IJE Advance Access originally published online on July 14, 2006
International Journal of Epidemiology 2006 35(5):1246-1252; doi:10.1093/ije/dyl128
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Article |
Predicting coronary heart disease mortality—assessing uncertainties in population forecasts and death probabilities by using Bayesian inference
National Public Health Institute, Helsinki, Finland
* Corresponding author. Department of Health and Functional Capacity, National Public Health Institute, Mannerheimintie 166, 00300 Helsinki, Finland. E-mail: tommi.harkanen{at}ktl.fi
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Background Predictions concerning people and their health are influenced by many factors and have many sources of uncertainty. Even so predictions can give useful guidelines for health care planning. We present a Bayesian model based on past observations and prior knowledge to predict coronary heart disease (CHD) mortality in selected areas of Finland until the year 2030.
Methods CHD mortality data are based on official statistics. The study area consists of one western and two eastern parts of Finland. The modelling of the probability of death follows a Bayesian age-period-cohort model. Two models are used, one assuming that the trend from 1970 to 2002 will continue and the other that mortality will stay at the attained level.
Results If the observed trend in CHD mortality were to continue, death probabilities would decrease significantly among men aged 50–69 and women aged 50–59. In the older age groups (men aged 70 and women 60 years or more) the changes were found to be negligible. If the trend continues, the number of CHD deaths will decrease from 2002 to 2030 significantly among men [81% decrease; 95% credible interval (95% CI) 54–96%] and women (90%; 67–100%) aged 50–59. In the age group 60–79 the changes will be smaller and non-significant. In the oldest age group (80–99 years) the predicted increase in the number of deaths will be great, from 284 to 1297 (95% CI 474–2620) in men and from 722 to 1970 (717–4017) in women.
Conclusions Our predictions emphasize the significance of maintaining the recent decline of CHD mortality among middle-aged adults. Special attention should be paid to CHD mortality among men and women aged 80 and over. Considerable improvements in prevention and treatment are needed to compensate for the effects of ageing of the population.
Keywords Coronary heart disease, prediction, Bayesian inference, mortality
Accepted 25 May 2006
Cardiovascular diseases have been the most significant causes of death in developed countries for several decades.1 During the last few decades a decline has been reported in coronary heart disease (CHD) mortality, which seems to be caused more by changing coronary event rates than by changing survival.2 Changes in known risk factors explain a great deal of the observed decline in CHD incidence and mortality rates.3,4 In addition to this, improved survival after myocardial infarction and better prognosis of coronary syndromes have decreased CHD mortality during the last few decades.5,6 Finland has also experienced a decreasing trend in the incidence of coronary events and in CHD mortality among the middle-aged population.7,8 However, the decline in CHD mortality seems to be greater than that of incidence.7,9 Thus one would expect the prevalence of CHD and the number of patients with CHD to increase. However, decreasing trends have also been reported in the prevalence of CHD during the last few decades in Finland,10–12 elderly Finns aged 75 years or more being an exception with increasing CHD prevalence.11 Although both incidence and prevalence of CHD have declined, the number of deaths caused by CHD has remained steady in Finland during the past two decades13 owing to the growing number of elderly people. The population is ageing all over the world,14 and, therefore, the total number of people with CHD is expected to increase in the future.
Predictions about CHD trends are needed to estimate the need for care due to this common disease. Previous studies forecasting cardiovascular disease trends are quite rare. The age-period-cohort model has been used to predict mortality trends for strokes in Sweden.15 CHD incidence, mortality, and cost have been forecast by a simulation model in the USA16 as has heart disease morbidity in The Netherlands.17 An Australian study has used a mathematical prevention model to estimate the projected lifetime incidence of myocardial infarction among individuals with different CHD risks.18 A Finnish report on the future need for health care predicted an increasing need for care for ischaemic heart disease patients. According to this projection, the number of deaths from ischaemic heart disease will increase by over 50% among men and women aged 80 and from the mid-1990s to 2010.19
Predictions concerning people and their health depend on many factors, and accurate predictions are almost impossible. For example, changes in lifestyle, nutrition, treatment, and environmental factors influence health. Even so predictions can give guidelines for health care planning if the uncertainties are taken into account and the assumptions, upon which the predictions are based, are reported alongside the predictions. Furthermore, national population predictions are, in general, only point estimates without any prediction intervals, and application of such predictions would underestimate the uncertainty in the number of deaths from CHD in the future. A Bayesian inference is an adequate tool for creating predictive distributions based on past observations and prior knowledge.
