J CliaEpidemiol Vol. 43, No. 9, pp. 961-970, Printedin GreatBritain.All rights reserved
0895-4356/90 $3.00+ 0.00 Copyright0 1990Pergamon Press plc
1990
RISK RATIOS AND RISK DIFFERENCES IN ESTIMATING THE EFFECT OF RISK FACTORS FOR CARDIOVASCULAR DISEASE IN THE ELDERLY BRUCEM. P.sATY,‘*‘**THOMASD. KOEPSELL,~~~ TERI A. MANOLIO,~ W. T. LONGSTRETH JR,’ EDWARD H. WAGNER,~*~ PATRICIAW. WAHL~ and RICHARD A. KRONMAL~ Departments of ‘Medicine, 2Epidemiology, ‘Health Services, 4Biostatistics, University of Washington, Seattle, Wash., ‘Center for Health Studies, Group Health Cooperative of Puget Sound, Seattle, Wash. and 6National Heart Lung and Blood Institute, National Institutes of Health, Bethesda, Md, U.S.A. (Received in revised form 23 January 1990)
Abstract-This article reviews the nature of the effects of hypertension, smoking and cholesterol on the incidence of cardiovascular disease and emphasizes how these effects vary by age. In the Methods section, we discuss briefly the concepts of additive and multiplicative statistical models as tools for summarizing data. In the results section, we summarize available data on the association between incident stroke and coronary heart disease in the elderly and each of these major risk factors. The traditional multiplicative model parsimoniously characterizes the individual and joint effects of age and high blood pressure in terms of risk ratios; but, for smoking and cholesterol, an additive model appears to be the most parsimonious. We discuss the consequences of these observations for the study and prevention of cardiovascular disease in the elderly. Myocardial infarction Coronary heart disease mortality Cerebrovascular diseases Hypertension Smoking Cholesterol Risk factor Relative risk Risk difference Additive model Multiplicative model
“Patients 60 years of age and above are another issue. There is little direct clinical trial evidence on whether elderly patients will benefit from intervention, and the strength of the association between LDL-cholesterol and CHD diminishes with age.” The Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults, 1988 [l]
“Since there are two effect measures, the difference and ratio measures, . the concept of effect modification without further specification is too ambiguous to be useful as a description of nature.” Kenneth Rothman, 1986 [2]
INTRODUCTION
Between the beginning of the Framingham Study in 1948 and its first report of cardiovascular risk factors among the elderly in 1978 [3], the number of persons 65 years and over doubled *All correspondence should be addressed to: Bruce M. Psaty, MD, PhD, Dept of Medicine, ZA-60, Harborview Medical Center, 325 Ninth Avenue, Seattle, WA 98104, U.S.A. ce 43,9--H
in the U.S. [4]. In 1978, the Pooling Project Research Group also published their final report on risk factors for coronary heart disease [5]. But the information that they gathered from five prospective cohort studies in the U.S. included only data for men, and only those aged 40-64 years. What are perhaps our most precise estimates of the effects of major risk factors on the incidence of coronary heart disease thus exclude the elderly. Over the last several
961
962
BRUCEM. F%ATYet al.
decades, the research on heart disease-both epidemiologic studies and randomized trialshas focused on the middle-aged. In comparison, information about cardiovascular risk factors for the elderly remains scarce. It is nonetheless commonplace to read that risk factors for cardiovascular disease are weaker among the elderly than the middle-aged [3,6-81. The quotation that serves as the first headnote to this review is only one recent example. According to the interpretation offered by the Expert Panel, the risk of coronary heart disease among the elderly is only modestly related to the level of low-density-lipoprotein cholesterol, which is generally an even better predictor of coronary disease than total cholesterol [l]. Amid the intense national publicity about cholesterol reduction, then, the Expert Panel suggests that the elderly may experience little benefit from the new recommendations for screening, dietary changes, or the drug treatment of hypercholesterolemia. This is so despite the fact that more than half of the mortality among the elderly is the result of cardiovascular disease [9]. In this context, the notion that the strength of the association between risk factors and cardiovascular disease “diminishes with age” deserves our careful attention. This statement is equivalent to the observation that age modifies the effect of risk factors on the incidence of cardiovascular disease. But the presence of effect modification depends crucially upon the choice of a measure of effect-a choice that is often implicit in the selection of an additive or multiplicative model to estimate risk [2, 10-131. What Table
appears to be effect modification, for instance, from the point of view of a multiplicative model may well mean that an additive model nicely summarizes the individual and joint effects of the independent variables in the model. The rule of parsimony argues for using the simpler model. In this article, we review briefly the concepts of additive and multiplicative statistical models, which are important to discussions of effect modification. These models represent the two traditional methods of summarizing data. In the results section, we apply these ideas to the available data on the major risk factors for incident cardiovascular disease among the elderly, and our purpose here is to examine which model most simply characterizes how smoking, cholesterol, and high blood pressure influence the incidence of these diseases across age groups. The last section discusses the consequences of our observations for the study and prevention of cardiovascular disease in the elderly. METHODS
Additive and multiplicative models One of the differences between additive and multiplicative models is the scale on which the dependent variable is measured, and the traditional measures of risk operate on either an arithmetic or a logarithmic scale [2, 12, 131. In an additive model, the effect associated with a particular exposure is the difference in incidence rates between the exposed and the unexposed (Table 1). If no interaction terms are included, this risk difference is assumed to be the same
1. Additive and multiplicative models of disease incidence* (A) Two-factor model Risk factor A
Risk factor B
Absent
Present
I00 Iob
Absent Present
Ia0 I ab
(B) Summary of additive and multiplicative measures of risk Factor A
Risk difference
RD, = I,, - I00 =
Risk ratio
I,,
-
RR, = L/I,, =
l,b/lob
Factors A and B
Factor B
Measure of risk
I,,
RD, = I,, - I,, =
Ia,
-
I,
RR, = Ios/Ioo =
lab/lao
RD,b = =
RR,, = =
Ia,
-
10,
RD, + RD, l,b/l,
RR, z RR,
*I, = incidence in those exposed neither to factor A nor to factor B; I,, = incidence in those exposed to factor A but not factor B; I,, = incidence in those exposed to factor B but not to factor A; I,, = incidence in those exposed to both factors A and B; RD, = risk difference for factor A; RD, = risk difference for factor B; RD,, = risk difference for factors A and B; RR, = risk ratio for factor A; RR, = risk ratio for factor B; RR,, = risk ratio for factors A and B. We assume that al1 four groups have the same distribution of risk factors other than A and B.
Cardiovascular Risk Factors in the Elderly
regardless of the levels of other risk factors. The multiplicative model expresses the effect of an exposure as the ratio of the incidence of disease in the exposed to the incidence of disease in the unexposed. Here, a risk factor increases the likelihood of disease by an amount, the risk ratio, that is assumed to be constant across the levels of the other risk factors. These two measures. of association, risk difference and risk ratio, emphasize different aspects of an effect. The risk difference is a measure of the excess incidence of disease experienced by those who are exposed to the risk factor; and this statistic highlights, for the exposed group, the burden of disease over and above the incidence in an unexposed group. In contrast, the risk ratio is a unit-free measure of how many times more (or less) likely the disease is among the exposed than the unexposed. Additive and multiplicative models differ in their scale of measurement, and the difference is most apparent in the way that they represent the joint effect of several exposures when only the main effects are included in the model. In the two-factor example of Table 1, the joint effect of two risk factors is modeled either as the sum of the risk differences or as the product of the risk ratios associated with their individual effects. Insofar as the observed joint effect of the two risk factors is, for instance, the sum of their risk differences, then the data satisfy the assumptions of a simple additive model with no interactions. For either model, if the joint effect is considerably more or less than predicted, then we have an instance of effect modification. In other words, effect modification depends importantly on the choice of the underlying model [l 11. Data that satisfy the assumptions of one model will, if the sample be large enough, evidence effect modification in the other model except in the trivial case of no effect of at least one of the two factors on risk. This brief discussion has focused on the two traditional models in epidemiology. The additive and multiplicative models are the most commonly used methods of describing the potential relationships between risk factors and disease incidence. Breslow and Storer have proposed a family of parametric models that estimate risk on a scale ranging from subadditive to supramultiplicative [ 131. Data from epidemiologic studies are subject to variation from a number of sources, and we expect any estimate of the joint effect of two risk factors to exhibit variability. This variability often makes it
963
difficult to detect the presence of effect modification and, thus, determine whether the underlying structure of the data is likely to be additive or multiplicative. As Breslow and Storer point out, showing statistically that one model is superiortoanotheroftenrequireslargedatasets[13]. Subjects For the elderly, information is generally scarce about the risk of cardiovascular disease associated with cigarette smoking, high blood pressure, and elevated levels of cholesterol. Using Medline and available bibliographies 1141,we searched the literature for studies of the effects of these major risk factors on the incidence of coronary heart disease and stroke in the elderly. Because we were interested in estimating both risk differences and risk ratios for various age groups, the studies had to include enough information for us to determine the numbers of events and the age-specific incidences of disease in those exposed and those not exposed to the risk factor for each age group. These restrictions encouraged us to use data from cohort studies published in tabular form [15]. While, in a few instances, estimates were available from several cohort studies, we present the results of only one in our tables and indicate in the text how the other results may differ, if at all, from the ones that we discuss in detail. Statistical methoa3 The information from available studies included estimates of both incidence density and cumulative incidence. We used the maximumlikelihood approach to calculate pooled estimates of risk difference and risk ratio across the age strata. These maximum-likelihood estimates are efficient and minimally biased asymptotically. For incidence density and cumulative incidence [2], Rothman gives expressions for the first derivative of the relevant log-likelihood functions, which require iterative solution for the pooled estimates and, in some instances, for nuisance parameters as well. Rothman also describes the methods of obtaining the variances of the stratum-specific point estimates, the variances of the pooled estimates, and the likelihood-ratio tests for effect modification [2]. The null hypothesis of this test for effect modification is that the effect of a risk factor is uniform across all strata. For both risk differences and risk ratios, the result is a chi-squared statistic with degrees of freedom that are equal to one less than the number of strata.
964
BRUCEM. F%ATYet al.
