The health risks of tobacco smoking have been demonstrated in many studies. Smoking increases the risks for lung and other cancers, chronic obstructive lung disease, cardiovascular diseases, and other diseases. To evaluate the impact of tobacco smoking on public health, knowledge about smoking prevalence and associations between smoking and diseases is necessary. The effect can of course be estimated by means of etiologic fractions, but time dimensions such as duration of smoking and age at starting to smoke must be taken into account, as well as the fact that smoking affects the risks for various diseases differently.
A simulation model, “Prevent,” was developed in the late 1980s, 1 in which a multifactorial generalization of the etiologic fraction is used. Thus, several diseases and time dimensions are introduced simultaneously to estimate the health benefits of prevention. The model can, for instance, be used to estimate mortality from smoking.
In the beginning of the 1990s, a method for estimating mortality from smoking was suggested that was based on the results of the second large, prospective Cancer Prevention Study (CPS-II) of the American Cancer Society on smoking and mortality. 2
The purpose of the present study was to estimate mortality due to cigarette smoking from lung cancer, chronic bronchitis, emphysema, ischemic heart disease, and stroke, and to estimate the effect of cigarette smoking on life expectancy in Denmark by means of the Prevent model and the method proposed by Peto et al. 2 The two methods are fundamentally different, but the results can be compared because the calculations are based to some extent on common data and assumptions.
Subjects and Methods
The Prevent Model
The Prevent model was developed to predict the effect on mortality in a population of changes in exposure to one or more risk factors. Model simulations describe changes in total mortality and mortality due to selected causes. The model allows one risk factor to be associated with more than one disease and one disease to be associated with more than one risk factor. The simulations can take into account a gradual reduction in the risk for disease over time as exposure ceases. Demographic evolution is also taken into account in the simulation. The calculations are based on the “potential impact fraction,” which is a measure of the reduction in the proportion of new cases of disease in a population after changes in exposure to risk factors resulting from intervention. Similarly, the “trend impact fraction” is a measure of changes due to autonomous trends that are not due to the intervention. The model operates with the size of the population, total and cause-specific mortality rates for the year in which the simulation starts, the prevalence of exposure to risk factors and trends in this respect, and relative risks. The result of a simulation is the evolution of mortality in two populations: (1) the reference population, which reflects demographic changes and autonomous trends in exposure to the risk factors, and (2) the intervention population, which is also affected by reduced exposure to the risk factors. As a result, several descriptions of the mortality in the two populations are given, including mortality rates, survival curves, and life expectancy, together with measures of differences between the two populations.
The Prevent model is described in detail in a dissertation. 1 The basic method is summarized in Appendix 1.
In this study, the simulation is based on data for the period up to 1993. The size of population (on January 1, 1993) and the total mortality rates (1992–1993) were derived from the Danish National Bureau of Statistics. Cause-specific death rates for 1993 were calculated from the Cause of Death Register at the Danish National Institute of Public Health. The specific causes of death were ischemic heart disease [International Classification of Diseases, 8th revision (ICD-8: 410–414)], stroke (ICD-8: 430–438), lung cancer (ICD-8: 162), and chronic bronchitis and emphysema (ICD-8: 491, 492). The model includes data on changes in the prevalence of cigarette smoking by sex and age. 3,4 These data were based on personal interviews carried out nationally each year in the period 1973–1993 by Gallup Market Analysis. Each year during 1973–1987, approximately 20,000 Danes were asked questions on smoking habits, and between 1988 and 1993, approximately 9,000 were interviewed. Men and women 15 years of age and older were asked whether they had smoked yesterday; if the answer was no, they were classified as nonsmokers, and if the answer was yes, they were classified according to type and quantity of tobacco smoked. Cigarette smokers were divided into the categories light/moderate smokers (1–14 cigarettes per day) and heavy smokers (≥15 cigarettes per day).
Table 1 shows the relative risks chosen for the model in the present study. The estimates were provided by Michael Thun, American Cancer Society, and are based on results from the CPS-II for more than 1 million adult Americans. 5 This choice was made because the method proposed by Peto et al 2 relies heavily on the results of this study (see below). We made one exception with respect to the relative risks of lung cancer in women: in the CPS-II study, the relative risks of men are approximately twice as high as those of women, according to estimates made in the mid-1980s, when the full effect of cigarette smoking had not yet appeared among the women who participated in the study. Women in Denmark smoke more heavily than most other female populations in the world. The proportion of cigarette smokers in 1993 was 38% among both men and women, and the percentage of heavy cigarette smokers has increased for several decades. 4 Women smoked on average three fewer cigarettes per day than men (unpublished data from the Danish Health Interview Survey 1994), and among heavy smokers (≥15 cigarettes per day), the difference was about two cigarettes per day. A recent Danish study reported that the risk for lung cancer was similar among male and female smokers and that the incidence rates among women within smoking categories were higher than those in the CPS-II. 6 Therefore, in the present study, we assumed that the relative risks for lung cancer were the same for men and women.