The aim of this study is to predict CHD mortality in selected areas of Finland by using Bayesian modelling. In addition to the uncertainty in the individual probability of dying from CHD, we also account for the uncertainty in the population predictions.
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Material and methods |
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In this study we have used the CHD mortality data based on official statistics. As this study is intended as a baseline for further work also using risk factor data, we restrict the analyses to the two areas examined in the Finmonica study.8,20 The study areas were the provinces of North Karelia and Kuopio in eastern Finland and the Turku/Loimaa area in south-western Finland, the eastern parts being high cardiovascular risk areas and the western part a low risk area. We use annual mortality data for the period 1972–2002, given by gender and age (5 year age groups from 30 years up to 99 years). Deaths from CHD (underlying cause of death) include diagnoses 410–414 in ICD-8 and ICD-9 and diagnoses I20–I25 in ICD-10.
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Statistical modelling |
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The first part of the model is for the population size, i.e. the number at risk, in a cell defined by different calendar years, genders, areas, and age groups with a width of 1 year. The number of births was assumed to follow Poisson distribution depending on gender, area, and calendar time trend. The cohort size in cells with age greater than zero was assumed to follow a normal distribution. The mean was the product of the cohort size in the previous year and the average proportional annual change. The average proportional annual changes were assumed to be constant within cells defined by gender, area, age in years, and calendar time intervals 1970–79, 1980–89, ... , 2020–29, and 2030–. It is reasonable to assume that the differences between neighbouring cells are small and, therefore, the mean of the normal prior distribution of a cell was assumed to be the average of the cells corresponding to the previous calendar time interval and the 1 year younger age group. This prior structure smoothes the observed average proportional annual changes in the cohort sizes, because, for example, average proportional annual changes of neighbouring age groups are assumed to be more similar than elements far away from each other. The second part is for modelling the probability of death following a Bayesian age-period-cohort model presented in Knorr-Held and Reiner.21 They applied a logistic regression model with age, period, and cohort as explanatory, categorical variables. The regression parameters corresponding to age, period, and cohort were assigned the so-called random walk prior distributions. Here we used the area and the age group in interaction with gender as categorical explanatory variables. The calendar time in interaction with the age group was used as a continuous explanatory variable modelling the linear trend. Linearity is a strong assumption and, therefore, we added a random component to the calendar time effect. The calendar time was divided into 5 year intervals, and the difference between the linear trend and the ‘true’ calendar time effect was assumed to be constant during a 5 year time interval. The prior distribution of the difference during the first interval 1970–74 was set to zero, and for the following intervals a random walk prior based on a normal distribution with the mean equal to the difference during the previous interval. The trend from 1970 to 2002 has been strong, and it is reasonable to assume that the trend cannot continue much longer. Therefore, we consider two scenarios. In the first scenario the trend is assumed to continue in the same way, but in the second scenario the trend is assumed to stop at the level of 2002. In Knorr-Held and Reiner21 the predictive distributions (see, for example, Gelman et al.22) for the number of cases were based on the known (i.e. fixed) population size, which we consider unrealistic in our case. By applying the model for the population size with observed data, the Bayesian inference yields a predictive distribution for future population sizes. A combination of that with the predictive distribution of the probability of death from CHD results in the predictive distribution for the number of cases, which properly accounts for the various sources of uncertainty. The analyses were performed by using WinBUGS software23 and R software.24 The details of the model are presented in the Appendix, and the WinBUGS code is available from Tommi Härkänen.
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Results |
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The eastern parts showed somewhat greater death rates compared with the western parts. The results are presented for the whole study area.
Among the youngest age groups (30–49 years) the number of CHD deaths was small and the probability of dying from CHD was near zero. Therefore, the results are mainly reported for men and women aged 50–99. Predicted CHD mortality and deaths in 2010–30 are compared with those observed in 2002.
