J CUn EpMemiol Vol. 44, No. 11, pp. 1187-l 196, 1991 Printed in GreatBritain. All rightsreserved
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STRATEGIES OF PREVENTION REVISITED: EFFECTS OF IMPRECISE MEASUREMENT OF RISK FACTORS ON THE EVALUATION OF “HIGH-RISK” AND “POPULATION-BASED” APPROACHES TO PREVENTION OF CARDIOVASCULAR DISEASE DAVID STRACHAN
and GEO~EY
ROSE
Department of Epidemiology and Population Sciences, London School of Hygiene and Tropical Medicine, Keppel Street, London WClE7HT, U.K. (Received in revised form 22 May 1991)
Abstract-Imprecise measurement of risk factors causes misclassification of individuals, limits sensitivity to detect those with high true levels, and dilutes associations between risk factors and disease. The implications of these effects for two particular examples were explored using data from a large prospective study relating plasma cholesterol to coronary heart disease (CHD) mortality and diastolic blood pressure (DBP) to fatal stroke. The absolute and relative effectiveness of three “high-risk” strategies of screening and treatment and a “population-based” shift in the risk factor distribution were compared, assuming different degrees of measurement error. The absolute benefits of each strategy were greater than suggested by unadjusted estimates from survey data. For cholesterol and CHD (a linear relationship in this cohort), uncorrected estimates tended to exaggerate the effectiveness of “high-risk” strategies relative to the “populationbased” approach. For DBP and stroke (an exponential relationship), the relative effectiveness of screening and treatment was underestimated if no allowance was made for measurement error. These findings are strictly applicable only to the middle-aged men from whom they were derived, but the effects of misclassification and regression dilution need to be considered in any assessment of preventive strategies. Prevention Screening
Cardiovascular
disease
Risk factors
INTRODUCTION
A high proportion of the morbidity and mortality statistically attributable to cardiovascular risk factors such as blood pressure [l] and serum cholesterol [2] arises not from the minority of the population with exceptionally high levels, but from the majority near to the mode of the distribution whose individual excess risk is *All correspondence should be addressed to: Dr Strachan, Department of Public Health Sciences, St George’s Hospital Medical School, Cranmer Terrace, London SW17 ORE, U.K.
Measurement
Reliability
small. This observation underlies the suggestion that a relatively small downward shift in the distribution of a risk factor throughout the population (the “population-based” strategy for prevention) might have unexpectedly large benefits by comparison with the identification and treatment of individuals in the upper tail of the distribution (the “high-risk” approach) V, 3941. Such comparisons are based upon risk factor distributions and dose-response relationships obtained from epidemiological studies where risk factors are usually measured on one
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DAVIDSTRACHAN and GEOFFREY ROSE
occasion only. Single measurements of physiological characteristics are likely to deviate from the long-term (true or “usual”) level for a given individual, because of technical errors in the measurement and variation in the true level within persons over time. This imprecision in the measurement of risk factors influences both their distribution and their association with disease outcomes [5-71, and therefore may have important consequences for the evaluation of preventive strategies. Treatment of individuals at high risk of disease is rarely recommended on the basis of a single measurement. Repeated measurements are obtained from subjects with high initial readings, and treatment is offered only to those with persistently high levels. Often, the readings display “regression to the mean”, whereby an initially extreme observation tends to become less abnormal with replication. Regression to the mean is part of a more general phenomenon of misclassification of individuals, which impairs the performance of any criteria chosen to define a “high-risk” group using an imprecisely measured characteristic [5]. A further consequence of measurement error is dilution (or “attenuation”) of the association between risk factor and disease, so that the doseresponse gradient for measured values is less steep than for true levels of the risk factor [5,6]. The precise nature of these effects depends upon the form of the measurement errors, the shape of the distribution of true values, and the
nature of their relationship to the disease outcome. There may be uncertainty concerning each of these. Predicting the consequences of imprecise measurements becomes mathematically complex except for a few specific circumstances [7J The most tractable case is where the risk factor is normally distributed with measurement errors which are also normally distributed with mean zero and variance independent of the true level of the characteristic. In these circumstances, when the dependent variable is a mean (or proportion) [7], or the logarithm of a person-time incidence rate [8], and is linearly related to true levels of a risk factor, the dose-response relationship to measured values is also linear, and the degree of attenuation of the slope is equal to the coefficient of reliability for the measurement (Fig. 1). There is some evidence that these conditions are approximated by, respectively, cholesterol and coronary heart disease, and blood pressure and stroke. Clinical trials [9-131 suggest that these specific associations of risk factor and disease are fairly rapidly reversible if levels of the risk factor are modified. We shall use these examples to illustrate the possible effect of imprecise risk factor assessment upon the benefits of “high-risk” and “population-based” strategies for prevention of cardiovascular disease. In formulating policy [13], these benefits need to be balanced against costs and risks, but these will not be considered further in this paper.
