**Assuming independence of risk factor**prevalences in simulation models like PREVENT When are the outcomes seriously biased? PERLA J. VAN DE MHEEN, LOUISE J. GUNNING-SCHEPERS * Little is known about the clustering of risk factors at a nation-wide level. As a result the prevalence of combinations of risk factors in models like PREVENT, designed to calculate the hearth benefits of a change in risk factor prevalences, is computed assuming an independent distribution. This assumption may not be valid. The aim of the present study was to quantify the maximum extent to which outcome measures of PREVENT may be biased, if the assumed independent distribution of risk factors is incorrect. We therefore calculated to what extent the life expectancy and the potential years of life gained were biased when independent risk factor prevalences were assumed, while they were in fact completely dependent. We used population data, mortality figures and risk factor prevalences from The Netherlands to obtain a realistic estimate of how serious the bias might be. Furthermore, sensitivity analyses were carried out to explore the extent of bias in the case of different risk factor prevalences. The results show that the assumed independence has little impact on the estimated life expectancy and the potential years of life gained, both in the case of the current risk factor prevalences and in the case of higher or lower prevalences. Given that the dependency between risk factors will probably be smaller in reality, we conclude that the assumption of independence may be used since It is not likely to cause substantial bias. This greatly reduces the data requirements necessary as input for simulation models such as PREVENT. Downloaded from https://academic.oup.com/eurpub/article-abstract/7/2/216/505644 by guest on 04 May 2020 Key words: clustering, independent risk factors, simulation models, life expectancy, years of life gained will affect not only the coronary heart disease mortality rate, but also the mortality rates of lung cancer, stroke and chronic obstructive lung diseases. The population in PREVENT consists of several subgroups characterized by exposure to certain risk factors, e.g. part of the population may smoke and therefore increase its risk of several causes of deadi. Since individuals may be exposed to more dian 1 risk factor, the prevalence of combinations of risk factors is also needed. Unfortunately, these are not available at a population level in The Netherlands. Therefore, an inde- pendent distribution of risk factor prevalences is assumed in PREVENT. That risk factors cluster more than expected under die assumption of independence has been shown by several authors. Criqui et al. showed diat clustering of cardio- vascular risk factors (smoking, high blood pressure, high cholesterol levels and obesity) was strongest in subjects with the highest levels of these risk factors. This means that persons at greater risk of 1 risk factor for cardiovas- cular disease, also have a higher risk of more risk factors. The Bogalusa Heart Study shows an example of clustering of cardiovascular disease risk factors at a younger age (5-24 years of age).5'6 Obese school children had more clustering of other risk factors than could be expected, assuming an independent distribution of risk factors. In The NerJierlands, Kok et al. have shown diat smoking, obesity, physical inactivity and inadequate nutrition clus- tered more than expected under die assumption of inde- pendent risk factor prevalences. Clustering of risk factors e PREVENT model was designed specifically for policy makers, to enable them to weigh policy alternatives quantitatively.1'2 This simulation model calculates the potential health benefits of primary prevention pro- grammes that focus on reducing risk factor prevalences. The model is not used for analysis of empirical data, but rather to bring together information available from em- pirical studies for decision-making purposes at die popu- lation level. It uses the currently available information to quantify the future effects of changing risk factor preval- ences in a population. The methodology of the model is based on the potential impact fraction, a well-known epidemiological measure. PREVENT uses existing epidemiological knowledge about the relationship between risk factors and mortality and combines this with a dynamic population model to include demographic effects and interrelationships be- tween causes of death. Another feature of the model is that a time dimension has been incorporated, to simulate a gradual reduction in excess risk after cessation of expos- ure. Furthermore, mortality risks have been linked through common risk factors, to include the fact that for instance a change in smoking behaviour in die population * PJ. van de Mheen', LJ. Gunning-Schepen1 Academic Medical Center, Institute of Social Medicine, Amsterdam, The Netherlands Correspondence: Ms. Perla J. van de Mheen, PhD. Academic Medical Center, Institute of Social Medicine. Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands, tel. +31 20 S664S92, fax +31 20 6972316Assuming independence of risk factors may be an issue when one is interested in the magnitude of the risk associated with a combination of risk factors, in order to find die group of people that is at extremely high risk. However, is it an issue in public health when one is interested in the average health or mortality of a population? The aim of the present study was to estimate the max- imum extent of bias in the estimated life expectancy, 1 of the outcome measures of PREVENT, if an independent distribution of risk factor prevalences is wrongly assumed. Since overall life expectancy may be a relatively insensit- ive measure, we also estimated the maximum bias in the potential years of life gained. Dutch data were used to calculate to what extent these outcome measures were biased when independent risk factor prevalences would be assumed, while the risk factor prevalences were com- pletely dependent in reality. Since the observed depend- ence between risk factors is probably smaller than this complete dependence, the bias in practice will probably be smaller than calculated in this paper. Furthermore, the influence of the assumption in the case of higher and lower risk factor prevalences was explored, since these may exist in certain groups of the population or in other countries and this higher or lower prevalence may result in a different extent of bias in the outcomes of PREVENT. If die assumption would not affect the outcome measures of PREVENT, this would greatly reduce data require- ments for the input data and enable people to use the model with the data already available. ences. On the basis of the mortality rates for each sub- group, the mortality rate in the total population and the life expectancy were calculated. Then the total mortality rate was computed in the case of completely dependent risk factor prevalences, assuming that the mortality rate for each subgroup was the same as in the case of inde- pendent risk factor prevalences, so that the only differ- ence was the prevalence of combinations of risk factors. Completely dependent risk factor prevalences for this purpose were defined as all persons with hypertension who also had hypercholesterolaemia and were (former) smokers. Given a difference in the prevalences of smoking, hypertension and hypercholesterolaemia, with the prevalence of hypertension being the lowest, this definition will give the maximum extent of dependence between the 3 risk factors. Since the overall life expectancy may be a relatively insensitive outcome measure, we also investigated the influence of the assumption of independence on the potential years of life gained. An intervention was simu- lated reducing the overall prevalence of smoking by 50%, thereby increasing the prevalence of former smokers and assuming that the dependency of risk factors was not affected by the intervention (i.e. completely dependent risk factors were also completely dependent after the inter- vention). Dutch population18 and mortality data were used to assess whether the effect of an intervention in terms of the potential years of life gained would be greatly overestimated or underestimated by wrongly assuming an independent distribution of risk factor prevalences. Downloaded from https://academic.oup.com/eurpub/article-abstract/7/2/216/505644 by guest on 04 May 2020 METHODS Details of the basic methodology of PREVENT can be found in die appendix. Since PREVENT is based upon life table techniques, standard life table techniques8 were used to calculate the mortality experience of a cohort of men from 0 to 95 years of age, using Dutch mortality data. As in PREVENT, the cohort was assumed to consist of subgroups characterized by exposure to different combi- nations of the risk factors: smoking, hypertension and hypercholesterolaemia. For smoking, a distinction was made between current smokers, former smokers and never smokers. For the other risk factors, we distinguished only 2 exposure categories: with or without the risk factor. The prevalences of the risk factors were taken from a repres- entative sample of the Dutch population.10 The popula- tion thus consisted of 40.8% of smokers, 9% of persons with hypertension and 19% of persons with hyper- cholesterolaemia. The proportion of former smokers, however, was not reported in that sample. We assumed 45% to be a realistic estimate, as we had calculated in an earlier study.'1 We furthermore assumed that exposure to risk factors occurred from the age of 20 years onwards. For smokers this age is reported in other studies.12 The relat- ive risks of death were used to quantify the higher risk of those exposed compared to those not exposed to the risk factor and these were taken from published prospective studies.13"17 At every age, the mortality experience for each subgroup was calculated assuming independent risk factor preval- Sensitivity analyses It was tested whether the results were sensitive to the relative risks chosen for joint exposure of risk factors. We used multiplicative versus additive relative risks, which can be seen as the 2 extremes reported in epidemiological research. Multiplicative risks are often assumed. How- ever, Silberberg19 found, using coronary heart disease death rates from the population screened for the MRFIT study, that the relationship between cholesterol, smoking and blood pressure was closer to additive than to multi- plicative. We therefore initially used multiplicative relat- ive risks, with additive relative risks as an alternative. Furthermore, it was assessed whether the results were sensitive to the magnitude of the risk factor prevalences. The effect of the assumption was evaluated in the case of 25% higher risk factor prevalences and in the case of 50% lower risk factor prevalences. Moreover, 2 analyses were carried out to test whether the results were sensitive to a smaller difference between the overall risk factor preval- ences. In the first analysis the effect of the assumption was estimated in the case of a 100% higher prevalence of hypertension and a 100% higher prevalence of hyper- cholesterolaemia (i.e. 40.8% of smokers, 18% of the popu- lation with hypertension and 38% of the population with hypercholesterolaemia). In the second analysis the effect of the assumption was evaluated in the case of a 50% lower prevalence of smoking and no change in the prevalences of hypertension and hypercholesterolaemia.