RESULTS
In Tables 2-4, we summarize the risk of cardiovascular disease associated with cigarette smoking, high blood pressure, and elevated levels of cholesterol. For these three major risk factors, we have included separate sub-tables for coronary heart disease [Tables 2(A)-4(A)] and stroke [Tables 2(B)-4(B)]. Within each of the six sub-tables, we list the age-specific incidence of disease in both the exposed and the unexposed groups. The number of events used to calculate each rate appears in parentheses. These data enabled us to calculate the risk ratios, the risk differences, and their 95% confidence intervals not only for each of the various age strata but also for the pooled estimates. We include the results of the test for heterogeneity as well. Table 2 focuses on smoking and the risk of cardiovascular disease. For coronary heart disease in Table 2(A), the age-specific risk ratios decreased from 3.3 among those aged 35-44 years down to 1.1 among those 65-74 years and even to 0.8 among those aged 75-84 years in the Framingham Study [15]. This is the typical pattern of relative risks that are said to diminish
with age. The age-specific risk differences ranged from 0.9 to 4.4 for those less than 75. Among those aged 75-84, the incidence of coronary heart disease was actually higher among non-smokers than smokers with the result that the risk ratio was less than 1.0 and the risk difference is negative. The likelihood ratio test for heterogeneity provided strong evidence against a uniform relative risk across the 5 age strata. Despite a risk difference that was small for those aged 65-74, and despite a risk difference that was negative for the oldest group, these data from the Framingham Study were compatible with an additive model of risk differences. For the effect of smoking on the risk of stroke, Table 2(B) includes data from the Honolulu Heart Program [16]. Age was more finely stratified than in the example for coronary heart disease, and the oldest group included only those 65-69 years. The risk ratios diminished from 4.0 for the youngest to 1.4 for the eldest stratum. The incidence of stroke in both smokers and non-smokers increased steadily, however, from one 5-year age stratum to the next. The risk differences remained fairly constant
Table 2. Smoking and the risk of cardiovascular disease* (A) Annual incidence (per 1000) of coronary heart disease in men and women in the Framingham Heart Study (30-year follow-up): data from Table 1-13 in Ref. [15] Incidence (n) in Aee
Nonsmokers
354l 45-54 55-64 65-74 75-84
1.0 (8) 5.1 (88) 11.9 (284) 17. I (256) 25.5 (128)
Current smokers
RR
95%
3.3 (41) 8.3 (149) 16.4 (249) 18.0 (96) 19.7 (18)
3.3 1.6 1.4 1.1 0.8
1.6 1.2 1.2 0.8 0.5
Pooled estimate Chi-squared test for heterogeneity p-Value for chi-square with 4df
1.31
1.17 18.38 0.001
CI
RD
95%
CI
7.1 2.1 1.6 1.3 1.3
2.4 3.1 4.4 0.9 -5.8
1.1 1.4 2.0 -3.3 -17
3.6 4.8 6.8 5.2 5.6
1.47
2.76
1.85 5.40 0.248
3.67
*n = number of events; RR = risk ratio; RD = risk difference; CI = confidence interval; df = degrees of freedom. (B) The 12-year cumulative incidence (per 1000) of stroke from the Honolulu Heart Program: data from Ref. [16] Incidence (n) in Age 4549 50-54 55-59 60-64 6569
Nonsmokers
Current smokers
RR
95%
CI
RD
7.4 (7) 17.2 (26) 27.9 (26) 47.4 (37) 80.2 (21)
29.7 (26) 37.0 (46) 64.7 (41) 76.9 (40) 110.4(18)
4.0 2.2 2.3 1.6 1.4
2.0 1.3 1.4 1.0 0.8
8.2 3.5 3.7 2.5 2.5
22.3 19.8 36.7 29.5 30.2
2.01
1.59 5.93 0.204
2.52
24.1
Pooled estimate Chi-squared test for heterogeneity p-Value for &i-square with 4 df
95%
CI
9.7 7.2 15.7 2.5 -28
35 32 58 57 88
16.3 2.07 0.723
31.9
*n = number of events; RR = risk ratio; RD = risk difference; CI = confidence interval; df = degrees of freedom.
Cardiovascular Risk Factors in the Elderly
throughout the 5 age strata, and if age had any effect on the risk of stroke among smokers, these data suggest that it was to increase the risk slightly as measured on an additive scale-from about 20 to about 30 excess events per 1000 smokers. Neither of the tests for heterogeneity was statistically significant although the chisquared statistic suggests a better fit for the additive than the multiplicative model. Data from the Framingham Study were also more consistent with an additive model [15]. Table 3 focuses on the risk of coronary heart disease and stroke from high blood pressure [15]. Definite hypertension was defined as a systolic blood pressure of 160 mmHg or greater or a diastolic blood pressure of 95 mmHg or greater; and the comparison group had a blood pressure less than 140/90 mmHg. In Table 3(A), the age-specific risk ratios for coronary heart disease decreased from 5.3 down to 2.0 while the age-specific risk differences increased from 6.8 up to 16.8 across the 6 age strata. Neither of the tests for heterogeneity was statistically significant although the chi-squared statistic suggests that the data were more compatible with a
965
multiplicative than an additive model. The youngest age group, which included only 4.8% of the coronary events in this analysis, was responsible for most of the heterogeneity. For those aged 45-85, in whom the age-specific risk ratios ranged from 2.8 to 2.0, the chi-squared statistic for heterogeneity was 1.85 for the multiplicative model (p = 0.605) and 7.17 for the additive model (p = 0.067). Even for those 75-94 years, hypertension still doubled the risk of coronary heart disease. A multiplicative model probably best summarized these data. The incidence of stroke and TIA according to age and hypertensive status had a similar pattern [Table 3(B)]. The age-specific risk differences increased from 2.6 for those aged 44-55 to 23.0 for those aged 85-94, and the test for heterogeneity provided strong evidence against a uniform risk difference across the 5 age strata. For those aged 45-74, definite hypertension almost quadrupled the risk of cerebrovascular disease. Although the age-specific risk ratios did decline to 1.7 and 2.6 for those aged 75-84 and 85-94 years, respectively, the test for the heterogeneity of risk ratios did not reach the
Table 3. High blood pressure and the risk of cardiovascular disease* (A) Annual incidence (per 1000) of coronary heart disease in men and women in the Framingham Heart Study (30-year follow-up): data from Table 1-3B in Ref. [15] Incidence (n) in subjects with blood pressure Age
< 140/90
> 160195
RR
95%
CI
RD
95%
CI
3544 45-54 5564 65-74 75-84 85-94
1.6(22) 4.4 (87) 8.3 (152) 10.5 (77) 18.0 (33) 17.2 (2)
8.4 (14) 12.3 (66) 21.1 (167) 24.7 (121) 35.4 (57) 34.1 (3)
5.3 2.8 2.5 2.4 2.0 2.0
2.1 2.0 2.0 1.8 1.3 0.3
10.3 3.9 3.2 3.1 3.0 11.8
6.8 8.0 12.8 14.2 17.5 16.8
1.4 4.6 9.4 9.4 6.7
12 11 16 19 28 61
2.55 6.28 0.280
2.21
8.83 9.99 0.075
12.7
Pooled estimate Chi-squared test for heterogeneity p-Value for chi-square with 5 df
2.94
-21
10.8
*n = number of events; RR = risk ratio; RD = risk difference; CI = confidence interval; df = degrees of freedom. Blood pressure is given in mmHg. (B) Annual incidence (per 1000) of stroke and transient ischemic attack in men and women in the Framingham Heart Study (30-year follow-up): data from Table 13-3B in Ref. [15] Incidence (n) in subjects with blood pressure Age
< 140/90
> 160/95
RR
95%
CI
RD
95%
CI
45-54 5564 65-74 75-84 85-94
0.8 (16) 1.8 (27) 3.9 (32) 13.1 (28) 14.7 (2)
3.4 (19) 7.0 (60) 15.0 (85) 22.4 (43) 31.1(4)
4.3 4.0 3.8 1.7 2.6
2.2 2.5 2.6 1.1 0.5
8.4 6.3 5.8 2.7 14.0
2.6 5.3 11.1 9.2 23.0
0.5 3.3 8.0 1.1
4.7 7.2 14 17 63
3.26
2.58 8.96 0.062
Pooled estimate Chi-squared test for heterogeneity p-Value for chi-square with 4 df
4.14
5.36
-17 4.10 21.73 0.000
6.63
*n = number of events; RR = risk ratio; RD = risk difference; CI = confidence interval; df = degrees of freedom. Blood pressure is given in mmHg.
BRUCEM. PSATY et al.
966
Table 4. Cholesterol and the risk of cardiovascular disease* (A) Annual incidence (per 1000) of coronary heart disease in men and women in the Framingham Heart Study (30-year follow-up): data from Table l-4 in Ref. [15] Incidence (n) in subjects with serum cholesterol Age
< 205
2 265
RR
95%
CI
3544 45-54 5564 65-74 75-84 85-94
0.6 (4) 3.9 (30) 10.2 (79) 16.1 (65) 22.0 (33) 23.8 (3)
1.6 (20) 9.6 (79) 16.6 (182) 20.4 (120) 19.3 (26) 50.0 (2)
13.8 2.5 1.6 1.3 0.9 2.1
4.1 1.6 1.3 0.9 0.5 0.4
40.3 3.7 2.1 1.7 1.5 12.6
Pooled estimate Chi-squared test for heterogeneity p-Value for chi-square with 5 df
1.65
1.40 33.12 0.000
1.95
RD
95%
CI
7.1 5.1 6.4 4.4 -2.7 26.2
3.9 3.1 3.1 -1.0 -13 -38
10 8.2 9.7 9.6 8.2 90
5.93
4.33 3.11 0.582
7.52
*n = number of events; RR = risk ratio; RD = risk difference; CI = confidence interval; df = degrees of freedom. Cholesterol is given in units of mg/dl. (B) Annual incidence. (per 1000) of atherothrombotic brain infarction in men and women in the Framingham Heart Study (30-year follow-up): data from Table 14-4 in Ref. [15] Incidence (n) in subjects with serum cholesterol Age
< 205
,265
RR
95%
CI
45-54 55-64 65-74 75-84
0.6 (5) 1.7 (14) 5.8 (27) 14.7 (24)
1.5 (13) 1.9 (23) 3.5 (23) 5.0 (8)
2.4 1.1 0.6 0.3
0.8 0.6 0.3 0.2
6.7 2.2 1.0 0.8
0.76
0.54 11.89
Pooled estimate Chi-squared test for heterogeneity p-Value for chi-square with 3 df
0.008
1.06
RD
95%
0.9 0.2 -2.3 -9.7
-0.1 -0.9 -4.8 -17
0.37
- 0.47 14.11 0.003
CI 1.9 1.4 0.2 -2.8 0.98
*n = number of events; RR = risk ratio; RD = risk difference;CI = confidenceinterval;df = degrees of freedom. Cholesterol is given in units of mg/dl.