LEVEL OF RISK FACTOR Fig. 1. Dose-response relationship and distribution of true levels (solid lines) and measured levels (batched lines) of a hypothetical normally distributed risk factor, measured with reliability coefficient 0.5. The shaded area denotes the position within the measured risk factor distribution of subjects with levels in the top decile of the true distribution.
Measurement Error and Evaluation of Preventive Strategies METHODS
Single measurements of diastolic blood pressure (phase 4) and capillary blood cholesterol were included in a medical examination of male Whitehall civil servants during 1967-1969 [14]. Mortality during follow-up to 31 January 1987 was analysed in relation to risk factors measured at entry. The relationship between 18-year cumulative mortality from coronary heart disease (ICDS codes 410-414) and cholesterol level was modelled by an iteratively weighted linear regression, using weights inversely proportional to the variances of the fitted proportions. Stroke mortality (ICD8 430438) was modelled as an exponential function of diastolic blood pressure, adjusting for age at risk by proportional hazards regression. Each risk function (dose-response relationship) was then applied to a hypothetical population with a normal distribution of the relevant risk factor. The mean and variance of the distribution was adjusted in each case to the mean and variance of the corresponding distribution in the Whitehall study. Additive normal measurement errors of constant variance were assumed to apply for each risk factor. The error variance was chosen, in turn, to correspond to different levels of reliability, defined as the ratio of the true to the measured variance of a characteristic [7]. The dose-response relationship of cumulative coronary mortality to true cholesterol level was derived by dividing the linear regression coefficient for measured cholesterol by the reliability [7, 151. Prentice [8] has suggested that a similar procedure can be used to correct proportional hazards coefficients for attenuation. We confirmed by simulation that this approximation holds, even for reliability coefficients as low as 0.25. Accordingly, the association between the logarithm of the instantaneous (person-time) stroke mortality rate and true diastolic blood pressure was assumed to be linear, with a slope estimated by the coefficient from the proportional hazards model for the measured values divided by the reliability of blood pressure measurement. For each value of reliability, and each true level of the risk factor, the probability was calculated of the corresponding measured value falling within the top 10% and the top 25% of the measured risk factor distribution (Fig. 1). It was assumed for simplicity that the aim of a
1189
policy of screening and treatment would be to identify the individuals above a cut-off defined as the 90th percentile of the true risk factor distribution. Three “high-risk” strategies were then compared. In the first, all subjects in the top decile of the true distribution would be identified and offered treatment, regardless of their initial measurement. This approach maximizes the yield of screening but would involve repeated measurements on a large proportion of the population. In the second approach, only those with risk factor levels in the top 25% of the measured distribution would be followed up with repeated measurements, and treatment offered to those above the 90th percentile of the true distribution. The third strategy is similar, except that only the top 10% of the measured distribution would be asked to return for repeated measurements. The overall impact of each of these three “high-risk” strategies on mortality was estimated for various degrees of risk factor modification among those offered treatment, assuming that the whole population was covered by the screening programme and that risk factor reduction resulted in complete reversal of the corresponding disease risks. These public health effects were compared with the hypothetical result of various degrees of shift in the distribution of the risk factor throughout the population (the “population-based” approach), again assuming complete reversibility of the association between risk factor and disease. The particular findings derived from this cohort of middle-aged men will not necessarily apply to other populations or other combinations of risk factors and disease. However, the principles of the approach are generalizable. RESULTS
Distributions and risk functions for measured risk factors
Figures 2 and 3 show the distribution of plasma cholesterol and phase 4 diastolic blood pressure as measured among men aged 40-59 years at entry to the Whitehall study. These were based on 15,406 men with cholesterol measurements and 16,008 men with a recording of diastolic blood pressure. The distributions were unimodal with slight positive skew, but were not as highly skewed as a log-normal distribution. The corresponding normal distributions which have been used for subsequent simulation are superimposed.
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ROSE DAWD STRACIUN and GEOFFREY
2
3
4
5
7
6
8
9
PLASMA CHOLESTEROL (xtmol/l) Fig. 2. Distribution of measured plasma cholesterol levels among 15,406 Whitehall men aged 40-59 at entry (bars), and ll-year coronary heart disease mortality (squares) by level of measured cholesterol. The normal distribution and linear risk function assumed in subsequent analyses are superimposed.
Figure 2 also shows the relationship between measured cholesterol and cumulative 18-year coronary heart disease mortality among men aged 40-59 at entry. Overall, 1143 men died of coronary heart disease during follow-up. The risk function was approximately linear (x2 for goodness of fit = 24.4, df = 18), with a slope corresponding to an increase in 18-year mortality of 15.7 per 1000 men per mmol/l increase in cholesterol. Inclusion of a quadratic term for cholesterol did not significantly
40
50
60
70
80
DIASTOLIC
90
improve
the
fit
of
the
model
(x2 = 1.39,
df = 1).