In 2002 CHD mortality was 0.14% among men aged 50–59 years, 0.55% at the age of 60–69, 1.44% at 70–79, and 4.07% at 80–99 (Figure 1). Among women the corresponding mortality rates were: 0.04, 0.10, 0.71, and 3.86% (Figure 1). If the declining trend in CHD mortality from 1970 to 2002 was to continue, by 2030 death probabilities would decrease among men aged 50–59 years to 0.04% [95% credible intervals (95% CIs) 0.01–0.10], among men aged 60–69 to 0.24% (0.08–0.52), and among men aged 70–79 to 1.00% (0.34–2.13), and among women to 0.006% (0–0.02), 0.07% (0.02–0.15), and 0.50% (0.17–1.07) correspondingly (Figure 1). Among men and women aged 80–99 years, assuming the trend from 1970 to 2002 continues there will be a non-significant increase to 7.39% (95% CIs 2.74–14.9) among men and to 6.61% (2.40–13.30) among women (Figure 1).
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In this study predictions were calculated with two models: the ‘with trend –model’, which assumes that the trend in CHD mortality observed during 1970–2002 will continue, and the ‘without trend –model’, which assumes that CHD mortality will stay at the level observed in 2002. The ‘with trend –model’ predicts a 70% decrease (95% CIs 28–93) in CHD mortality among men aged 50–59 by 2030 compared with the observed mortality rate in 2002, a 57% (7–86) decrease in men aged 60–69 and a 31% non-significant decrease in men aged 70–79. Among women the corresponding decreases are estimated to be 85% (95% CIs 51–100), and 32 and 29%, which were found non-significant (Figure 1). The increase in the oldest age group (80–99 years) was found to be negligible.
The population is ageing and the proportion of older people is increasing (Table 1). If the declining trend continues, the number of CHD deaths will decrease among men and women aged 50–59, among men and women aged 60–79 changes will be small and non-significant (Table 1 and Figure 2). On the other hand, in the oldest age group (80–99) the predicted numbers of deaths will increase, although the CIs get wide. Among men aged 80 and over, the predicted number of deaths in 2030 (1297 deaths: 95% CI 474–2620) would be more than 4-fold higher compared with the observed deaths in 2002 (284 deaths) and among women this increase is expected to be almost 3-fold (from 722 deaths in 2002 to 1970 deaths; 95% CI 717–4017 in 2030) (Table 1 and Figure 2).
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‘Without trend’ predictions of the number of CHD deaths show the effect of the ageing population. The decrease in the age group 50–59 is expected to be smaller compared with the model assuming the previous trend to continue. The number of expected CHD deaths will increase in men and women aged 60 or more and, but only among men in the oldest age group this increase is significant (202%; 95% CI 12–530%). Among women the increase is not so great with CIs including the number of observed deaths in 2002 (Table 1 and Figure 2).
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Discussion |
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If the declining trend in CHD mortality continues among men and women aged 50–69 years, the number of CHD deaths will also decrease in this age group in the study areas despite the ageing population. However, if the probability of CHD death stays at the current level, the number of deaths will increase among men aged 60–79 but only slightly. Among old people aged 80 or more, the expected number of CHD deaths will increase in both scenarios. Although the calculations have been restricted to two areas in Finland, the main conclusions are likely to be valid for the whole country and many other western countries as well, as a recent decline in CHD mortality and population ageing have been observed in most Western countries.2,14
There has been a remarkable decline both in CHD prevalence10 and incidence7 as well as in CHD mortality7 during the past few decades in Finland. Prevention programmes have been effective and the levels of known risk factors, such as high blood pressure, high levels of serum cholesterol, and smoking have decreased4,20,25 and will probably continue to do so.25 In the1970s almost all the decrease in CHD mortality could be explained by changes in these risk factors mentioned above. Later in the 1980s and 1990s the decline was larger than would have been expected on the basis of risk factor trends, and improvements in treatment seem to explain nearly one-quarter of the decrease in CHD mortality.20 New forms of treatment were introduced at that time, e.g. coronary bypass surgery, balloon angioplasty, and thrombolytic therapy. In addition, drug therapy has improved, including effective preventive treatments. However, the decline in CHD mortality seen during the last few decades has been so strong that it will not continue easily with the same intensity. Predictions assuming that the trend from 1970 to 2002 will continue may underestimate the future burden of cardiovascular diseases. Our results are based on two models, one assuming that the declining trend will continue and the other assuming that the mortality will stay at the attained level. Thus we arrive at two visions of the future. Attaining the more optimistic scenario will require significant improvements in preventive activities, especially among young adults. The recent increase in obesity among young and middle-aged adults26 may affect CHD morbidity and mortality in the future. Also diabetes increases the risk of cardiovascular diseases and coronary mortality,27 and this effect is likely to be highly significant in the future because of the rising prevalence of diabetes.28