EUROPEAN JOURNAL OF PUBLIC HEALTH VOL. 7 1997 NO. 2 die assumption in estimated life expectancy is approx- imately die same and dius very small. However, in die case of a smaller difference between die overall preval- ence of die risk factors, die possible bias in die estimated life expectancy increases (tables 5 and 6). The possible bias is still small, ranging from 0.1% in life expectancy at birdi, to 2.4% in life expectancy at 85 years of age in die case of multiplicative relative risks for joint exposure and 100% higher prevalences of hypertension and hyper- cholesterolaemia (table 5). The possible bias in die estim- ated potential years of life gained also increases, but remains below 1% (data not shown). RESULTS Table I shows that the estimated life expectancy at differ- ent ages is only slightly biased by wrongly assuming inde- pendent risk factor prevalences, both when multiplicative and additive relative risks are used for joint exposure to risk factors. The possible bias introduced by wrongly assuming an independent distribution of risk factors is strongest in the case of additive relative risks for joint exposure and at older ages but is still only 0.1 and 1.5% respectively. Part of diis minimal bias may be due to the fact that the overall life expectancy is a relatively insen- sitive outcome measure. Table 2 shows the effect of the assumption on the potential years of life gained. When independent risk factors are wrongly assumed, the effect of die intervention is overes- timated in the case of multi- plicative relative risks for joint exposure to risk factors, and underestimated in the case of additive relative risks. However, as a percentage of die total years lived by the average Dutch population in tliat year, die bias is smaller dian 1%. Expressed as a per- centage of die total effect of die intervention, die bias in- troduced by diis assumption is also around 1% (data not shown). The bias in the es- timated potential years of life gained was slightly stronger when an intervention was simulated diat reduced die proportion of individuals ex- posed to 3 risk factors by 50%, but die bias remained below 1% of die total num- ber of years lived (data not shown). Downloaded from https://academic.oup.com/eurpub/article-abstract/7/2/216/505644 by guest on 04 May 2020 Table 1 Effect of assuming independent risk factor prevalences on estimated life expectancy Multiplicative relative risks Independent risk factors 73.85 14.06 4.55 Additive relative risks Independent risk factors 73.85 14.06 4.55 Dependent risk factors 73.91 14.13 4.61 Dependent risk factors 73.84 14.14 4.62 Life expectancy At birth At 65 years of age At 85 years of age Table 2 Overestimation of the potential years of life gained due to wrongly assuming an independent distribution of risk factor prevalences (intervention: 50% reduction of smoking prevalence) Additive relative risks Number % of total years lived -847 -25 -822 Multiplicative relative risks Number % of total years lived 952 1651 -699 -0.01 -0.00 -0.11 All ages <65 years 565 years 0.01 0.03 -0.10 Table 3 Effect of assumption in the case of 25% higher risk factor prevalences Additive relative risks Independent risk factors 73.85 14.06 4.55 Multiplicative Independent risk factors 73.85 14.06 4.55 relative risks Dependent risk factors 73.84 14.13 4.61 Dependent risk factors 73.90 14.11 4.60 Life expectancy At birth At 65 years of age At 85 years of age Table 4 Effect of assumption in the case of 50% lower risk factor prevalences Sensitivity analyses Anodier reason for die min- imal error due to wrongly as- suming an independent dis- tribution of risk factors, may be die radier small risk factor prevalences. There may be subgroups widiin die popula- tion widi higher risk factor prevalences, in which die as- sumption of risk factor prevalences may lead to serious bias in die es- timated life expectancy or die potential years of life gained. Tables 3 and 4 show 3 diat die possible bias due to Additive relative risks Independent risk Dependent risk factors 73.85 14.06 4.55 Multiplicative relative risks Independent risk factors 73.85 14.06 4.55 Dependent risk factors 73.84 14.12 4.59 factors 73.90 14.11 4.58 Life expectancy At birth At 65 years of age At 85 years of age Table 5 Effect of assumption in the case of 100% higher prevalences of hypertension and hypercholesterolaemia independent relative risks Dependent risk factors 73.84 14.18 4.66 Additive relative risks Independent risk Dependent risk factors 73.85 14.06 4.55 Multiplicative Independent risk factors 73.85 14.06 4.55 Life expectancy At birth At 65 years of age At 85 yean of age factors 73.94 14.16 4.64