In an ordinary Prevent simulation, an increased risk of disease is assumed to decrease gradually when exposure ceases. In this study, however, the risk decreased immediately on cessation of smoking. Thus, total cessation of smoking by the intervention population was assumed to affect mortality within 1 year. The number of smoking-attributable deaths was derived by comparison with the reference population. Version 2.1 of Prevent was used.
The Peto et al Method
The size of the CPS-II study allows estimation of lung cancer death rates among people who have never smoked. Peto et al 2 used the rates and relative risks from this study. 2 We calculated the proportion of smoking-attributable deaths from lung cancer using rates of death from lung cancer in Denmark and the rates for never-smokers estimated from the CPS-II. We then estimated a sex- and age-specific “synthetic smoking prevalence” rate for Denmark, which is the prevalence that would be necessary to result in the observed rate of death from lung cancer in the population. It depends on the proportion of smokers, the amount smoked, the duration of smoking, the age at starting to smoke, and the prevalence of inhaling. On the basis of the synthetic smoking prevalence and the relative risks, we calculated the etiologic fractions for other smoking-related diseases. Table 1 shows the relative risks used, which were taken from the CPS-II and estimated by univariate analyses adjusted only for the effects of sex and age 2; for instance, smoking intensity was not divided into categories. The estimates are larger than those used in the Prevent model, which are based on multivariate analyses. The etiologic fractions were adjusted downward to ensure that the hazards of tobacco were not exaggerated.
The method is described in Appendix 2.
Comparing the Two Methods
Our Prevent model includes lung cancer, chronic bronchitis, emphysema, ischemic heart disease, and stroke, which account for almost half of all deaths in Denmark. Cigarette smoking is a risk factor for all of these diseases. To obtain comparable results, the method of Peto et al 2 was used with the assumption that only these causes of death were related to cigarette smoking. The number of smoking-attributable deaths in 1993 from these causes of death was estimated by the two methods, and the effect of cigarette smoking on life expectancy was calculated.
The estimated numbers of deaths in 1993 by cause of death are shown in Table 2. The proportion of deaths from the selected causes in 1993 that were attributable to cigarette smoking were 33% with the Prevent model and 35% with the Peto et al 2 method for men and 23% and 25%, respectively, for women. The greatest differences between the two methods were found for lung cancer in men and ischemic heart disease and stroke in women.
The Prevent model gave a smaller number of smoking-attributable deaths from lung cancer among men than the Peto et al 2 method, and use of higher relative risks for lung cancer (15 for 1–14 cigarettes per day and 25 for ≥15 cigarettes per day) did not change the results materially, with 1,847 (84%) male and 1,015 (83%) female lung cancer deaths being related to smoking.
Self-reported data on smoking tends to result in an underestimate of the prevalence of cigarette smoking. 7 If it is assumed that the prevalence of cigarette smoking was in fact 10% higher in both categories of smoker and in all age groups, the Prevent model showed that the estimated proportions of smoking-attributable lung cancer deaths would be 84% for men and 83% for women, the percentage of smoking-attributable deaths from chronic bronchitis and emphysema would increase by 2, and the percentage of smoking-attributable deaths from ischemic heart disease and stroke would increase by 1.
When the analysis was restricted to deaths that occurred in people under 65, an almost identical number of smoking-attributable lung cancer deaths was obtained: 531 (89%) by the Prevent model and 537 (90%) by the Peto et al 2 method for men and 362 (89%) and 349 (86%), respectively, for women.
If there were no smoking-related deaths due to lung cancer, chronic bronchitis, emphysema, ischemic heart disease, or stroke, life expectancy would increase by 1.7 years, from 72.5 to 74.2 years, for newborn boys and by 1.2 years, from 77.8 to 79.0, for newborn girls, according to the Prevent model. By the Peto et al 2 method, the estimated gains in life expectancy would be 1.8 and 1.3 years, respectively.
The method of Peto et al, 2 which is not restricted to deaths from lung cancer, chronic bronchitis, emphysema, ischemic heart disease and stroke, was used recently to estimate the total effect of cigarette smoking on life expectancy in Denmark. 8 The conclusion was that life expectancy in 1995 would increase by 3.0 years for boys and 2.1 years for girls if none of them died as a result of smoking.
The actual rate of smoking-attributable mortality reflects previous exposure to cigarette smoking in the population, including the proportion of smokers, the amount smoked, the duration of smoking, the age at starting to smoke, and the prevalence of inhaling. The Prevent model simulation of mortality attributable to cigarette smoking takes into account the development of smoking habits between 1973 and 1993. Few detailed retrospective data are available on the prevalence of cigarette smoking; for instance, information on ex-smokers is not available from the same source as data on smoking prevalence, and information on ex-smokers was derived from the Danish Health Interview Survey carried out in 1994 by the Danish Institute for Clinical Epidemiology. The available data do, however, allow estimation of trends by sex, age, and smoking category, and these trends were used to predict smoking-attributable mortality. In contrast, the method of Peto et al 2 does not require information about cigarette smoking, because the estimated synthetic smoking prevalence summarizes the history of smoking in the population.