The excess risk associated with raised cholesterol was fairly constant at different ages, favouring an additive model, rather than the more usual assumption of a multiplicative relationship. The regression coefficients for men aged 40-49, 50-54 and 55-59 at entry were, respectively, 13.8, 15.3 and 19.2 per 1000 increase in 18-year mortality per mmol/l increase in cholesterol. These should be compared with
100
110
BLOOD PRESSURE
120
130
140
(mIig)
Fig. 3. Distribution of measured diastolic blood pressure levels among 16,008 Whitehall men aged 4&59 at entry (bars), and 18-year stroke mortality (squares) by level of measured blood pressure. The normal distribution and exponential risk function assumed in subsequent analyses are superimposed.
Measurement Error and Evaluation of Preventive Strategies
the very different observed risks for men with average cholesterol in these age-groups: 42 per 1000,86 per 1000 and 124 per 1000, respectively. Men aged 60-64 at entry have been excluded because the coefficient for cholesterol in this group was substantially greater (32.7 per 1000 per mmol/l increase). Within the age-range 40-59 at entry, measured cholesterol was almost independent of age, blood pressure and cigarette smoking, so its additive relationship to coronary heart disease was assumed to be free of substantial confounding effects. Figure 3 shows the relationship between measured diastolic blood pressure and 18-year stroke mortality rates among men aged 40-59 at entry. The risk function, based on 183 deaths from stroke, was approximately exponential (x2 for goodness of fit = 12.0, df = 8) and appeared to be a multiplicative function of age-specific rates. A proportional hazards model was therefore fitted to adjust for age at risk and confirmed that the assumption of a log-linear relationship
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to measured diastolic blood pressure was appropriate (x2 for quadratic term = 1.02, df = 1). The proportional hazards regression coefficient was 0.435 per 10mmHg increase in measured diastolic blood pressure, this varying little with age within the range 40-59 at entry (test for x2 = 1.39, age-blood pressure interaction: df = 1). As with cholesterol, the coefficient for men aged 60-64 at entry was substantially different (0.319 per 10 mmHg) and this group was excluded from the analysis. Comparison of strategies for reduction of plasma cholesterol
Table 1 shows, for different degrees of reliability of cholesterol measurement, the distribution of cholesterol levels and the strength of the relationship between cholesterol and coronary heart disease mortality. The standard deviation of the true distribution is less than that of the measured distribution (Fig. 1) and the cut-off points defining the top and
Table 1. Effect of measurement error on the relationship between plasma cholesterol and fatal coronary heart disease Corrected for measurement error with reliability coefficient of: As measured
0.75
0.50
0.25
5.15 1.06 3.78 6.51
5.15 0.87 4.04 6.26
5.15 0.61 4.36 5.94
Distribution of plasma cholesterol (mmoljl)
Mean Standard deviation 10th percentile 90th percentile Dose-response
5.15 1.23 3.57 6.72
relationship with coronary heart disease
Overall 18-year CHD mortality (per 1000 men) CHD mortality difference (per 1000 men) per mmol/l increase in plasma cholesterol Ill-year CHD mortality (per 1000) in bottom decile Population attributable CHD mortality (per lOOO)* Proportion of attributable mortality in top decilet “High-risk”
0.5 mmol/l 0.75 mmol/l 1.Ommol/l
74.2 31.4
74.2 62.8
40.0 34.2 19.4%
34.7 39.5 19.4%
25.8 48.4 19.4%
5.8 68.4 19.4%
1.05 1.57 2.09
1.57 2.36 3.14
3.14 4.71 6.28
0.78 1.18 1.57
strategy 2: Identtfy and treat all from true top docile in top 25% of measured distribution
Proportion of true decile identified Reduction (per 1000) in 18-year CHD mortality per 1.Ommol/l reduction of cholesterol with treatment$ “High-risk”
74.2 20.9
strategy 1: bienttfy and treat all in top decile of true distribution
Reduction (per 1000) in ll-year CHD mortality assuming reduction of cholesterol with treatment3 of: “High-risk”
74.2 15.7
(100%)
89.9%
75.0%
62.8%
1.57
1.88
2.36
3.94
strategy 3: Identtfy and treat all from true top decile in top 10% of measured distribution
Proportion of true top decile identified Reduction (per 1000) in ll-year CHD mortality per 1.Ommol/l reduction of cholesterol with treatmentt “Population-based”
(100%)
62.9%
46.5%
38.4%
1.57
1.31
1.46
2.41
1.57 3.14 7.85
3.14 6.28 15.70
strategy: Shift entire distribution of cholesterol levels downward by ltfestyle change
Reduction (per 1000) in 18-year CHD _ ._ mortality . _ .assuming reduction of all cholesterol levels by:
0.05 mmol/l 0.1 mmol/l 0.25 mmol/l
0.78 1.57 3.92
1.05 2.09 5.23
*18-year CHD mortality in the whole population minus 18-year CHD mortality in the lowest decile. tProportion of population attributable mortality occurring among men in the top decile. SAverage reduction among all those offered treatment (taking into account acceptance and compliance). CE +4,11-E
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DAVID S~CHAN
bottom deciles therefore vary with the level of reliability assumed for the cholesterol measurement. The true dose-response gradient is steeper than it appears in the measured data, leading to underestimation of the proportion of deaths statistically attributable to raised cholesterol (population attributable mortality), unless correction is made for measurement error. Table 1 also shows, for each level of reliability, the estimated effects of the three “high-risk” strategies and various “populationbased” shifts upon cumulative 18-year mortality from coronary heart disease. The most effective “high-risk” strategy involves identifying all men in - the top decile of the distribution of true cholesterol. Measurement error results in underestimation, using observed data, of the attributable mortality in this group. However, the proportion of all the attributable deaths which occur in the top decile is unaffected by measurement error. Table 1 shows the reductions in coronary heart disease mortality that might