Assuming independence of risk factors dependency between risk factor prevalences is prob- ably smaller in reality, die bias in outcome measures will also be smaller. Only in die case of extremely high risk factor prevalences of ap- proximately die same magni- tude widi very strong de- Table 6 Effect of assumption in the case of 50% lower prevalences of smoking Multiplicative Independent risk factors 73.85 14.06 4.55 relative risks Dependent nsk factors 73.84 14.17 4.63 Additive relative risks Independent risk factors 73.85 14.06 4.55 Dependent risk factors 73.94 14.16 4.62 Life expectancy At birth At 65 years of age At 85 years of age pendency, will die outcome measures possibly be biased. However, given die current risk factor prevalences, diis is not very likely to occur simultaneously. This study suggests diat we may dien assume independence of risk factors, which will greatly reduce die data requirements needed for models such as PREVENT and enable people to use die model widi die data already available. DISCUSSION The present study indicates that an assumed independent distribution of risk factor prevalences in simulation mod- els like PREVENT is not likely to have a substantial influence on the estimated life expectancy at birth or die potential years of life gained, given die current level of 3 traditional risk factors. Should risk factors be added with much higher or lower prevalences, die bias in die out- come measures may increase if independence is wrongly assumed. Furthermore, in die case of risk factors widi prevalences of equal magnitude, die impact of die as- sumption may be stronger. However, die sensitivity ana- lyses in diis study indicate diat even in diese cases die bias is very small. Moreover, die dependency of risk factors is probably smaller in reality, suggesting diat die possible bias of die outcome measures will be smaller dian calculated in diis paper. The lack of impact of diis as- sumption is caused by die fact diat assuming complete dependency of risk factors leads to a simultaneous increase in die prevalence of people not exposed to any risk factor. In this way, die higher mortality due to a higher preval- ence of people exposed to 3 risk factors is counterbalanced by die fact diat die prevalence of people not exposed to any risk factor is also higher. In diis paper we only simulated die mortality experience and die influence of differential mortality. In general, differential mortality will result in smaller proportions of people exposed widi increasing age and die proportion of people not exposed will increase. For risk factors such as hypertension and hypercholesterolaemia, however, die prevalence is diought to increase widi age.20 This would only affect our results if diis increase widi age were to differ between individuals exposed and not exposed to odier risk factors. To our knowledge, it is not known whedier diis increase widi age is different for exposure groups. Furthermore, Lowik et al.21 found in an elderly population diat die risk factors smoking, hypertension, hypercholesterolaemia and obesity did not cluster more dian expected under die assumption of independence. Given diat a stronger clustering dian expected under die assumption of independence is found at younger ages,7 die findings of Ldwik et al.21 might be die result of differential mortality. Therefore, aldiough clustering of risk factors may be an issue widi regard to die (reduction of) risk associated widi diat clustering, it is not likely to be an issue in terms of die average healdi or mortality in a population. Our results indicate diat even in the case of risk factors being completely dependent, the bias in the outcome measures of models such as PREVENT is very small. Since die Downloaded from https://academic.oup.com/eurpub/article-abstract/7/2/216/505644 by guest on 04 May 2020 Gunning-Schepers U, Barendregt JJ, van der Maas PJ. Population interventions reassessed. Lancet 1989;i:479-81. 2 Gunning-Schepers U. The health benefits of prevention: a simulation approach. Hrth Policy 1989; 12:1-256. 