conventional level of statistical significance. In short, these data on hypertension and cerebrovascular disease were more compatible with a multiplicative than with an additive model. Table 4 focuses on the risk of cardiovascular disease associated with elevated levels of cholesterol. These data are again from the Framingham Heart Study [15]. In Table 4(A), the incidence of coronary heart disease is listed for those with a cholesterol level less than 205 mg/dl and for those with a level greater than or equal to 265 mg/dl. The pattern of risks from cholesterol was similar to the pattern of risk from smoking. The risk ratios declined from 13.8 for those aged 35-44 down to 0.9 for those aged 75-84, and the test for heterogeneity provided strong evidence against a uniform effect measured in terms of risk ratios. For the same age groups, the risk difference declined from 7.1 down to -2.7. Although the risk difference for those aged 75-84 years was negative, the 95% confidence interval was wide (- 13 to 8.2). In short, these data were statistically compatible with an additive model. Across all age groups, in other words, elevated levels of cholesterol appeared to increase the incidence of coronary
disease by 5.93 events per 1000 person years. Table 4(B) lists the incidence of atherothrombotic brain infarction in men and women in the Framingham Heart Study [ 151.Across the 4 age strata, the risk ratios declined from 2.4 down to 0.3 while the risk differences decreased from 0.9 down to -9.7. The tests for heterogeneity suggest that neither the additive nor the multiplicative model was appropriate. Measured on the additive or the multiplicative scale, the relationship between cholesterol and the risk of stroke reversed itself with advancing age. This is an example of effect modification that did not depend on the choice of the model. DISCUSSION
The purpose of this review was to characterize the relations among age, incidence, and the three major risk factors for cardiovascular disease. For each combination of risk factor and disease, we sought to determine which of the two traditional epidemiologic measures, risk differences or risk ratios, provided a better estimate of the effect of risk factors on the incidence of cardiovascular disease. Table 5
Cardiovascular Risk Factors in the Elderly Table 5. Relationship among incidence disease, age, and the major risk factors for cardiovascular disease* Risk factor Smoking Smoking Hypertension Hypertension Cholesterol Cholesterol
Outcome CHD Incidence Stroke Incidence CHD Incidence Stroke or TIA Incidence CHD Incidence ABI Incidence
Model Additive Additive Multiplicative Multiplicative Additive ?
*Abbreviations: CHD = coronary heart disease; TIA = transient ischemic attack; ABI = atherothrombotic brain infarction; ? =uncertain, since effect modification was present for both the additive and the multiplicative models using data from the Framingham Study [Table 4(B)].
summarizes the results. For coronary heart disease, the risks from smoking and elevated levels of cholesterol appeared to be best modeled in terms of risk differences; but the risk from hypertension was best modeled in terms of risk ratios. For cerebrovascular disease, a similar pattern emerged for smoking and hypertension. The risk from smoking was more compatible with an additive model, and the risk from hypertension more consistent with a multiplicative one. Regardless of the model, elevated levels of cholesterol did not appear to be a risk factor for atherothrombotic brain infarction in the Framingham Heart Study. We set out, in part, to examine the notion that the effects of risk factors for cardiovascular disease in the elderly diminish with age-a claim of effect modification. Age did appear, for instance, to modify the effect of smoking on the incidence of stroke when we described the effect in terms of risk ratios, which decreased from 4.0 to 1.4 across the 5 age strata [Table 2(B)]. Measured in terms of risk differences, on the other hand, the risk of stroke from smoking was approximately the same for all persons regardless of their age. Of course, the incidence of stroke increased dramatically with age even among those who did not smoke. From the point of view of a multiplicative model, age modified the effect of smoking on the risk of stroke not because the excess risk of stroke attributable to smoking declined with age but because the incidence of stroke in the nonsmokers rose so rapidly with age. The addition of a relatively constant risk difference to this increasing incidence among the non-smokers made the risk ratios for the older age groups decline toward 1.0. Summarizing these data in terms of a multiplicative model may actually complicate rather than clarify the association between smoking and stroke.
961
It is true that for smoking and the risk of stroke, the tests for heterogeneity only suggested that the additive model was superior to the multiplicative model. Neither test for heterogeneity was statistically significant. As Breslow and Storer have pointed out, however, it may be difficult to distinguish between additive and multiplicative models “unless the data are quite extensive” [13]. The tests for heterogeneity depend, in other words, importantly on sample size. The results of other studies are in general agreement with those that we have presented here [ 17-211. In two large cohort studies that examined cause-specific mortality among participants with or without a previous history of coronary disease [19,20], risk differences provide a better model of the association between smoking and mortality from coronary heart disease than do risk ratios for those 45-84 years of age. Similarly, data from the study of British male doctors done by Doll and Peto are consistent with an additive but not with a multiplicative model for the risk of ischemic heart disease mortality from smoking [21]. For those aged 65-74 years, the risk ratios for current smokers are generally in the range of 1.33-1.43; and for those aged 75-84, they are 1.08-1.17 [19-211. In the Framingham Study, however, smoking has not been clearly shown to increase the risk of an incident event of coronary heart disease among the elderly [22]. This sub-group finding may be explained in part by the nature of the association between smoking and coronary heart disease. Although alternative interpretations of the data from the Framingham Study are possible [23], the risk of coronary disease from smoking appears to be modeled better in terms of risk differences than risk ratios [Table 2(A)]. If an additive model is the best one, the lack of an association between smoking and coronary disease in the elderly may be largely the result of inadequate power, which depends importantly on the magnitude of the risk measured as a risk ratio. For instance, a case-control study using a two-sided alpha of 0.05 would require 3479 elderly cases and an equal number of elderly controls to detect a relative risk of 1.2 with 80% power if the prevalence of smoking is 15%. Even though the excess risk attributable to smoking may remain constant for all age strata, the increasing incidence of disease with age pushes the risk ratios toward 1.O for the elderly and, therefore, makes
968
BRUCEM. PSATY et al.
it difficult to detect an increase in risk if one is present. For hypertension, on the other hand, the risk ratios for stroke and coronary heart disease are generally 2.0 or greater for all persons regardless of their age, and studies designed to detect risk ratios of this size require only modest sample sizes. While hypertension is a well-established risk factor for cardiovascular disease among the elderly, the data for cholesterol are less convincing. Whether cholesterol is a risk factor for stroke at all remains an open question [24]. One recent report from the Honolulu Heart Program suggests that the curve describing the association between the stroke and cholesterol is J-shaped: in other words, those with the highest and lowest levels of cholesterol appear to be at increased risk of cerebrovascular disease [25]. Distinguishing between hemorrhagic and non-hemorrhagic strokes is likely to be important, and for most of the Framingham Study, this distinction was based on clinical grounds rather than evidence from computed tomography. Recent data from the MRFIT screenes suggest not only that high serum cholesterol levels are a risk factor for nonhemorrhagic stroke but also that low serum cholesterol levels may be a risk factor for intracranial hemorrhage and perhaps subarachnoid hemorrhage as well [26]. Such a pattern of associations might explain the Jshaped association between cholesterol and stroke noted in the Honolulu Heart Program. If data that satisfy an additive model make it difficult to demonstrate an association between the incidence of cardiovascular disease and smoking or cholesterol among the elderly, they also have important consequences for the prevention of cardiovascular disease in the elderly. Even though the risk ratios may diminish with age, the risk differences may remain constant. The pooled estimate of the excess incidence of coronary heart disease attributable to an elevated cholesterol is 5.93 events per 1000 person years [Table 4(A)]. If we have a safe, inexpensive, and effective therapy for elevated cholesterol levels, and if the efficacy and the yearly costs of treatment are independent of age, then the potential benefit of treating those over 65 years is the same, in terms of the absolute numbers of events prevented or postponed per 1000 person years, as it is for those under 65 years. From the point of view of public health [l 11, the elderly experience the same risk as the middle-aged, and, despite diminishing risk
ratios, they are no less likely to benefit from effective interventions. While data are scarce about cardiovascular risk factors among the elderly, we have even less information about the potential effects of various forms of treatment. For elevated levels of cholesterol, for instance, the randomized trials of primary prevention included only middleaged men [27-301. Although a pilot study is planned for the elderly [31], we do not have evidence from a randomized trial that diet or drug therapy for hypercholesterolemia reduces the risk of major disease endpoints in the elderly. Of course, we need to be cautious in generalizing to the elderly the results of the primary-prevention trials of drug therapy conducted in middle-aged men; but the dietary recommendations appear to be safe; and, based on an analysis of risk differences, the potential benefit of dietary therapy is likely to be as large in the elderly as in the middle aged. For high blood pressure, on the other hand, the evidence from randomized trials suggests that drug treatment does reduce morbidity and mortality among the elderly [32,33]. Since the data on the association between disease and hypertension generally satisfy a multiplicative model, the risk attributable to high blood pressure actually rises across the various age strata [Tables 3(A) and 3(B)]. The use of risk differences also facilitates the comparison of the excess incidence of coronary heart disease attributable to different risk factors such as elevated levels of blood pressure and cholesterol [Tables 3(A) and 4(A)]. Among the exposed within each age stratum, hypertension is responsible for more disease than hypercholesterolemia, and this difference in risk differences actually becomes more pronounced with advancing age. A full cost-benefit analysis would require, of course, taking into account the prevalence of the risk factors as well as the efficacy and the costs of various therapies for these two risk factors. CONCLUSION
For several reasons, it is the language of multiplicative models that dominates the literature of epidemiology and clinical medicine. First, risk ratios can be estimated from either cohort studies or from case-control studies; but we can directly estimate risk differences only from cohort studies, which are generally more expensive and less common than case-control
969
Cardiovascular Risk Factors in the Elderly
studies. Secondly, software for analyzing data with additive models, though available [13,34], is not yet in general use. Most of the conventional methods of multivariable analysisMantel-Haenszel analysis of stratified data [35], logistic regression [36], log-linear models [37] and the Cox proportional hazards model [38]assume a multiplicative model. The use of logistic regression in epidemiology is so common that effect modification often means deviation from the tacit, frequently unstated assumption of a multiplicative model. Statistical models enable us to summarize and recognize patterns in the results of epidemiologic studies, which are systematic collections of individual histories. The traditional model in epidemiology is multiplicative although others, such as the additive model, are available. Importantly, the initial choice of a statistical model frames the way in which we talk about estimates of risk and perceive the results of studies. In this article, we have focused on the three major risk factors for cardiovascular disease in the elderly. Using the available published data required that we treat each of the three major risk factors separately. Of course cardiovascular disease has multiple causes, and we cannot exclude the possibility that additional stratification might influence the statistical tests for heterogeneity. But our analysis of each of the risk factors alone revealed patterns of risk across various age groups that are similar to the published estimates adjusted for potential confounding factors [16, 18, 21,221. This review suggests that smoking and cholesterol appear to increase the risk of coronary heart disease in a manner that is consistent with an additive model. The risk of stroke from smoking also appears to be additive. The data for high blood pressure and cardiovascular disease, on the other hand, suggest a multiplicative model of disease incidence. The finding that high blood pressure doubles or triples the risk of cardiovascular disease is really quite remarkable since the incidence of disease itself increases sharply with age. Hypertension probably operates as a risk factor in a manner different from either smoking and cholesterol, and the differences among these risk factors may result from the various ways in which they affect the processes of atherosclerosis and thrombosis. To speak of risk ratios that “diminish with age” in this context may unfortunately minimize the risks associated with smoking and cholesterol among the elderly. For these risk factors,
the exposed groups experience an excess risk that is constant and independent of the incidence of disease in an age-matched comparison group. As the incidence of disease increases with age in the comparison group, proving that this constant risk difference is still a consequence of exposure to a risk factor becomes steadily more difficult. But it is no less important to do so since the benefit, measured as the excess incidence in the exposed population, is probably the same for all age groups. This preliminary review also suggests that the wider use of alternative models may be important for our understanding of risk factors for cardiovascular disease in the elderly. Acknowledgement-The research reported in this article was supported in part by a contract (NOl-HC-85079) from the National Heart, Lung and Blood Institute of the National Institutes of Health.