be expected in the population as a whole, as a result of reductions in cholesterol levels of 0.5, 0.75 and 1.0 mmol/l (approximately 7, 11 and 15%, respectively) among the men in the top decile of risk who were all identified and offered treatment (“high-risk” strategy 1). The equivalent calculations for “high-risk” strategies 2 and 3 in Table 1 take into account the failure to detect all the men truly at high risk, when repeated measurements are restricted to a subgroup of the population. If 25% of men were followed up with repeated measurements, then this loss of sensitivity is more than offset by the steeper gradient of the risk function. However, if only 10% have repeated cholesterol measurements, then the public health benefits are slightly less than predicted from measured data, unless reliability is low. These reductions associated with policies of screening and treatment may be compared to the effect of a small decline in the cholesterol levels throughout the population, assuming a corresponding reduction in disease risks. Survey measurements suggest that the public health benefits of a “population-based” strategy that led to a 0.1 mmol/l (approximately 2%) decrease in cholesterol in all men would be comparable to a screen-and-treat policy that identified all individuals in the top decile of plasma cholesterol and achieved a reduction in their cholesterol levels of 1.0 mmol/l. As far as the optimal “high-risk” strategy is concerned,
and GEOFFIWROSE
this comparison is unaffected by measurement error, since the benefits of different degrees of cholesterol reduction are additive and independent of the level before modification. However, the relative effectiveness of the less sensitive policies of selective follow-up (“high-risk” strategies 2 and 3) is less than suggested by measured data. Comparison of strategies for reduction of blood pressure
Table 2 shows similar findings for the relationship between diastolic blood pressure and fatal stroke. The outcome here has been expressed as the hypothetical proportion of men dying of stroke during the 18 years of follow-up, in the absence of changes in mortality from other causes. Calculations based on observed data, without adjustment for measurement error, underestimate the strength of the association more seriously here than for cholesterol and heart disease, because the dose-response relationship rather than linear. The is exponential attributable mortality for men truly at high risk is greater than it appears in measured data, even when expressed as a proportion of the population attributable mortality (Table 2). The greater concentration of attributable mortality among men with high levels of blood pressure implies relatively greater potential benefits from the policy of screening and treatment. Thus, even if the sensitivity of the screening programme is limited, the benefits of the “highrisk” approach are greater than they appear in observed data, particularly when the reliability of measurement is low (Table 2). The estimates for the policies of selective follow-up make allowance for the fact that men with extremely high values are more likely to be detected as abnormal at initial screening than men with blood pressures just above the 90th percentile. These men at extremely high risk stand to benefit more, in absolute terms, from a constant proportional reduction in risk as a result of treatment. The relative effectiveness of the optimal “high-risk” strategy and the “populationbased” approach varies with the reliability of measurement, in contrast to the position for cholesterol and coronary heart disease. Thus, the most effective screen-and-treat policy which identified all men at high risk and achieved a 5 mmHg reduction in their diastolic blood pressure would be matched by the effects of a
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Measurement Error and Evaluation of Preventive Strategies Table 2. Effect of measurement error on the relationship between diastolic blood pressure and fatal stroke
Corrected for measurement error with reliability coefficient OE
Distribution
relationship
strategy
I: ldenttfy
84.1 13.5 66.8 101.4
84.1 11.7 69.2 99.1
84.1 9.5 71.9 96.4
84.1 6.8 75.5 92.8
11.44 1.79 1.81 9.63 37.4%
11.44 2.39 0.56 10.88 51.8%
11.44 5.70 0.006 11.43 89.7%
0.51 0.95 1.33
1.11 2.01 2.73
3.62 5.96 7.48
89.9%
75.0%
62.8%
0.91
1.70
5.34
11.44 1.55 3.05 8.39 31.5%
strategy
2.5 mmHg 5 mmHg 7.5 mmHg
strategy
(100%) 0.57
3: Identify and treat all from true top &cile in top 10% of measured distribution
Proportion of true top decile identified Reduction (per 1000) in Is-year stroke mortality for 5 mmHg reduction of DBP with treatment$ “Population-based”
0.30 0.57 0.82
2: Identtfy and treat all from true top docile in top 25% of measured distribution
Proportion of true top decile identified Reduction (per 1000) in Is-year stroke mortality for 5 mmHg reduction of DBP with treatmentt “High-risk”
0.25
and treat all in top decile of true distribution
Reduction (per 1000) in 18-year stroke mortality assuming reduction of DBP with treatmentz of: “High-risk”
0.50
with fatal stroke
Overall 18-year stroke mortality (per 1000 men) Stroke mortality ratio per 10 mmHg increase in DBP Is-year stroke mortality (per 1000 men) in bottom decile Population attributable stroke mortality (per lOOO)* Proportion of attributable mortality in top decilet “High-risk”
0.15
of phase 4 diastolic blood pressure (mmHg)
Mean Standard deviation 10th percentile 90th percentile Dose-response
As measured
strategy:
Shtft entire distribution
Reduction (per 1000) in ll-year stroke mortality assuming reduction of all diastolic pressures by:
(loo%)
62.9%
46.5%
38.4%
0.57
0.69
1.20
3.21
0.95 1.83 2.63 4.04
1.83 3.36 4.65 6.65
of blood pressure downward by ltfestyle change
1 mmHg 2 mmHg 3 mmHg 5 mmHg
0.49 0.95 1.40 2.24
0.64 1.25 1.83 2.88
l18-year stroke mortality in the whole population minus Is-year stroke mortality in the lowest decile. tproportion of population attributable mortality occurring among men in the top decile. fAverage reduction among all those offered treatment (taking into account acceptance and compliance).