3 Gunning-Schepers U, Barendregt JJ. Timeless epidemiology or history cannot be ignored. J Clin Epidemiol 1992;45:365-72. 4 Criqui MH, Barrett-Connor E, Holdbrook MJ, Austin M, Turner JD. Clustering of cardiovascular disease risk factors. Prevent Med 1980;9:525-33. 5 Smoak CG. Burke GL, Webber LS, Harsha DW, Srinivasan SR, Berenson GS. Relation of obesity to clustering of cardiovascular disease risk factors in children and young adults: the Bogalusa heart study. Am J Epidemiol 1987;125:364-72. 6 Webber LS, Voors AW, Srinivasan SR, Frerichs RR, Berenson GS. Occurrence in children of multiple risk factors for coronary artery disease: the Bogalusa heart study. Prevent Med 1979;8:407-18. 7 Kok FJ, Matroos AW, van den Ban AW, Hautvast JGAJ. Characteristics of individuals with multiple behavioral risk factors for coronary heart disease: The Netherlands. Am J Public Hlth 1992;72:986-91. 8 Namboodiri K, Suchindran CM. Ufe table techniques and their applications. Orlando: Academic Press, 1987. 9 Central Bureau of Statistics. Ufe tables, 1990 and 1986-1990. Monthly Popul Stat 1991;12:74-5. 10 Kromhout D, Obermann-de Boer GL, Blokstra A, Verschuren WMM. Monitoring cardiovascular diseases 1990 (in Dutch). Bilthoven: Rijks Instrtuut voor Volksgezondheid en Milieuhygiene (RIVM), 1991. 11 van de Mheen PJ, Gunning-Schepers U. Reported prevalences of former smokers in survey data: the importance of differential mortality and misclassification. Am J Epidemiol 1994:140:52-7. 12 US Department of Health and Human Services. Reducing the health consequences of smoking: 25 years of progress. Rockville, MD: US Department of Hearth and Human Services, Office on Smoking and Health, 1989. 13 US Department of Health and Human Services. The health benefits of smoking cessation. Rockville, MD: US Department of Health and Human Services, Public Health Service, Centers for Disease Control, Center for Chronic Disease Prevention and Health Promotion, Office on Smoking and Health, 1990. 14 Doll R, Peto R. Mortality in relation to smoking: 20 years' observation on male British doctors. BMJ 1976;2:1525-36. 15 Kannel WB. The role of blood pressure in cardiovascular morbidity and mortality. Prog Cardiovasc Dis 1974;17:5-24. 16 Yano K, McGee D, Reed DM. The impact of elevated blood pressure upon 10-year mortality among Japanese men in Hawaii: the Honolulu Heart Program. J Chronic Dis 1983,36:569-79. 17 Cowan LD, O'Connell DL, Criqui MH, Barrett-Connor E, Bush TL, Wallace RB. Cancer mortality and lipid and lipoprotein levels: the lipid research clinics program mortality follow-up 1

EUROPEAN JOURNAL OF PUBLIC HEALTH VOL. 7 1997 NO. 2 study. Am J Epidemiol 1990;131:468-82. 18 Central Bureau of Statistics. Age composition of The Netherlands, January 1tt 1990. Monthly Popul Stat 1990;4:24-5. 19 Silberberg JS. Estimating the benefits of cholesterol lowering: are risk factors for coronary heart disease multiplicative? J Clin Epidemiol 1990:43:875-9. 20 Wherton PK. Blood pressure in adults and the elderly. In: Bulpitt C, editor. Epidemiology of hypertension. Amsterdam, New York, Oxford: Elsevier, 1985:51-69. 21 L6wik MRH, Borsboom ABG, Bun CJE, Kok FJ, Schouten EG, Odink J. Clustering of cardiovascular risk indicators in the elderly (in Dutch). Hart Bull 1991;22:95-9. Received 21 August 1995, accepted I November 1995 Appendix Basic methodology of PREVENT model' Downloaded from https://academic.oup.com/eurpub/article-abstract/7/2/216/505644 by guest on 04 May 2020 A IDRA xPOPo xM0 Risk Factor TIF,A POPt° Prevalence Pt° TIF,B B IDRB xM0 xPOPo Trend (0) Risk Factor A = Health Benefit Prevalence P° Trend + intervention (1) PlF,A X TIF,A xPOPo xM0 M.A.1 Risk Factor TIF,B X PIF,B Prevalence Pt1 IDRB xPOPo en ID PIDR;"VI"=£ x n = 1 i = 0 - p / D Ro -PIDR, .O.w.A Where: P: proportion en: total number of exposure categories r: index for risk factor i: index for ex-exposure level A: index for age z: index for disease 1DR: incidence density ratio n: index for exposure category 1L> total number of ex-exposure levels j-0,1: index for reference (0) or intervention population (1) s: index for sex t: index for time M : constant overall mortality quotient Mt : adjusted overall mortality quotient a: The appendix has been published earlier in: Gunning-Schepers LJ. Central issues in future research and policy for chronic diseases. Eur J Public Hlth 1995;5:3-7. Reprinted by permission of Oxford University Press.