REFERENCES 1. The Expert Panel. Report of the National Cholesterol Education Program Expert Panel on detection, evaluation, and treatment of high blood cholesterol in adults. Arch Intern Med 1988; 148: 36-69. 2. Rothman KJ. Modem Epidemiology. Boston: Little, Brown; 1986. 3. Kannel WB, Gordon T. Evaluation of cardiovascular risk in the elderly: the Framingham Study. Bull NY Acad Med 1978; 54: 573-591. 4. Whelton PK, Klag MJ. Epidemiological considerations in the treatment of hypertension. Drugs 1986; 31 (Suppl. 4): 8-22. 5. The Pooling Project Research Group. Relationship of blood pressure, serum cholesterol, smoking habit, relative weight and ECG abnormalities to the incidence of major coronary events: final results of the pooling project. J Chron Dis 1978; 31: 201-306. 6. Abramson JH. Prevention of cardiovascular disease in the elderly. Public Health Rev 1985; 13: 165-233. 7. Gerstenblith G, Weisfeldt ML, Lakatta EG. Disorders of the heart. In: Andres R, Bierman EL, Hazzard WR, Eds. Prlociples of Geriatric Medicine. New York: McGraw Hill; 1985: 515-526. 8. Kannel WB. Brand FN. Cardiovascular risk factors in the elderly. in: Andres R, Bierman EL, Hazzard WR, Eds. Principles of Geriatric Medicine. New York: McGraw Hill; 1985: 104-119. 9. National Center for Health Statistics. Advance Report of Final Mortality Statistics, 1986. Monthly Vital Statistics Report, Vol. 37, No. 6, Suppl. DHHS Pub. No. (PHS) 88-l 120. Hyattsville, Maryland: National Center for Health Statistics; 1988. 10. Sara& R. Interaction and synergism. Am J Epidemiol 1980; 112: 465-466. 11. Rothman KJ, Greenland S, Walker AM. Concepts of interaction. Am J Epidemiol 1980; 112: 467-470. 12. Schlesselman JJ. Case-Control Studies: Design, Conduct, Analysis. New York: Oxford University Press; 1982. 13. Breslow NE, Storer BE. General relative risk functions for casecontrol studies. Am J Epidemiol 1985; 122: 149-162. 14. Wenger NK, Furberg CD, Pitt E, Eds. Coronary heart disease in the elderly. Working Conference on the
970
BRUCEM.
Recognition and Management of Coronary Heart Disease in the Elderly, National Institutes of Health, Bethesda, Md, U.S.A., 4-6 September 1985. New York: Elsevier; 1986. 15 Cupples LA, D’Agostino RB. Some risk factors related to the annual incidence of cardiovascular disease and death using pooled repeated biennial measurements: Framingham Heart Study, 30-year follow-up. Section 34. In: Kannel WB, Wolf PA, Garrison RJ, Eds. The Framingham Study: an Euidemiological .Investigation of C&diovascul& Disea&, NIH Publ. No. 87-2703. Bethesda: National Institutes of Health; 1987. 16 Abbott RD, Yin Y, Reed DM, Yano K. Risk of stroke in male cigarette smokers. N Engl J Med 1986; 315: 717-720. 17. Jajich CL, Ostfeld AM, Freeman DH. Smoking and coronary heart disease mortality in the elderly. JAMA 1984; 252: 283 l-2834. 18. Shinton R, Beevers G. Meta-analysis of relation between cigarette smoking and stroke. Br Med J 1989; 298: 789-794. 19. Kahn HA. The Dom study of smoking and mortality among US veterans: report on eight and one-half years of observation. In: Haenszel W, Ed. Epidemiological Approaches to the Study of Cancer and Other Chronic Diseases, National Cancer Institute Monograph, No. 19. Bethesda, Md: U.S. Dept of Health, Education and Welfare; 1966: 1-126. 20. Hammond EC. Smoking in relation to the death rates of one million men and women. In: Haenszel W, Ed. Epidemiological Approaches to the Study of Cancer and Other Chronic Diseases, National Cancer Institute Monograph, No. 19. Bethesda, Md: U.S. Dept of Health, Education and Welfare; 1966: 127-204. 21. Doll R, Peto R. Mortality in relation to smoking: 20 years’ observation on male British doctors. Br Med J 1976; 2: 1525-1536. 22. Gordon T, Kannel WB, McGee D. Death and coronary attacks in men after giving up cigarette smoking. Lancet 1974; 2: 1345-1348. 23. Seltzer CC. Framingham study data and “established wisdom” about cigarette smoking and coronary heart disease. J ClIn Euidemiol 1989: 42: 743-750. 24. Dyken ML, WoliPA, Barnett HJM et al. Risk factors in stroke: a statement for physicians by the subcommittee on risk factors and stroke of the stroke council. Stroke 1984; 15: 1105-1111. 25. Reed D, Yano K, Kagan A. Lipids and lipoproteins as predictors of coronary heart disease, stroke, and
PSAT%’ et al.
26.
27.
28.
29.
30.
31. 32.
33.
34.
35. 36. 37. 38.
cancer in the Honolulu Heart Program. Am J Med 1986; 80: 871-877. Iso H, Jacobs DR Jr, Wenworth D, Neaton JD, Cohen JD. and the MRFIT Research Grotto. Serum cholesterol levels and six-year mortality-from stroke in 350,977 men screened for the Multiple Risk Factor Intervention Trial. N Engl J Med 1989: 320: 904910. Report from the Committee of Principal Investigators. A cooperative trial in the primary prevention of ischaemic heart disease using clofibrate. Br Heart J 1978; 40: 1069-1118. Oliver MF, Heady JA, Morris JN, Cooper J, for the Committee of Principal Investigators. WHO cooperative trial on primary prevention of ischaemic heart disease with clofibrate to lower serum cholesterol: final mortality follow-up. Lancet 1984; 2: 600-604. Lipid Research Clinics Program. The Lipid Research Clinics Coronary Primary Prevention Trial results: I. Reduction in incidence of coronary heart disease. JAMA 1984; 251: 351-364. Frick MH, Elo 0, Haapa K et al. Helsinki Heart Study: primary prevention trial with gemfibrozil in middle-aged men with dyslipidemia. N Engl J Med 1987; 317: 1237-1245. Anonymous. HMG CoA reductase inhibitors in the elderly: pilot study (RFA 89-HL-06-H). NM Guide for Grants and Contracts 1989; 18(3): 4. Amery A, Birkenhager W, Brixko P, Bulpitt C, Clement D, Deruyttere M et al. Mortality and morbidity from the European Working Party on High Blood Pressure in the Elderly trial. Lancet 1985; i: 1350-1354. Amery A, Brixko R, Clement D et al. Efficacy of anti-hypertensive drug treatment according to age, sex, blood pressure, and previous cardiovascular disease in patients over the age of 60. Lancet 1986; 2: 589-595. EGRET: Epidemiological Graphics, Estimation, and Testing Package. Statistics and Epidemiology ResearchCorpora%on, Software Division, 909 NE 43rd, Suite 310. Seattle. WA 98105. U.S.A. Mantel N, Haenkzel W. Statistical aspects of the analysis of data from retrospective studies of disease. J Nat1 Cancer Inst 1959; 22: 719-748. McCullagh P, Nelder JA. Generalized Linear Models. London: Chapman and Hall; 1983. Fienberg SE. The Analysis of Cruss-classiIiedCategorlcal Data, 2nd edn. Cambridge, England: The MIT Press; 1980. Cox DR, Oakes D. Analysis of Survival Data. London: Chapman and Hall; 1984.