downward shift of the whole blood pressure distribution of 1.2 mmHg (taking the measured data at face value), 1.5 mmHg (assuming reliability to be 0.75) or 2.2 mmHg (assuming reliability to be 0.5). Confidence limits for the estimates
The 95% confidence interval for the coefficient relating coronary heart disease mortality to measured cholesterol was 15.70 f 4.08 per 1000 men per mmol/l increase. Confidence limits for the estimates in Table 1 may therefore be derived from the published figures plus or minus 26%. The 95% confidence interval for the proportional hazards coefficient relating stroke mortality (on a logarithmic scale) to measured diastolic blood pressure is 0.435 + 0.084 per 10 mmHg increase. Approximate confidence limits for the estimates in Table 2 may therefore be derived from the published figures plus or minus 9% (e”.OW - 1).
A similar approach may be used with estimates of risk functions derived from other studies. For instance, the estimate used by MacMahon et al. [6] from pooled data relating measured diastolic blood pressure to stroke incidence lies close to (but below) the upper 95% confidence interval quoted above. Allowance for versibility
coverage,
compliance
and re-
The impact of preventive programmes is limited by incomplete coverage, poor acceptance of and compliance with treatment, and lack of reversibility of the relationship between risk factor and disease [16]. The estimates of benefit presented in the tables are based upon the average reduction in levels of each risk factor achieved among those offered treatment. This reduction reflects both the effectiveness of the treatment and the level of acceptance and compliance among truly high-risk men identified by screening.
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DAVIDSTRACIUNand Georwus
The estimates assume that the screening programme or population-based strategy covers the whole population and that relationships between the risk factors and mortality outcomes are wholly and rapidly reversible when risk factors are modified. These assumptions are unrealistically optimistic, but the benefits accruing under different conditions can easily be obtained by multiplying the results in the tables by the likely coverage and by the presumed degree of reversibility. DISCUSSION
Attenuation of dose-response
relationships
The dilution of associations and attenuation of regression coefficients by errors of measurement in the independent variable have long been recognized by statisticians [5,7, 15, 161and have recently been discussed more widely in an epidemiological context [6, 18, 191. Few longitudinal studies, however, have obtained the replicate measurements required to demonstrate this phenomenon in relation to disease incidence. Gardner and Heady [5] quote an example from a study of London busmen. The proportional increase in IO-year incidence of coronary heart disease was 19% per 10 mmHg increase in casual systolic blood pressure but 26% per 10 mmHg increase in the average of six blood pressure readings (which may be taken as a good approximation to true systolic blood pressure). More recently, MacMahon et al. [6] have used replicate measurements of diastolic blood pressure in the Framingham cohort to estimate the degree of attenuation of the log-linear association of diastolic blood pressure with coronary heart disease and stroke in pooled longitudinal data. They suggest a larger degree of attenuation than in the study of busmen: the proportional increase in age-adjusted coronary heart disease incidence being 19% per 6 mmHg increase in measured diastolic blood pressure but 32% per 6 mmHg increase in true diastolic pressure (recalculated from Ref. [6]). Reliability of risk factor measurement
We have made simplifying assumptions about the shape of the true risk factor distributions, the nature of the measurement errors and the mathematical form of the dose-response relationships. We have not made any assumptions about the magnitude of the errors, which influence the reliability of the measurement. These are likely to vary according to attention
Row
to protocol, technical advances, and the period of time over which a single measurement is taken to represent true level of a risk factor. The assumption of additive normal errors of constant variance may be questioned. In the Lipid Research Clinics study [20] and the Medical Research Council Mild Hypertension Trial [21], within-subject variability of cholesterol was greater in men with high measured levels, suggesting that the error variance might be proportional to the true value. This could account for part of the positive skew in the measured distribution seen here (Fig. 2) and elsewhere [21,22], but would tend to invalidate our simple procedure for correcting the slope of the dose-response relationship. The coefficient of variation over a 2-3 month period in the Lipid Research Clinics study was 8% [20], and over a 12-month period in the MRC Mild Hypertension Trial was 7% [21]. These are consistent with smaller studies under controlled dietary conditions [23]. Using this estimate, the short-term reliability of cholesterol measurement in the Whitehall study would be approximately 0.9. However, if a single measurement is to be taken as representative of a period of several years, the reliability is likely to be lower. In a large Swedish study [24], the reliability of cholesterol measurement at 6-week intervals was 0.74, but at an interval of 2 years this fell to 0.66. The early work of Armitage et al. [17] suggested a within-subject standard deviation of about 6 mmHg for diastolic blood pressures measured annually over 4 years. This would imply a reliability of 0.80 for the distribution of measured values in the Whitehall study. The factor used by MacMahon et al. [6] to adjust for attenuation was 1.6, implying a reliability of 0.625 (= l/l .6). Prentice [8] derived a reliability of 0.36 for survey measurements of diastolic blood pressure in women. These wide discrepancies highlight the uncertainties involved in making quantitative adjustments of observed data for presumed measurement error in the absence of better information on within-person variability over a period of months and years. Cholesterol and coronary heart disease