Both methods require information about the associations between cigarette smoking and smoking-related diseases. The relative risks for both were derived from the CPS-II, although the relative risks for lung cancer of men were used for Danish women. Thus, the essential difference between the two methods is that Prevent is a dynamic model that takes the evolution of cigarette smoking into account, whereas this factor is included in the Peto et al 2 method only indirectly by the synthetic smoking prevalence. Because this prevalence is calculated on the basis of estimated lung cancer death rates among smokers and never-smokers estimated in an American population, it is unclear whether these rates are valid for other populations. Use of the method of Peto et al 2 for populations other than that from which it was deduced is based on the assumption that mortality from lung cancer among never-smokers is the same in different populations.
The calculations in the Prevent model rely on the relative risk estimates chosen for the cause-specific deaths that are included, whereas the method of Peto et al 2 does not include relative risks for lung cancer. Fewer smoking-attributable deaths from lung cancer were estimated with the Prevent model than with the Peto et al 2 method, especially for men, and this difference did not disappear when higher relative risks for lung cancer were chosen. Similarly, the difference was not noticeably reduced by assuming that the prevalence of cigarette smoking in 1993 was 10% higher than that reported. An obvious explanation for the difference is that the death rates from lung cancer among never-smokers in the CPS-II study are lower than those of Danish never-smokers. Furthermore, the death rates from lung cancer for men estimated from the CPS-II study appear to be lower than the national rates. 9 The overestimate of smoking-attributable death from lung cancer is less pronounced among women, in accordance with the fact that women were less frequently exposed than men to risk factors for lung cancer in the working environment. Thus, the close agreement between the two methods for lung cancer deaths before the age of 65 may be due to improvements in the working environment, with the risk for lung cancer being reduced for younger generations.
In a recent study, the method of Peto et al 2 was evaluated by comparing its estimates with direct estimates of smoking-attributable mortality in eight cohort studies in Denmark, Finland, the Netherlands, Norway, and Sweden. 10 Generally, reasonably uniform results were found; however, an unconvincing correspondence was found between the two methods for the results for Denmark. The Prevent model is more suitable than conventional formulae for direct estimation of smoking-attributable mortality. Our findings validate the method of Peto et al, 2 as close agreement between the estimates obtained by the two methods was found. The advantage of the Prevent model is that it can be used with various scenarios of the health benefits of prevention and can include risk factors other than cigarette smoking. Nevertheless, it requires more data than the method of Peto et al, 2 which can be used in the absence of knowledge of the prevalence of cigarette smoking. The method of Peto et al 2 can be used only to estimate smoking-attributable mortality.
The Danish version of the Prevent model was developed within the European Biomed Public Health Models project. The participants were Caroline Baan, Jan Barendregt, Luc Bonneux, Henrik Brønnum-Hansen, Louise Gunning-Schepers, Finn Kamper-Jørgensen, Paul van der Maas, Perla Marang-van de Mheen, Joke Mooy, Klim McPherson, Bhash Naidoo, Måns Rosén, Magnus Stenbeck, Margaret Thorogood, and Rianna Welvaart. We thank the participants for their contribution to this project. We also thank Michael Thun of The American Cancer Society, who provided the relative risk estimates for the Prevent model.
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Basic Method of the Prevent Model (Version 2.1)
Let the proportion of exposed individuals be MATH 1 and let RR signify the relative risk, where the indices are:t for time, r for risk factor, j = 0 or 1 for reference (0) or intervention population (1), s for sex, A for age, n for exposure category, i for previous exposure level, z for disease, and LAT for latency (number of years that the risk remains unchanged after a change in exposure to a risk factor).
The trend impact fraction, TIF, and the potential impact fraction, PIF, are defined as MATH 2 MATH 3 where MATH 4 cn is the total number of exposure categories and LAG is the number of years to reduce the excess risk LAT years after exposure ceases. Thus, the full effect will be reached after LAG +LAT years.
In the present study the results for the intervention population were derived by modifying the model with the assumption of no effect of cigarette smoking in the past (no LAG or LAT and no remaining risk after cessation of exposure).
For the specific disease, z, associated with rf risk factors, MATH 5 MATH 6
Let M and M signify the baseline total and cause-specific mortality rates and let zt be the total number of diseases. The simulated mortality rates for the reference (j = 0) and intervention populations (j = 1) are MATH 7 MATH 8
Basic description of the method of Peto et al.
For a specific sex and age group, the proportion of smoking-attributable deaths from lung cancer is calculated as (L−A)/L, where L is the Danish lung cancer death rate in 1993 and A is the lung cancer death rate among never-smokers according to the CPS-II.
Let P signify the sex- and age-specific proportion of smokers in Denmark and C the lung cancer death rate among smokers according to the CPS-II. Then, MATH 9 from which the “synthetic smoking prevalence” is calculated:MATH 10 Let RR signify the relative risk for a smoking-related disease other than lung cancer. Then, the etiologic fraction is:MATH 11 To ensure that the hazards of tobacco were not exaggerated, the conservative estimate MATH 12 was used.