age-standardized trends using formula (1), i.e. Z = (u1Z1 + .... + ukZk)/u. Also let Y denote the trend in the age-standardized event rates defined in (2). We assume that the trends in event rates are exponential, and Y and the Zj are the change rates, so r = exp(a + Yt) and rj = exp(b+ Zjt) where t denotes time, and therefore

 

Y = r'/r and Zj = rj'/rj,

(3)

where r' and rj' denote the derivatives of the event rates with respect to time (as in reference [1]).

Our aim now is to find a relationship between the two sets of weights, u1, ...., uk and w1, ...., wk, such that age-standardized trends in event rates Y and Z, which were calculated using the two different approaches, are similar. We need to assume that the age group-specific event rates rj are approximately proportional to fixed constants cj ; specifically, that there is a function s of time such that

rj about.gif (844 bytes) cjs for all  j = 1,..,k.

(4)

Note that equality in (4) would not be appropriate because it would imply that the age group-specific trends Zj were all equal. However, the assumption of the approximate equality is feasible for our purpose because any differences in age-specific trends Zj are very small compared with the differences between the age group-specific event rates rj. Assumption (4) implies

r = (w1r1 + .... + wkrk)/w about.gif (844 bytes) s(w1c1 + .... + wkck)/w,

so that

s/w about.gif (844 bytes) r/(w1c1 + .... + wkck).

(5)

Using equations (3), (2), (4) and (5), we obtain

Y = r'/r = (w1r1' + .... + wkrk')/wr = (w1Z1r1 + .... + wkZkrk)/wr

about.gif (844 bytes) (w1Z1c1s + .... + wkZkcks)/wr = s(w1c1Z1 + .... + wkckZk)/wr

about.gif (844 bytes) (w1c1Z1 + .... + wkckZk)/(w1c1 + .... + wkck).

If we define  uj = wjcj, the last expression is equal to Z. Therefore, the two approaches for calculating age-standardized trends are approximately equal if the weights uj and wj are related by uj = wjcj.

In the populations of the WHO MONICA Project, the age group-specific rates for coronary events are, on average, proportional to the coefficients cj specified in Table 1.

Table 1. Values for cj
Age group 35-39 40-44 45-49 50-54 55-59 60-64
Men 1 2 4 7 11 16
Women 1 2 4 8 16 29

The annual event rates were standardized to the world population shown in Table 2 [5].

Table 2. World standard population weights wj
Age group 35-39 40-44 45-49 50-54 55-59 60-64
wj 6 6 6 5 4 4

Multiplying cj and wj of Tables 1 and 2 gives the weights uj for the second approach, as shown in Table 3.

Table 3. Values for uj = wjcj
Age group 35-39 40-44 45-49 50-54 55-59 60-64
Men 6 12 24 35 44 64
Women 6 12 24 40 64 116

When these are summarized to ten-year age groups, they are are similar to the weights 1, 3 and 7 which have been used for age-standardizing case fatality rates in the WHO MONICA Project [6], as shown in Table 4.

Table 4. Comparison of weights
Age group 35-44 45-54 55-64 Total
uj Men 18 (10 %) 59 (32 %) 108 (58 %) 185 (100%)
Women 18 (7 %) 64 (24 %) 180 (69 %) 262 (100%)
MONICA event weights 1  (9 %) 3 (27 %) 7 (64 %) 11 (100%)

Therefore, weights of 1, 3 and 7 (in Table 4) were used for age-standardizing the trends in risk scores and the individual risk factors for the regression analyses against trends in age-standardized event rates (calculated using weights wj in Table 2).

4. Overall quality score

The overall quality score, which was used for weighting the data in the regression analyses in reference [1], has values between zero and two. If the score is two, no problems were identified in the quality of the data for a population, whereas a score of zero indicates major concern about the data quality. The overall quality score was derived from the quality scores of the individual data components. The values of the overall quality score and its components are shown in Table A1. The definition of the overall quality score is included in the following description of the columns of Table A1:

References

  1. Kuulasmaa K, Tunstall-Pedoe H, Dobson A, Fortmann S, Sans S, Tolonen H, Evans A, Ferrario M, Tuomilehto J for the WHO MONICA Project. Estimation of contribution of changes in classic risk factors to trends in coronary-event rates across the WHO MONICA Project populations. Lancet 2000:355;675-87.
  2. Kuulasmaa K, Dobson A for the WHO MONICA Project. Statistical issues related to following populations rather than individuals over time. Bulletin of the International Statistical Institute: Proceedings of the 51st Session; 1997 Aug 18-26; Istanbul, Turkey.Voorburg: International Statistical Institute; 1997. Book 1; 295-8. Also available from: URL:http://www.thl.fi/publications/monica/isi97/isi97.htm.
  3. Pocock SJ, Cook DG, Beresford SAA. Regression of area mortality rates on explanatory variables: what weighting is appropriate? Appl Statist 1981:30;286-95.
  4. Rosenbaum PR, Rubin DB. Difficulties with regression analysis of age-adjusted rates. Biometrics 1984;40:437-43.
  5. Waterhouse J, Muir CS, Correa P, Powell J, eds. Cancer incidence in five continents. Lyon: IARC, 1976: 456.
  6. Tunstall-Pedoe H, Kuulasmaa K, Amouyel P, Arveiler D, Rajakangas A-M, Pajak A. for WHO MONICA Project. Myocardial infarction and coronary deaths in the World Health Organization MONICA Project. Registration procedures, event rates and case fatality in 38 populations from 21 countries in 4 continents. Circulation 1994;90:583-612.
  7. Moltchanov V, Kuulasmaa K, Torppa J for the WHO MONICA Project. Quality assessment of demographic data in the WHO MONICA Project. (April 1999). Available from: URL:http://www.thl.fi/publications/monica/demoqa/demoqa.htm, URN:NBN:fi-fe19991073.
  8. Mähönen M, Tolonen H, Kuulasmaa K, Tunstall-Pedoe H, Amouyel P for the WHO MONICA Project. Quality assessment of coronary event registration data in the WHO MONICA Project. (January 1999). Available from: URL:http://www.thl.fi/publications/monica/coreqa/coreqa.htm, URN:NBN:fi-fe19991072.
  9. Wolf H, Kuulasmaa K, Tolonen H, Ruokokoski E for the WHO MONICA Project. Participation rates, quality of sampling frames and sampling fractions in the MONICA surveys. (September 1998). Available from: URL:http://www.thl.fi/publications/monica/nonres/nonres.htm, URN:NBN:fi-fe19991076.
  10. Molarius A, Kuulasmaa K, Evans A, McCrum E, Tolonen H for the WHO MONICA Project. Quality assessment of data on smoking behaviour in the WHO MONICA Project. (February 1999). Available from: URL:http://www.thl.fi/publications/monica/smoking/qa30.htm, URN:NBN:fi-fe19991077.
  11. Kuulasmaa K, Hense HW, Tolonen H for theWHO MONICA Project. Quality assessment of data on blood pressure in the WHO MONICA Project. (May 1998). Available from: URL:http://www.thl.fi/publications/monica/bp/bpqa.htm, URN:NBN:fi-fe19991082.
  12. Ferrario M, Kuulasmaa K, Grafnetter D, Moltchanov V for the WHO MONICA Project. Quality assessment of total cholesterol measurements in the WHO MONICA Project. (April 1999). Available from: URL: http://www.thl.fi/publications/monica/tchol/tcholqa.htm, URN:NBN:fi-fe19991083.
  13. Molarius A, Kuulasmaa K, Sans S for the WHO MONICA Project. Quality assessment of weight and height measurements in the WHO MONICA Project. (May 1998). Available from: URL:http://www.thl.fi/publications/monica/bmi/bmiqa20.htm,   URN:NBN:fi-fe19991079.

Acknowledgements

The MONICA Centres are funded predominantly by regional and national governments, research councils, and research charities. Coordination is the responsibility of the World Health Organization (WHO), assisted by local fund raising for congresses and workshops. WHO also supports the MONICA Data Centre (MDC) in Helsinki. Not covered by this general description is the ongoing generous support of the MDC by the National Public Health Institute of Finland, and a contribution to WHO from the National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland, USA for support of the MDC. The completion of the MONICA Project is generously assisted through a Concerted Action Grant from the European Community. Likewise appreciated are grants from ASTRA Hässle AB, Sweden, Hoechst AG, Germany, Hoffmann-La Roche AG, Switzerland, the Institut de Recherches Internationales Servier (IRIS), France, and Merck & Co. Inc., New Jersey, USA, to support data analysis and preparation of publications.