The adoption of an additive, rather than a multiplicative model to describe the relationship between cholesterol and coronary heart disease is supported by data from the Pooling Project Research Group [25] and the Multiple Risk Factor Intervention Trial [26,27] showing that
Measurement Error and Evaluation of Preventive Strategies
excess risks remain more constant than relative risks when the effect of cholesterol is considered in different age-groups. However, neither model fits perfectly, and variation in the excess risk associated with a given level of cholesterol has been suggested as a basis for selective screening [28]. The MRFIT study showed an upwardly concave relationship between 6-year mortality from coronary heart disease and serum cholesterol [26]. However, cumulative mortality over a longer period of follow-up may be expected to more closely approximate the linear pattern assumed here, because increased all-cause mortality limits the period of risk among subject with higher levels. The approximately linear relationship between coronary heart disease mortality and measured cholesterol makes the “populationbased” strategy of prevention highly effective by comparison with the “high-risk” approach. This difference is reinforced by the practical problems of identifying all subjects truly at high risk (Table 1). Randomized trials of drug treatment for hyperlipidaemia have achieved reductions of between 8 and 13% in total cholesterol in the intervention group [29]. Although these comparisons with a placebotreated group may underestimate the reductions that are possible when pharmacological treatment is supplemented by dietary advice, compliance is likely to be lower in clinical practice. Furthermore, it is unlikely that all those who are offered treatment will accept it. These factors will limit the average degree of cholesterol reduction that can be achieved among the high-risk individuals identified by screening and follow-up. On the most optimistic assumption that all men with cholesterol levels above the true 90th percentile could be identified and treated, our calculations suggest that the resulting decrease in coronary heart disease mortality could be matched by the effect of a general downward shift of cholesterol levels by as little as l-2%. A similar conclusion can be reached from observed data. Estimation of the actual magnitude of such effects, however, depends upon the level of reliability assumed for the cholesterol measurements (Table 1). Blood pressure and stroke
The association between measured diastolic blood pressure and fatal stroke was close to log-linear, as reported by others [6]. This exponential dose-response relationship tends to
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make the “high-risk” approach more effective, because a greater proportion of the attributable cases are found among those with high measured values than is the case with a linear association. Opportunistic measurement of blood pressure is also better suited than cholesterol screening to obtaining repeated measurements on large sections of the population, which are required to identify all those with high true values. Randomized trials of pharmacological treatment for mild hypertension have achieved a mean reduction of 6.4 mmHg in diastolic blood pressure among the attenders [9]. The effect of treatment in clinical practice is likely to be closer to 5 mmHg. If the reliability of blood pressure measurement is in the range 0X5-0.8, as suggested above, then the most effective policy of screening and treatment could probably be matched by the preventive effect of a general downward shift of less than 2 mmHg. This is less than the change in diastolic blood pressure apparently resulting from migration between the north and south of Britain [30], and within the range that can be expected from modest dietary modifications can be expected from modest dietary modifications throughout a whole population [31,32]. Thus, even for this example which is well suited to a policy of screening and treatment, a “population-based” strategy of prevention could pay unexpectedly large dividends. CONCLUSIONS
Our analyses are intended to be illustrative rather than authoritative. A number of important assumptions have been made, not all of which may be justified. We have also shown that quantitative results may be extremely sensitive to these assumptions and to local circumstances. We hope that our simulations will encourage others to explore the nature and effects of measurement error in greater detail than was possible here. Nevertheless, these two specific examples illustrate general principles of broader relevance to public health. The results will be particularly applicable to situations where the distribution of a imprecisely measured risk factor, occupational or environmental exposure is approximately normal and a linear or log-linear dose-response relationship can be assumed. In an earlier discussion of preventive strategies [l], it was argued that small but widespread lifestyle changes, from which each
DAVIDS~CHAN and GEOFPREY ROSE
1196
individual gains little, may cumulate to produce substantial improvements in public health. We have shown here that the attributable (excess) risk among those with high levels of a risk factor is underestimated unless the dose-response relationship is corrected for measurement error. The potential benefits of small changes in levels of an imprecisely measured risk factor are also underestimated by uncorrected survey data. The relative effectiveness of different strategies may or may not be reliably indicated by unadjusted estimates based on epidemiological studies. The “high-risk” and “population-based” approaches to prevention are not mutually exclusive. Where risk factors are measured with error, each strategy is potentially more effective than it appears at first sight. However, misclassification of individuals may limit the effectiveness of a policy of screening to identify a subgroup at high risk.
