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 notice
• Document identification:
  • WHO MONICA Project e-publications (ISSN 2242-1246), No. 20
  • URL:http://www.thl.fi/publications/monica/earwig/appendix.htm
  • URN:NBN:fi-fe19991356

Contents

• 1. Introduction
• 2. Regression analysis
• 3. Age-standardization
• 4. Overall quality score
• References
• Acknowledgements
• Specific tables
  • Table A1. Overall quality score and its components
• Annex: Sites and key personnel of contributing MONICA Centres

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:

• brief description of the regression analysis and the output statistics used in the paper;
• justification for the age-standardization used for calculating risk factor trends for the regression analysis;
• derivation of the quality score which was used to weight the populations in the regression analysis.

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:

where y_i's, i = 1,….n, are the trends in event rates in the n populations, x_i's are the trends in risk scores, and 's are independent random variables with normal distributions where the W_i's are quality weights of the populations. Instead of y_i and x_i we observe

and

where and are independent random variables with distributions and respectively. We consider the terms and to be known, having the values of the variances of the trend estimates. The regression model now becomes:

which can be written as

where the 's are independent random variables with normal distributions , where .

The parameters were estimated using an iterative reweighting procedure [2]. The estimation procedure weights the populations properly, but does not correct for the regression dilution caused by the errors 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 Y_i's), we define four sums of squares:

• is the sum of squares for the variation explained by the model;
• is the sum of squares for the variation explained by the known variances of the trend estimates;
• is the sum of squares of the regression error term, where n-k is the residual degrees of freedom of the weighted regression (k = 2 for the regression analysis with one explanatory variable, as described above);
• is the total sum of squares. (Note that usually TV < SM + ST + SE due to the individual observations which happen to be nearer to the regression line than suggested by the variances of the trend estimates, i.e the 's.)

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 would not affect the total residual variation, but it would increase the 's on the expense of (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:

where

• j = 1,....,k denotes the age groups;
• X is the age-standardized trend in risk scores;
• X_j are the age group-specific trends in risk scores;
• u_j are the age-standardization weights; and
• u = u₁ + .... + u_k.

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:

where

• r is the age-standardized event rate;
• r_j are the age group-specific event rates;
• w_j are the age-standardization weights; and
• w = w₁ + .... + w_k.

Let Z₁, .... , Z_k denote the trends in age group-specific event rates and let Z denote the age-standardized trends using formula (1), i.e. Z = (u₁Z₁ + .... + u_kZ_k)/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 Z_j are the change rates, so r = exp(a + Yt) and r_j = exp(b_j + Z_jt) where t denotes time, and therefore

where r' and r_j' 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, ...., u_k and w₁, ...., w_k, 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 r_j are approximately proportional to fixed constants c_j ; specifically, that there is a function s of time such that

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

r = (w₁r₁ + .... + w_kr_k)/w s(w₁c₁ + .... + w_kc_k)/w,

so that

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

Y = r'/r = (w₁r₁' + .... + w_kr_k')/wr = (w₁Z₁r₁ + .... + w_kZ_kr_k)/wr

(w₁Z₁c₁s + .... + w_kZ_kc_ks)/wr = s(w₁c₁Z₁ + .... + w_kc_kZ_k)/wr

(w₁c₁Z₁ + .... + w_kc_kZ_k)/(w₁c₁ + .... + w_kc_k).

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

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

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

Multiplying c_j and w_j of Tables 1 and 2 gives the weights u_j for the second approach, as shown in Table 3.

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.

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 w_j 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:

• Population: The abbreviation of the population name, as described in Table 1 of reference [1]. The lower case letter at the end of the abbreviation (a, b etc.) identifies the exact definition of the population, and has been described in the MONICA quality assessment reports [7-13].
• Event trends: Quality items related to the trends in the coronary event rates.
  • Dem: Square root of two times the Summary score of quality of the population demographic data [Table 6 of reference 7]. In the cases where the population is a combination of several reporting units, the mean of the scores of the contributing reporting units was taken.
  • Event: The Summary score for coronary event trends quality [8]
  • Event trends score: Geometric mean of (Dem+0.2)/1.1 and Event. (Note: 0.2 is added to Dem so that it cannot make the geometric mean zero regardless of the value of Event).
• Risk factor trends: Quality items related to the trends in the risk factors. Even though three surveys were considered for most of the populations, the quality score is based on the initial and final survey only. The middle survey has a relatively small influence in the estimates of the linear trends. Furthermore, for the two populations where the quality of the middle survey was much lower than the quality of the initial and final survey, the middle survey was not used for estimating the trends in the risk factors.
  • Response rate: Response rates in the MONICA surveys have been reported using two definitions, A and B, which differ in the way of counting those people whose eligibility for the survey could not be assessed because they could not be contacted [9]. For the quality score, the mean of item response rates A and B for Body Mass Index (BMI) was used. BMI was chosen because it reflects best the response rate for the clinical examination. The overall response rate concerns the questionnaire data, and in some populations only a portion of those people who were interviewed at home came to the clinical examination.
    • Ini: Response rate in the initial survey.
    • Fin: Response rate in the final survey.
    • Response rate score: 2×Square root of  [1 - (1 - Ini)×(1 - Fin) - (|Ini - Fin|)]
  • Risk factors
    • Smok: This is based on Section 6 (Recommendations for using MONICA data on smoking behaviour), Subsection 6.3 (Trend analyses) of the Quality Assessment of Data on Smoking Behaviour [10]. Score 0 was given where the quality assessment report recommends that the data should not be used for analysis of trends of daily smoking. Score 1.41 (i.e. the square root of two) was given where there was a change in the relevant question on smoking but there was evidence that the change did not affect the trend estimates much. All other populations were given a score of 2.
    • Bp: Quality score for blood pressure trends (QST) between the initial and the final surveys from Table 19 of the Quality Assessment of Data on Blood Pressure [11].
    • Chol: Total cholesterol overall summary score (TCOSS) for the initial and final surveys from Table 16 of the Quality Assessment of Total Cholesterol Measurements [12].
    • BMI: This is derived from the summary score for weight and height measurements for the initial and the final surveys from Table 10 of the Quality Assessment of Weight and Height Measurements [13]. The score is 0 if the summary score for the initial or final survey was 0. Otherwise the score is the mean of the scores for the initial and final surveys.
    • Risk factors mean: The geometric mean of (Bp+0.2)/1.1, (Smok+0.2)/1.1, (Chol+0.2)/1.1 and (BMI+0.2)/1.1. (Note: 0.2 is added to the individual risk factors scores so that none of them can make the geometric mean zero regardless of the value of the other risk factors scores).
  • Risk factor trends score: Half of the product of Response rate score and Risk factors mean.
• Overall quality score: Geometric mean of Event trends score and Risk factor trends score.

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.