0895-4356/90 $3.00+ 0.00 Copyright0 1990Pergamon Press plc
1990
RISK RATIOS AND RISK DIFFERENCES IN ESTIMATING THE EFFECT OF RISK FACTORS FOR CARDIOVASCULAR DISEASE IN THE ELDERLY BRUCEM. P.sATY,‘*‘**THOMASD. KOEPSELL,~~~ TERI A. MANOLIO,~ W. T. LONGSTRETH JR,’ EDWARD H. WAGNER,~*~ PATRICIAW. WAHL~ and RICHARD A. KRONMAL~ Departments of ‘Medicine, 2Epidemiology, ‘Health Services, 4Biostatistics, University of Washington, Seattle, Wash., ‘Center for Health Studies, Group Health Cooperative of Puget Sound, Seattle, Wash. and 6National Heart Lung and Blood Institute, National Institutes of Health, Bethesda, Md, U.S.A. (Received in revised form 23 January 1990)
Abstract-This article reviews the nature of the effects of hypertension, smoking and cholesterol on the incidence of cardiovascular disease and emphasizes how these effects vary by age. In the Methods section, we discuss briefly the concepts of additive and multiplicative statistical models as tools for summarizing data. In the results section, we summarize available data on the association between incident stroke and coronary heart disease in the elderly and each of these major risk factors. The traditional multiplicative model parsimoniously characterizes the individual and joint effects of age and high blood pressure in terms of risk ratios; but, for smoking and cholesterol, an additive model appears to be the most parsimonious. We discuss the consequences of these observations for the study and prevention of cardiovascular disease in the elderly. Myocardial infarction Coronary heart disease mortality Cerebrovascular diseases Hypertension Smoking Cholesterol Risk factor Relative risk Risk difference Additive model Multiplicative model
“Patients 60 years of age and above are another issue. There is little direct clinical trial evidence on whether elderly patients will benefit from intervention, and the strength of the association between LDL-cholesterol and CHD diminishes with age.” The Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults, 1988 [l]
“Since there are two effect measures, the difference and ratio measures, . the concept of effect modification without further specification is too ambiguous to be useful as a description of nature.” Kenneth Rothman, 1986 [2]
INTRODUCTION
Between the beginning of the Framingham Study in 1948 and its first report of cardiovascular risk factors among the elderly in 1978 [3], the number of persons 65 years and over doubled *All correspondence should be addressed to: Bruce M. Psaty, MD, PhD, Dept of Medicine, ZA-60, Harborview Medical Center, 325 Ninth Avenue, Seattle, WA 98104, U.S.A. ce 43,9--H
in the U.S. [4]. In 1978, the Pooling Project Research Group also published their final report on risk factors for coronary heart disease [5]. But the information that they gathered from five prospective cohort studies in the U.S. included only data for men, and only those aged 40-64 years. What are perhaps our most precise estimates of the effects of major risk factors on the incidence of coronary heart disease thus exclude the elderly. Over the last several
961
962
BRUCEM. F%ATYet al.
decades, the research on heart disease-both epidemiologic studies and randomized trialshas focused on the middle-aged. In comparison, information about cardiovascular risk factors for the elderly remains scarce. It is nonetheless commonplace to read that risk factors for cardiovascular disease are weaker among the elderly than the middle-aged [3,6-81. The quotation that serves as the first headnote to this review is only one recent example. According to the interpretation offered by the Expert Panel, the risk of coronary heart disease among the elderly is only modestly related to the level of low-density-lipoprotein cholesterol, which is generally an even better predictor of coronary disease than total cholesterol [l]. Amid the intense national publicity about cholesterol reduction, then, the Expert Panel suggests that the elderly may experience little benefit from the new recommendations for screening, dietary changes, or the drug treatment of hypercholesterolemia. This is so despite the fact that more than half of the mortality among the elderly is the result of cardiovascular disease [9]. In this context, the notion that the strength of the association between risk factors and cardiovascular disease “diminishes with age” deserves our careful attention. This statement is equivalent to the observation that age modifies the effect of risk factors on the incidence of cardiovascular disease. But the presence of effect modification depends crucially upon the choice of a measure of effect-a choice that is often implicit in the selection of an additive or multiplicative model to estimate risk [2, 10-131. What Table
appears to be effect modification, for instance, from the point of view of a multiplicative model may well mean that an additive model nicely summarizes the individual and joint effects of the independent variables in the model. The rule of parsimony argues for using the simpler model. In this article, we review briefly the concepts of additive and multiplicative statistical models, which are important to discussions of effect modification. These models represent the two traditional methods of summarizing data. In the results section, we apply these ideas to the available data on the major risk factors for incident cardiovascular disease among the elderly, and our purpose here is to examine which model most simply characterizes how smoking, cholesterol, and high blood pressure influence the incidence of these diseases across age groups. The last section discusses the consequences of our observations for the study and prevention of cardiovascular disease in the elderly. METHODS
Additive and multiplicative models One of the differences between additive and multiplicative models is the scale on which the dependent variable is measured, and the traditional measures of risk operate on either an arithmetic or a logarithmic scale [2, 12, 131. In an additive model, the effect associated with a particular exposure is the difference in incidence rates between the exposed and the unexposed (Table 1). If no interaction terms are included, this risk difference is assumed to be the same
1. Additive and multiplicative models of disease incidence* (A) Two-factor model Risk factor A
Risk factor B
Absent
Present
I00 Iob
Absent Present
Ia0 I ab
(B) Summary of additive and multiplicative measures of risk Factor A
Risk difference
RD, = I,, - I00 =
Risk ratio
I,,
-
RR, = L/I,, =
l,b/lob
Factors A and B
Factor B
Measure of risk
I,,
RD, = I,, - I,, =
Ia,
-
I,
RR, = Ios/Ioo =
lab/lao
RD,b = =
RR,, = =
Ia,
-
10,
RD, + RD, l,b/l,
RR, z RR,
*I, = incidence in those exposed neither to factor A nor to factor B; I,, = incidence in those exposed to factor A but not factor B; I,, = incidence in those exposed to factor B but not to factor A; I,, = incidence in those exposed to both factors A and B; RD, = risk difference for factor A; RD, = risk difference for factor B; RD,, = risk difference for factors A and B; RR, = risk ratio for factor A; RR, = risk ratio for factor B; RR,, = risk ratio for factors A and B. We assume that al1 four groups have the same distribution of risk factors other than A and B.
Cardiovascular Risk Factors in the Elderly
regardless of the levels of other risk factors. The multiplicative model expresses the effect of an exposure as the ratio of the incidence of disease in the exposed to the incidence of disease in the unexposed. Here, a risk factor increases the likelihood of disease by an amount, the risk ratio, that is assumed to be constant across the levels of the other risk factors. These two measures. of association, risk difference and risk ratio, emphasize different aspects of an effect. The risk difference is a measure of the excess incidence of disease experienced by those who are exposed to the risk factor; and this statistic highlights, for the exposed group, the burden of disease over and above the incidence in an unexposed group. In contrast, the risk ratio is a unit-free measure of how many times more (or less) likely the disease is among the exposed than the unexposed. Additive and multiplicative models differ in their scale of measurement, and the difference is most apparent in the way that they represent the joint effect of several exposures when only the main effects are included in the model. In the two-factor example of Table 1, the joint effect of two risk factors is modeled either as the sum of the risk differences or as the product of the risk ratios associated with their individual effects. Insofar as the observed joint effect of the two risk factors is, for instance, the sum of their risk differences, then the data satisfy the assumptions of a simple additive model with no interactions. For either model, if the joint effect is considerably more or less than predicted, then we have an instance of effect modification. In other words, effect modification depends importantly on the choice of the underlying model [l 11. Data that satisfy the assumptions of one model will, if the sample be large enough, evidence effect modification in the other model except in the trivial case of no effect of at least one of the two factors on risk. This brief discussion has focused on the two traditional models in epidemiology. The additive and multiplicative models are the most commonly used methods of describing the potential relationships between risk factors and disease incidence. Breslow and Storer have proposed a family of parametric models that estimate risk on a scale ranging from subadditive to supramultiplicative [ 131. Data from epidemiologic studies are subject to variation from a number of sources, and we expect any estimate of the joint effect of two risk factors to exhibit variability. This variability often makes it
963
difficult to detect the presence of effect modification and, thus, determine whether the underlying structure of the data is likely to be additive or multiplicative. As Breslow and Storer point out, showing statistically that one model is superiortoanotheroftenrequireslargedatasets[13]. Subjects For the elderly, information is generally scarce about the risk of cardiovascular disease associated with cigarette smoking, high blood pressure, and elevated levels of cholesterol. Using Medline and available bibliographies 1141,we searched the literature for studies of the effects of these major risk factors on the incidence of coronary heart disease and stroke in the elderly. Because we were interested in estimating both risk differences and risk ratios for various age groups, the studies had to include enough information for us to determine the numbers of events and the age-specific incidences of disease in those exposed and those not exposed to the risk factor for each age group. These restrictions encouraged us to use data from cohort studies published in tabular form [15]. While, in a few instances, estimates were available from several cohort studies, we present the results of only one in our tables and indicate in the text how the other results may differ, if at all, from the ones that we discuss in detail. Statistical methoa3 The information from available studies included estimates of both incidence density and cumulative incidence. We used the maximumlikelihood approach to calculate pooled estimates of risk difference and risk ratio across the age strata. These maximum-likelihood estimates are efficient and minimally biased asymptotically. For incidence density and cumulative incidence [2], Rothman gives expressions for the first derivative of the relevant log-likelihood functions, which require iterative solution for the pooled estimates and, in some instances, for nuisance parameters as well. Rothman also describes the methods of obtaining the variances of the stratum-specific point estimates, the variances of the pooled estimates, and the likelihood-ratio tests for effect modification [2]. The null hypothesis of this test for effect modification is that the effect of a risk factor is uniform across all strata. For both risk differences and risk ratios, the result is a chi-squared statistic with degrees of freedom that are equal to one less than the number of strata.
964
BRUCEM. F%ATYet al.