REFERENCES 1. Rose G. Strategy of prevention: lessons from cardiovascular disease. Br Med J 1981; 282: 1847-1851. 2. Khaw KT, Rose G. Cholesterol screening programmes: how much potential benefit? Br Med J 1989; 299: 606-607. 3. Rose G. Sick individuals and sick populations. Jnt J Epidemiol 1985; 14: 32-38. 4. Gardner MJ, Heady JA. Some effects of within-person variability in epidemiological studies. J Cbron Dls 1973; 26: 781-795. 5. Kottke TE, Gatewood LC, Wu SC, Park HA. Preventing heart disease: is treating high risk sufficient? J Clln Epidemiol 1988; 11: 1083-1093. 6. MacMahon S, Peto R, Cutler J et al. Blood pressure, stroke and coronary heart disease. Part 1: prolonged differences in blood pressure: prospective observational studies corrected for the regression dilution bias. Lancet 1990; 335: 765-774. 7. Carol1 RI. Covariance analysis in generalized linear measurement error models. Stat Med 1989; 8: 1075-1093. 8. Prentice R. On the ability of blood pressure effects to explain the relation between oral contraceptives and cardiovascular disease. Am J Epidemiol 1988; 127: 213-219. 9. Collins R, Peto R, MacMahon S et al. Blood pressure, stroke and coronary heart disease. Part 2, short-term reductions in blood pressure: overview of randomised drug trials in their epidemiological context. Laacet 1990; 335: 827-838. 10. Peto R, Yusuf S, Collins R. Cholesterol-lowering trial results in their epidemiologic context. Clrcalatlon 1985; 72(Suppl. III): 451. 11. Muldoon MF, Manuck SB, Matthews KA. Lowering cholesterol concentrations and mortality: a quantitative review of primary prevention trials. Br Med J 1990; 301: 309-314. 12. Roussouw JE, Lewis B, Rillcind B. The value of lowering cholesterol after myocardial infarction. N Engl J Med 1990; 323: 1112-1119.
13. Naylor CD, Basinski A, Frank JW, Rachlis MM. Asymptomatic hypercholesterolaemia: a clinical policy review. J Clln Epldemlol 1990; 43: 1029-1121. 14. Reid DD, Brett GZ, Hamilton PJS, Jarrett RI, Keen H, Rose GA. Cardiorespiratory disease and diabetes among middle-aged male civil servants. A study of screening and intervention. Lmcet 1974, i: 469472. 15. Co&an WG. Errors of measurement in statistics. Teclmometrlca 1968; lo: 637-665. 16. Browner WS. Estimating the impact of risk factor modification programs. Am J Epidemlol 1986; 123: 143-153. 17. Armitage P, Fox W, Rose GA, Tinker CM. Variability of measurements of casual blood pressure. II: survey experience. Clla Sel 1966; 30: 337-344. 18. Heederik D, Miller BG. Weak associations in occupational epidemiology: adjustment for exposure estimation error. Int J Epidemlol 1988; ll(Supp1.): 970-974. 19. Freudenheim JL, Johnson NE, Wardrop RL. Nutrient misclassification: bias in the odds ratio and loss of power in the Mantel test for trend. Int J Epidemlol 1989; 18: 232-238. 20. Jacobs D, Barrett-Connor E. Re-test reliability of plasma cholesterol and triglycerides. The Lipid Research Clinics Prevalence Study. Am J Enideralol 1982; 116: 878-885. 21. Thompson SG, Pocock SJ. The variability of serum cholesterol measurements: implications for screening and monitoring. J Clln Epidemlol 1990; 43: 783-789. 22. Martin MJ, Hulley SB, Browner WS, Kulier LH, Wentworth D. Serum cholesterol, blood pressure and mortality: implications from a cohort of 361662 men. Laneet 1986; ii: 933-936. 23. Hegsted DM, Nicolosi RI. Individual variation in serum cholesterol levels. Pree Natl Acad Sci USA 1987; 84: 62596261. 24. Tomberg SA, Jakobsson KFS, Eklund GA. Stability and validity of a single serum cholesterol measurement in a prospective cohort study. Int J Epidemiol 1988; 17: 797-803. 25. Pooling Project Research Group. Relationship of blood pressure, serum cholesterol, smoking habit, relative weight and ECG abnormalities to incidence of major coronary events: Final report of the Pooling Project. J Chmn Dls 1978; 31: 201-306. 26. Kannel WB, Neaton JD, Wentworth D et al. Overall and coronary heart disease mortality rates in relation to major risk factors in 325348 men screened for MRFIT. Am Heart J 1986; 112: 825-836. 27. Silberbera JS. Estimating the benefits of cholesterol lowering:-are risk factors for coronary heart disease multiplicative? J CUn Epidemiol 1990; 43: 875-879. 28. Tunstall-Pedoe H. Who is for cholesterol testing? Br Med J 1989; 298: 1593-1594. 