An ageing population brings its own special characteristics to disease forecasts. Improved treatment and more effective prevention of CHD have led to a decrease in fatality from coronary events. In this study the CHD mortality trend among the oldest people, aged 80 or more, differed considerably from that of other age groups. In contrast to the strong general declining trend in CHD mortality, it seems that there is no trend among elderly people. However, definition of causes of deaths among the elderly is not unambiguous, and this may partly explain the variation in CHD mortality among the elderly. If the increase in CHD mortality in the very oldest is mainly due to an improving definition of the cause of death, our predictions assuming a continuation of the recently observed time trend may overestimate the true number of CHD deaths in the elderly. On the other hand, the much smaller changes in mortality in the oldest age groups may also reflect a long-term cohort effect of risk factors in those groups. Also, the prevalence of CHD has been decreasing in Finland among men and women under age 65, but increasing among those aged 75 or more.11 The burden of CHD is thus moving to older age groups. Part of this movement may be due to changing diagnostics and treatment practices. CHD is changing from a fatal disease towards a more chronic condition, and with an extended life expectancy this places CHD deaths among the older age groups. In the present study the effect of ageing is seen clearly. In both scenarios, either assuming the observed trend will continue or assuming it will end at the level in 2002, the total number of coronary deaths will increase in the future.
A comparison between our results and previous predictions is not straightforward, because the methods are as different as are the study populations. The situation in Sweden is quite similar to that in Finland with regard to cardiovascular diseases and their risk factors. In a Swedish study predicting mortality rates due to strokes up to 2003, the findings were parallel to our results assuming the declining trend continues. Both mortality and the total number of deaths from stroke seem to be declining in Sweden.15 On the other hand, Weinstein et al.16 reported an increasing incidence and prevalence of CHD due to the ageing of the population and, in particular, the maturation of the so-called baby-boom generation born between 1946 and 1965 if there are no changes in risk factors or in therapies. After the Second World War we also had a baby-boom generation in Finland, and these large birth cohorts are now reaching the age of high CHD morbidity. This generation and its effect on CHD death numbers is clearly seen in the present study.
Uncertainty is always part of forecasting and this uncertainty increases with an increasing time span. Health predictions are greatly affected by the fast development of medicine. Revolutionary improvements in prevention and treatment may significantly impact on future trends. The strength of our study compared with previous predictions is that our model generated CIs, reflecting the uncertainties involved in the data and in the future. Our predictions, as well as those of others, always depend on the assumptions made in the modelling, and therefore the model assumptions should be examined alongside with the predictions.
Our population predictions matched relatively well with the predictions given by Statistics Finland,29 which fell within the CIs of our predictions. There is, however, scope for improvement in future work. Mortality and migration should be separated in the population data and model for more proper population forecasting. Then it would be possible, for example, to model the general trend in life expectancy more accurately or to make scenarios based on different magnitudes of migration. The changes in the number of deaths from CHD do not change the population sizes in our predictions, but this is likely to have a major influence only in the oldest age groups, where the probabilities of dying from other causes are also likely to change in the future. Furthermore, the assumption that mortality rates will stay at the level observed in the most recent year with available data is somewhat problematic since death rates in any 1 year are influenced by short-term period effects and random variation.
The predictions made in this study clearly illustrate both the effect of time trends and the ageing of the population in future CHD mortality. On the other hand, the uncertainty increases over time with all predictions, and our Bayesian approach addresses several sources of uncertainty. In the future we intend to take into account the effect of known risk factors. Our findings emphasize the significance of a continuously decreasing trend in CHD mortality that is likely to require improvements in CHD prevention and treatment. Even if CHD mortality rates continue to decline, the increasing number of old CHD patients will pose a great challenge for health care.
KEY MESSAGES
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We are indebted to Erkki Vartiainen MD, PhD and Jorma Torppa MSc (National Public Health Institute, Department of Epidemiology and Health Promotion) for providing us with the original data tables. This study is part of the research project ‘Forecasting health, diseases, disabilities and need for care in 2010, 2020, and 2030’ (project number 53580) funded by the Academy of Finland.
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