RESULTS
In Tables 2-4, we summarize the risk of cardiovascular disease associated with cigarette smoking, high blood pressure, and elevated levels of cholesterol. For these three major risk factors, we have included separate sub-tables for coronary heart disease [Tables 2(A)-4(A)] and stroke [Tables 2(B)-4(B)]. Within each of the six sub-tables, we list the age-specific incidence of disease in both the exposed and the unexposed groups. The number of events used to calculate each rate appears in parentheses. These data enabled us to calculate the risk ratios, the risk differences, and their 95% confidence intervals not only for each of the various age strata but also for the pooled estimates. We include the results of the test for heterogeneity as well. Table 2 focuses on smoking and the risk of cardiovascular disease. For coronary heart disease in Table 2(A), the age-specific risk ratios decreased from 3.3 among those aged 35-44 years down to 1.1 among those 65-74 years and even to 0.8 among those aged 75-84 years in the Framingham Study [15]. This is the typical pattern of relative risks that are said to diminish
with age. The age-specific risk differences ranged from 0.9 to 4.4 for those less than 75. Among those aged 75-84, the incidence of coronary heart disease was actually higher among non-smokers than smokers with the result that the risk ratio was less than 1.0 and the risk difference is negative. The likelihood ratio test for heterogeneity provided strong evidence against a uniform relative risk across the 5 age strata. Despite a risk difference that was small for those aged 65-74, and despite a risk difference that was negative for the oldest group, these data from the Framingham Study were compatible with an additive model of risk differences. For the effect of smoking on the risk of stroke, Table 2(B) includes data from the Honolulu Heart Program [16]. Age was more finely stratified than in the example for coronary heart disease, and the oldest group included only those 65-69 years. The risk ratios diminished from 4.0 for the youngest to 1.4 for the eldest stratum. The incidence of stroke in both smokers and non-smokers increased steadily, however, from one 5-year age stratum to the next. The risk differences remained fairly constant
Table 2. Smoking and the risk of cardiovascular disease* (A) Annual incidence (per 1000) of coronary heart disease in men and women in the Framingham Heart Study (30-year follow-up): data from Table 1-13 in Ref. [15] Incidence (n) in Aee
Nonsmokers
354l 45-54 55-64 65-74 75-84
1.0 (8) 5.1 (88) 11.9 (284) 17. I (256) 25.5 (128)
Current smokers
RR
95%
3.3 (41) 8.3 (149) 16.4 (249) 18.0 (96) 19.7 (18)
3.3 1.6 1.4 1.1 0.8
1.6 1.2 1.2 0.8 0.5
Pooled estimate Chi-squared test for heterogeneity p-Value for chi-square with 4df
1.31
1.17 18.38 0.001
CI
RD
95%
CI
7.1 2.1 1.6 1.3 1.3
2.4 3.1 4.4 0.9 -5.8
1.1 1.4 2.0 -3.3 -17
3.6 4.8 6.8 5.2 5.6
1.47
2.76
1.85 5.40 0.248
3.67
*n = number of events; RR = risk ratio; RD = risk difference; CI = confidence interval; df = degrees of freedom. (B) The 12-year cumulative incidence (per 1000) of stroke from the Honolulu Heart Program: data from Ref. [16] Incidence (n) in Age 4549 50-54 55-59 60-64 6569
Nonsmokers
Current smokers
RR
95%
CI
RD
7.4 (7) 17.2 (26) 27.9 (26) 47.4 (37) 80.2 (21)
29.7 (26) 37.0 (46) 64.7 (41) 76.9 (40) 110.4(18)
4.0 2.2 2.3 1.6 1.4
2.0 1.3 1.4 1.0 0.8
8.2 3.5 3.7 2.5 2.5
22.3 19.8 36.7 29.5 30.2
2.01
1.59 5.93 0.204
2.52
24.1
Pooled estimate Chi-squared test for heterogeneity p-Value for &i-square with 4 df
95%
CI
9.7 7.2 15.7 2.5 -28
35 32 58 57 88
16.3 2.07 0.723
31.9
*n = number of events; RR = risk ratio; RD = risk difference; CI = confidence interval; df = degrees of freedom.
Cardiovascular Risk Factors in the Elderly
throughout the 5 age strata, and if age had any effect on the risk of stroke among smokers, these data suggest that it was to increase the risk slightly as measured on an additive scale-from about 20 to about 30 excess events per 1000 smokers. Neither of the tests for heterogeneity was statistically significant although the chisquared statistic suggests a better fit for the additive than the multiplicative model. Data from the Framingham Study were also more consistent with an additive model [15]. Table 3 focuses on the risk of coronary heart disease and stroke from high blood pressure [15]. Definite hypertension was defined as a systolic blood pressure of 160 mmHg or greater or a diastolic blood pressure of 95 mmHg or greater; and the comparison group had a blood pressure less than 140/90 mmHg. In Table 3(A), the age-specific risk ratios for coronary heart disease decreased from 5.3 down to 2.0 while the age-specific risk differences increased from 6.8 up to 16.8 across the 6 age strata. Neither of the tests for heterogeneity was statistically significant although the chi-squared statistic suggests that the data were more compatible with a
965
multiplicative than an additive model. The youngest age group, which included only 4.8% of the coronary events in this analysis, was responsible for most of the heterogeneity. For those aged 45-85, in whom the age-specific risk ratios ranged from 2.8 to 2.0, the chi-squared statistic for heterogeneity was 1.85 for the multiplicative model (p = 0.605) and 7.17 for the additive model (p = 0.067). Even for those 75-94 years, hypertension still doubled the risk of coronary heart disease. A multiplicative model probably best summarized these data. The incidence of stroke and TIA according to age and hypertensive status had a similar pattern [Table 3(B)]. The age-specific risk differences increased from 2.6 for those aged 44-55 to 23.0 for those aged 85-94, and the test for heterogeneity provided strong evidence against a uniform risk difference across the 5 age strata. For those aged 45-74, definite hypertension almost quadrupled the risk of cerebrovascular disease. Although the age-specific risk ratios did decline to 1.7 and 2.6 for those aged 75-84 and 85-94 years, respectively, the test for the heterogeneity of risk ratios did not reach the
Table 3. High blood pressure and the risk of cardiovascular disease* (A) Annual incidence (per 1000) of coronary heart disease in men and women in the Framingham Heart Study (30-year follow-up): data from Table 1-3B in Ref. [15] Incidence (n) in subjects with blood pressure Age
< 140/90
> 160195
RR
95%
CI
RD
95%
CI
3544 45-54 5564 65-74 75-84 85-94
1.6(22) 4.4 (87) 8.3 (152) 10.5 (77) 18.0 (33) 17.2 (2)
8.4 (14) 12.3 (66) 21.1 (167) 24.7 (121) 35.4 (57) 34.1 (3)
5.3 2.8 2.5 2.4 2.0 2.0
2.1 2.0 2.0 1.8 1.3 0.3
10.3 3.9 3.2 3.1 3.0 11.8
6.8 8.0 12.8 14.2 17.5 16.8
1.4 4.6 9.4 9.4 6.7
12 11 16 19 28 61
2.55 6.28 0.280
2.21
8.83 9.99 0.075
12.7
Pooled estimate Chi-squared test for heterogeneity p-Value for chi-square with 5 df
2.94
-21
10.8
*n = number of events; RR = risk ratio; RD = risk difference; CI = confidence interval; df = degrees of freedom. Blood pressure is given in mmHg. (B) Annual incidence (per 1000) of stroke and transient ischemic attack in men and women in the Framingham Heart Study (30-year follow-up): data from Table 13-3B in Ref. [15] Incidence (n) in subjects with blood pressure Age
< 140/90
> 160/95
RR
95%
CI
RD
95%
CI
45-54 5564 65-74 75-84 85-94
0.8 (16) 1.8 (27) 3.9 (32) 13.1 (28) 14.7 (2)
3.4 (19) 7.0 (60) 15.0 (85) 22.4 (43) 31.1(4)
4.3 4.0 3.8 1.7 2.6
2.2 2.5 2.6 1.1 0.5
8.4 6.3 5.8 2.7 14.0
2.6 5.3 11.1 9.2 23.0
0.5 3.3 8.0 1.1
4.7 7.2 14 17 63
3.26
2.58 8.96 0.062
Pooled estimate Chi-squared test for heterogeneity p-Value for chi-square with 4 df
4.14
5.36
-17 4.10 21.73 0.000
6.63
*n = number of events; RR = risk ratio; RD = risk difference; CI = confidence interval; df = degrees of freedom. Blood pressure is given in mmHg.
BRUCEM. PSATY et al.
966
Table 4. Cholesterol and the risk of cardiovascular disease* (A) Annual incidence (per 1000) of coronary heart disease in men and women in the Framingham Heart Study (30-year follow-up): data from Table l-4 in Ref. [15] Incidence (n) in subjects with serum cholesterol Age
< 205
2 265
RR
95%
CI
3544 45-54 5564 65-74 75-84 85-94
0.6 (4) 3.9 (30) 10.2 (79) 16.1 (65) 22.0 (33) 23.8 (3)
1.6 (20) 9.6 (79) 16.6 (182) 20.4 (120) 19.3 (26) 50.0 (2)
13.8 2.5 1.6 1.3 0.9 2.1
4.1 1.6 1.3 0.9 0.5 0.4
40.3 3.7 2.1 1.7 1.5 12.6
Pooled estimate Chi-squared test for heterogeneity p-Value for chi-square with 5 df
1.65
1.40 33.12 0.000
1.95
RD
95%
CI
7.1 5.1 6.4 4.4 -2.7 26.2
3.9 3.1 3.1 -1.0 -13 -38
10 8.2 9.7 9.6 8.2 90
5.93
4.33 3.11 0.582
7.52
*n = number of events; RR = risk ratio; RD = risk difference; CI = confidence interval; df = degrees of freedom. Cholesterol is given in units of mg/dl. (B) Annual incidence. (per 1000) of atherothrombotic brain infarction in men and women in the Framingham Heart Study (30-year follow-up): data from Table 14-4 in Ref. [15] Incidence (n) in subjects with serum cholesterol Age
< 205
,265
RR
95%
CI
45-54 55-64 65-74 75-84
0.6 (5) 1.7 (14) 5.8 (27) 14.7 (24)
1.5 (13) 1.9 (23) 3.5 (23) 5.0 (8)
2.4 1.1 0.6 0.3
0.8 0.6 0.3 0.2
6.7 2.2 1.0 0.8
0.76
0.54 11.89
Pooled estimate Chi-squared test for heterogeneity p-Value for chi-square with 3 df
0.008
1.06
RD
95%
0.9 0.2 -2.3 -9.7
-0.1 -0.9 -4.8 -17
0.37
- 0.47 14.11 0.003
CI 1.9 1.4 0.2 -2.8 0.98
*n = number of events; RR = risk ratio; RD = risk difference;CI = confidenceinterval;df = degrees of freedom. Cholesterol is given in units of mg/dl.
conventional level of statistical significance. In short, these data on hypertension and cerebrovascular disease were more compatible with a multiplicative than with an additive model. Table 4 focuses on the risk of cardiovascular disease associated with elevated levels of cholesterol. These data are again from the Framingham Heart Study [15]. In Table 4(A), the incidence of coronary heart disease is listed for those with a cholesterol level less than 205 mg/dl and for those with a level greater than or equal to 265 mg/dl. The pattern of risks from cholesterol was similar to the pattern of risk from smoking. The risk ratios declined from 13.8 for those aged 35-44 down to 0.9 for those aged 75-84, and the test for heterogeneity provided strong evidence against a uniform effect measured in terms of risk ratios. For the same age groups, the risk difference declined from 7.1 down to -2.7. Although the risk difference for those aged 75-84 years was negative, the 95% confidence interval was wide (- 13 to 8.2). In short, these data were statistically compatible with an additive model. Across all age groups, in other words, elevated levels of cholesterol appeared to increase the incidence of coronary
disease by 5.93 events per 1000 person years. Table 4(B) lists the incidence of atherothrombotic brain infarction in men and women in the Framingham Heart Study [ 151.Across the 4 age strata, the risk ratios declined from 2.4 down to 0.3 while the risk differences decreased from 0.9 down to -9.7. The tests for heterogeneity suggest that neither the additive nor the multiplicative model was appropriate. Measured on the additive or the multiplicative scale, the relationship between cholesterol and the risk of stroke reversed itself with advancing age. This is an example of effect modification that did not depend on the choice of the model. DISCUSSION
The purpose of this review was to characterize the relations among age, incidence, and the three major risk factors for cardiovascular disease. For each combination of risk factor and disease, we sought to determine which of the two traditional epidemiologic measures, risk differences or risk ratios, provided a better estimate of the effect of risk factors on the incidence of cardiovascular disease. Table 5
Cardiovascular Risk Factors in the Elderly Table 5. Relationship among incidence disease, age, and the major risk factors for cardiovascular disease* Risk factor Smoking Smoking Hypertension Hypertension Cholesterol Cholesterol
Outcome CHD Incidence Stroke Incidence CHD Incidence Stroke or TIA Incidence CHD Incidence ABI Incidence
Model Additive Additive Multiplicative Multiplicative Additive ?
*Abbreviations: CHD = coronary heart disease; TIA = transient ischemic attack; ABI = atherothrombotic brain infarction; ? =uncertain, since effect modification was present for both the additive and the multiplicative models using data from the Framingham Study [Table 4(B)].
summarizes the results. For coronary heart disease, the risks from smoking and elevated levels of cholesterol appeared to be best modeled in terms of risk differences; but the risk from hypertension was best modeled in terms of risk ratios. For cerebrovascular disease, a similar pattern emerged for smoking and hypertension. The risk from smoking was more compatible with an additive model, and the risk from hypertension more consistent with a multiplicative one. Regardless of the model, elevated levels of cholesterol did not appear to be a risk factor for atherothrombotic brain infarction in the Framingham Heart Study. We set out, in part, to examine the notion that the effects of risk factors for cardiovascular disease in the elderly diminish with age-a claim of effect modification. Age did appear, for instance, to modify the effect of smoking on the incidence of stroke when we described the effect in terms of risk ratios, which decreased from 4.0 to 1.4 across the 5 age strata [Table 2(B)]. Measured in terms of risk differences, on the other hand, the risk of stroke from smoking was approximately the same for all persons regardless of their age. Of course, the incidence of stroke increased dramatically with age even among those who did not smoke. From the point of view of a multiplicative model, age modified the effect of smoking on the risk of stroke not because the excess risk of stroke attributable to smoking declined with age but because the incidence of stroke in the nonsmokers rose so rapidly with age. The addition of a relatively constant risk difference to this increasing incidence among the non-smokers made the risk ratios for the older age groups decline toward 1.0. Summarizing these data in terms of a multiplicative model may actually complicate rather than clarify the association between smoking and stroke.
961
It is true that for smoking and the risk of stroke, the tests for heterogeneity only suggested that the additive model was superior to the multiplicative model. Neither test for heterogeneity was statistically significant. As Breslow and Storer have pointed out, however, it may be difficult to distinguish between additive and multiplicative models “unless the data are quite extensive” [13]. The tests for heterogeneity depend, in other words, importantly on sample size. The results of other studies are in general agreement with those that we have presented here [ 17-211. In two large cohort studies that examined cause-specific mortality among participants with or without a previous history of coronary disease [19,20], risk differences provide a better model of the association between smoking and mortality from coronary heart disease than do risk ratios for those 45-84 years of age. Similarly, data from the study of British male doctors done by Doll and Peto are consistent with an additive but not with a multiplicative model for the risk of ischemic heart disease mortality from smoking [21]. For those aged 65-74 years, the risk ratios for current smokers are generally in the range of 1.33-1.43; and for those aged 75-84, they are 1.08-1.17 [19-211. In the Framingham Study, however, smoking has not been clearly shown to increase the risk of an incident event of coronary heart disease among the elderly [22]. This sub-group finding may be explained in part by the nature of the association between smoking and coronary heart disease. Although alternative interpretations of the data from the Framingham Study are possible [23], the risk of coronary disease from smoking appears to be modeled better in terms of risk differences than risk ratios [Table 2(A)]. If an additive model is the best one, the lack of an association between smoking and coronary disease in the elderly may be largely the result of inadequate power, which depends importantly on the magnitude of the risk measured as a risk ratio. For instance, a case-control study using a two-sided alpha of 0.05 would require 3479 elderly cases and an equal number of elderly controls to detect a relative risk of 1.2 with 80% power if the prevalence of smoking is 15%. Even though the excess risk attributable to smoking may remain constant for all age strata, the increasing incidence of disease with age pushes the risk ratios toward 1.O for the elderly and, therefore, makes
968
BRUCEM. PSATY et al.
it difficult to detect an increase in risk if one is present. For hypertension, on the other hand, the risk ratios for stroke and coronary heart disease are generally 2.0 or greater for all persons regardless of their age, and studies designed to detect risk ratios of this size require only modest sample sizes. While hypertension is a well-established risk factor for cardiovascular disease among the elderly, the data for cholesterol are less convincing. Whether cholesterol is a risk factor for stroke at all remains an open question [24]. One recent report from the Honolulu Heart Program suggests that the curve describing the association between the stroke and cholesterol is J-shaped: in other words, those with the highest and lowest levels of cholesterol appear to be at increased risk of cerebrovascular disease [25]. Distinguishing between hemorrhagic and non-hemorrhagic strokes is likely to be important, and for most of the Framingham Study, this distinction was based on clinical grounds rather than evidence from computed tomography. Recent data from the MRFIT screenes suggest not only that high serum cholesterol levels are a risk factor for nonhemorrhagic stroke but also that low serum cholesterol levels may be a risk factor for intracranial hemorrhage and perhaps subarachnoid hemorrhage as well [26]. Such a pattern of associations might explain the Jshaped association between cholesterol and stroke noted in the Honolulu Heart Program. If data that satisfy an additive model make it difficult to demonstrate an association between the incidence of cardiovascular disease and smoking or cholesterol among the elderly, they also have important consequences for the prevention of cardiovascular disease in the elderly. Even though the risk ratios may diminish with age, the risk differences may remain constant. The pooled estimate of the excess incidence of coronary heart disease attributable to an elevated cholesterol is 5.93 events per 1000 person years [Table 4(A)]. If we have a safe, inexpensive, and effective therapy for elevated cholesterol levels, and if the efficacy and the yearly costs of treatment are independent of age, then the potential benefit of treating those over 65 years is the same, in terms of the absolute numbers of events prevented or postponed per 1000 person years, as it is for those under 65 years. From the point of view of public health [l 11, the elderly experience the same risk as the middle-aged, and, despite diminishing risk
ratios, they are no less likely to benefit from effective interventions. While data are scarce about cardiovascular risk factors among the elderly, we have even less information about the potential effects of various forms of treatment. For elevated levels of cholesterol, for instance, the randomized trials of primary prevention included only middleaged men [27-301. Although a pilot study is planned for the elderly [31], we do not have evidence from a randomized trial that diet or drug therapy for hypercholesterolemia reduces the risk of major disease endpoints in the elderly. Of course, we need to be cautious in generalizing to the elderly the results of the primary-prevention trials of drug therapy conducted in middle-aged men; but the dietary recommendations appear to be safe; and, based on an analysis of risk differences, the potential benefit of dietary therapy is likely to be as large in the elderly as in the middle aged. For high blood pressure, on the other hand, the evidence from randomized trials suggests that drug treatment does reduce morbidity and mortality among the elderly [32,33]. Since the data on the association between disease and hypertension generally satisfy a multiplicative model, the risk attributable to high blood pressure actually rises across the various age strata [Tables 3(A) and 3(B)]. The use of risk differences also facilitates the comparison of the excess incidence of coronary heart disease attributable to different risk factors such as elevated levels of blood pressure and cholesterol [Tables 3(A) and 4(A)]. Among the exposed within each age stratum, hypertension is responsible for more disease than hypercholesterolemia, and this difference in risk differences actually becomes more pronounced with advancing age. A full cost-benefit analysis would require, of course, taking into account the prevalence of the risk factors as well as the efficacy and the costs of various therapies for these two risk factors. CONCLUSION
For several reasons, it is the language of multiplicative models that dominates the literature of epidemiology and clinical medicine. First, risk ratios can be estimated from either cohort studies or from case-control studies; but we can directly estimate risk differences only from cohort studies, which are generally more expensive and less common than case-control
969
Cardiovascular Risk Factors in the Elderly
studies. Secondly, software for analyzing data with additive models, though available [13,34], is not yet in general use. Most of the conventional methods of multivariable analysisMantel-Haenszel analysis of stratified data [35], logistic regression [36], log-linear models [37] and the Cox proportional hazards model [38]assume a multiplicative model. The use of logistic regression in epidemiology is so common that effect modification often means deviation from the tacit, frequently unstated assumption of a multiplicative model. Statistical models enable us to summarize and recognize patterns in the results of epidemiologic studies, which are systematic collections of individual histories. The traditional model in epidemiology is multiplicative although others, such as the additive model, are available. Importantly, the initial choice of a statistical model frames the way in which we talk about estimates of risk and perceive the results of studies. In this article, we have focused on the three major risk factors for cardiovascular disease in the elderly. Using the available published data required that we treat each of the three major risk factors separately. Of course cardiovascular disease has multiple causes, and we cannot exclude the possibility that additional stratification might influence the statistical tests for heterogeneity. But our analysis of each of the risk factors alone revealed patterns of risk across various age groups that are similar to the published estimates adjusted for potential confounding factors [16, 18, 21,221. This review suggests that smoking and cholesterol appear to increase the risk of coronary heart disease in a manner that is consistent with an additive model. The risk of stroke from smoking also appears to be additive. The data for high blood pressure and cardiovascular disease, on the other hand, suggest a multiplicative model of disease incidence. The finding that high blood pressure doubles or triples the risk of cardiovascular disease is really quite remarkable since the incidence of disease itself increases sharply with age. Hypertension probably operates as a risk factor in a manner different from either smoking and cholesterol, and the differences among these risk factors may result from the various ways in which they affect the processes of atherosclerosis and thrombosis. To speak of risk ratios that “diminish with age” in this context may unfortunately minimize the risks associated with smoking and cholesterol among the elderly. For these risk factors,
the exposed groups experience an excess risk that is constant and independent of the incidence of disease in an age-matched comparison group. As the incidence of disease increases with age in the comparison group, proving that this constant risk difference is still a consequence of exposure to a risk factor becomes steadily more difficult. But it is no less important to do so since the benefit, measured as the excess incidence in the exposed population, is probably the same for all age groups. This preliminary review also suggests that the wider use of alternative models may be important for our understanding of risk factors for cardiovascular disease in the elderly. Acknowledgement-The research reported in this article was supported in part by a contract (NOl-HC-85079) from the National Heart, Lung and Blood Institute of the National Institutes of Health.
REFERENCES 1. The Expert Panel. Report of the National Cholesterol Education Program Expert Panel on detection, evaluation, and treatment of high blood cholesterol in adults. Arch Intern Med 1988; 148: 36-69. 2. Rothman KJ. Modem Epidemiology. Boston: Little, Brown; 1986. 3. Kannel WB, Gordon T. Evaluation of cardiovascular risk in the elderly: the Framingham Study. Bull NY Acad Med 1978; 54: 573-591. 4. Whelton PK, Klag MJ. Epidemiological considerations in the treatment of hypertension. Drugs 1986; 31 (Suppl. 4): 8-22. 5. The Pooling Project Research Group. Relationship of blood pressure, serum cholesterol, smoking habit, relative weight and ECG abnormalities to the incidence of major coronary events: final results of the pooling project. J Chron Dis 1978; 31: 201-306. 6. Abramson JH. Prevention of cardiovascular disease in the elderly. Public Health Rev 1985; 13: 165-233. 7. Gerstenblith G, Weisfeldt ML, Lakatta EG. Disorders of the heart. In: Andres R, Bierman EL, Hazzard WR, Eds. Prlociples of Geriatric Medicine. New York: McGraw Hill; 1985: 515-526. 8. Kannel WB. Brand FN. Cardiovascular risk factors in the elderly. in: Andres R, Bierman EL, Hazzard WR, Eds. Principles of Geriatric Medicine. New York: McGraw Hill; 1985: 104-119. 9. National Center for Health Statistics. Advance Report of Final Mortality Statistics, 1986. Monthly Vital Statistics Report, Vol. 37, No. 6, Suppl. DHHS Pub. No. (PHS) 88-l 120. Hyattsville, Maryland: National Center for Health Statistics; 1988. 10. Sara& R. Interaction and synergism. Am J Epidemiol 1980; 112: 465-466. 11. Rothman KJ, Greenland S, Walker AM. Concepts of interaction. Am J Epidemiol 1980; 112: 467-470. 12. Schlesselman JJ. Case-Control Studies: Design, Conduct, Analysis. New York: Oxford University Press; 1982. 13. Breslow NE, Storer BE. General relative risk functions for casecontrol studies. Am J Epidemiol 1985; 122: 149-162. 14. Wenger NK, Furberg CD, Pitt E, Eds. Coronary heart disease in the elderly. Working Conference on the
970
BRUCEM.
Recognition and Management of Coronary Heart Disease in the Elderly, National Institutes of Health, Bethesda, Md, U.S.A., 4-6 September 1985. New York: Elsevier; 1986. 15 Cupples LA, D’Agostino RB. Some risk factors related to the annual incidence of cardiovascular disease and death using pooled repeated biennial measurements: Framingham Heart Study, 30-year follow-up. Section 34. In: Kannel WB, Wolf PA, Garrison RJ, Eds. The Framingham Study: an Euidemiological .Investigation of C&diovascul& Disea&, NIH Publ. No. 87-2703. Bethesda: National Institutes of Health; 1987. 16 Abbott RD, Yin Y, Reed DM, Yano K. Risk of stroke in male cigarette smokers. N Engl J Med 1986; 315: 717-720. 17. Jajich CL, Ostfeld AM, Freeman DH. Smoking and coronary heart disease mortality in the elderly. JAMA 1984; 252: 283 l-2834. 18. Shinton R, Beevers G. Meta-analysis of relation between cigarette smoking and stroke. Br Med J 1989; 298: 789-794. 19. Kahn HA. The Dom study of smoking and mortality among US veterans: report on eight and one-half years of observation. In: Haenszel W, Ed. Epidemiological Approaches to the Study of Cancer and Other Chronic Diseases, National Cancer Institute Monograph, No. 19. Bethesda, Md: U.S. Dept of Health, Education and Welfare; 1966: 1-126. 20. Hammond EC. Smoking in relation to the death rates of one million men and women. In: Haenszel W, Ed. Epidemiological Approaches to the Study of Cancer and Other Chronic Diseases, National Cancer Institute Monograph, No. 19. Bethesda, Md: U.S. Dept of Health, Education and Welfare; 1966: 127-204. 21. Doll R, Peto R. Mortality in relation to smoking: 20 years’ observation on male British doctors. Br Med J 1976; 2: 1525-1536. 22. Gordon T, Kannel WB, McGee D. Death and coronary attacks in men after giving up cigarette smoking. Lancet 1974; 2: 1345-1348. 23. Seltzer CC. Framingham study data and “established wisdom” about cigarette smoking and coronary heart disease. J ClIn Euidemiol 1989: 42: 743-750. 24. Dyken ML, WoliPA, Barnett HJM et al. Risk factors in stroke: a statement for physicians by the subcommittee on risk factors and stroke of the stroke council. Stroke 1984; 15: 1105-1111. 25. Reed D, Yano K, Kagan A. Lipids and lipoproteins as predictors of coronary heart disease, stroke, and
PSAT%’ et al.
26.
27.
28.
29.
30.
31. 32.
33.
34.
35. 36. 37. 38.
cancer in the Honolulu Heart Program. Am J Med 1986; 80: 871-877. Iso H, Jacobs DR Jr, Wenworth D, Neaton JD, Cohen JD. and the MRFIT Research Grotto. Serum cholesterol levels and six-year mortality-from stroke in 350,977 men screened for the Multiple Risk Factor Intervention Trial. N Engl J Med 1989: 320: 904910. Report from the Committee of Principal Investigators. A cooperative trial in the primary prevention of ischaemic heart disease using clofibrate. Br Heart J 1978; 40: 1069-1118. Oliver MF, Heady JA, Morris JN, Cooper J, for the Committee of Principal Investigators. WHO cooperative trial on primary prevention of ischaemic heart disease with clofibrate to lower serum cholesterol: final mortality follow-up. Lancet 1984; 2: 600-604. Lipid Research Clinics Program. The Lipid Research Clinics Coronary Primary Prevention Trial results: I. Reduction in incidence of coronary heart disease. JAMA 1984; 251: 351-364. Frick MH, Elo 0, Haapa K et al. Helsinki Heart Study: primary prevention trial with gemfibrozil in middle-aged men with dyslipidemia. N Engl J Med 1987; 317: 1237-1245. Anonymous. HMG CoA reductase inhibitors in the elderly: pilot study (RFA 89-HL-06-H). NM Guide for Grants and Contracts 1989; 18(3): 4. Amery A, Birkenhager W, Brixko P, Bulpitt C, Clement D, Deruyttere M et al. Mortality and morbidity from the European Working Party on High Blood Pressure in the Elderly trial. Lancet 1985; i: 1350-1354. Amery A, Brixko R, Clement D et al. Efficacy of anti-hypertensive drug treatment according to age, sex, blood pressure, and previous cardiovascular disease in patients over the age of 60. Lancet 1986; 2: 589-595. EGRET: Epidemiological Graphics, Estimation, and Testing Package. Statistics and Epidemiology ResearchCorpora%on, Software Division, 909 NE 43rd, Suite 310. Seattle. WA 98105. U.S.A. Mantel N, Haenkzel W. Statistical aspects of the analysis of data from retrospective studies of disease. J Nat1 Cancer Inst 1959; 22: 719-748. McCullagh P, Nelder JA. Generalized Linear Models. London: Chapman and Hall; 1983. Fienberg SE. The Analysis of Cruss-classiIiedCategorlcal Data, 2nd edn. Cambridge, England: The MIT Press; 1980. Cox DR, Oakes D. Analysis of Survival Data. London: Chapman and Hall; 1984.