29. Levv RI. Blankenhom D. Davis CE er al. State of the art -review. AHA conference report on cholesterol. Workshop V: Intervention trials. Circulation 1989; 80: 740-743. 30. Elford J, Phillips A, Thomson AG, Shaper AG. Migration and geographic variations in blood pressure in Britain. Br Med J 1990; 300: 291-295. 31. Stamler J, Rose G, Stamler R, Elliott P, Dyer A, Marmot M. Intersalt study findings--public health and medical care implications. Hypertension 1989; 14: 570-577. 32. Law MR, Frost CD, Wald NJ. By how much does dietary salt reduction lower blood pressure? IIIAnalysis of data from trials of salt reduction. Br Med J 1991; 302: 819-824.
0895-4356/91
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Copyright 0 1991Pergamon Pressplc
STRATEGIES OF PREVENTION REVISITED: EFFECTS OF IMPRECISE MEASUREMENT OF RISK FACTORS ON THE EVALUATION OF “HIGH-RISK” AND “POPULATION-BASED” APPROACHES TO PREVENTION OF CARDIOVASCULAR DISEASE DAVID STRACHAN
and GEO~EY
ROSE
Department of Epidemiology and Population Sciences, London School of Hygiene and Tropical Medicine, Keppel Street, London WClE7HT, U.K. (Received in revised form 22 May 1991)
Abstract-Imprecise measurement of risk factors causes misclassification of individuals, limits sensitivity to detect those with high true levels, and dilutes associations between risk factors and disease. The implications of these effects for two particular examples were explored using data from a large prospective study relating plasma cholesterol to coronary heart disease (CHD) mortality and diastolic blood pressure (DBP) to fatal stroke. The absolute and relative effectiveness of three “high-risk” strategies of screening and treatment and a “population-based” shift in the risk factor distribution were compared, assuming different degrees of measurement error. The absolute benefits of each strategy were greater than suggested by unadjusted estimates from survey data. For cholesterol and CHD (a linear relationship in this cohort), uncorrected estimates tended to exaggerate the effectiveness of “high-risk” strategies relative to the “populationbased” approach. For DBP and stroke (an exponential relationship), the relative effectiveness of screening and treatment was underestimated if no allowance was made for measurement error. These findings are strictly applicable only to the middle-aged men from whom they were derived, but the effects of misclassification and regression dilution need to be considered in any assessment of preventive strategies. Prevention Screening
Cardiovascular
disease
Risk factors
INTRODUCTION
A high proportion of the morbidity and mortality statistically attributable to cardiovascular risk factors such as blood pressure [l] and serum cholesterol [2] arises not from the minority of the population with exceptionally high levels, but from the majority near to the mode of the distribution whose individual excess risk is *All correspondence should be addressed to: Dr Strachan, Department of Public Health Sciences, St George’s Hospital Medical School, Cranmer Terrace, London SW17 ORE, U.K.
Measurement
Reliability
small. This observation underlies the suggestion that a relatively small downward shift in the distribution of a risk factor throughout the population (the “population-based” strategy for prevention) might have unexpectedly large benefits by comparison with the identification and treatment of individuals in the upper tail of the distribution (the “high-risk” approach) V, 3941. Such comparisons are based upon risk factor distributions and dose-response relationships obtained from epidemiological studies where risk factors are usually measured on one
1187
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DAVIDSTRACHAN and GEOFFREY ROSE
occasion only. Single measurements of physiological characteristics are likely to deviate from the long-term (true or “usual”) level for a given individual, because of technical errors in the measurement and variation in the true level within persons over time. This imprecision in the measurement of risk factors influences both their distribution and their association with disease outcomes [5-71, and therefore may have important consequences for the evaluation of preventive strategies. Treatment of individuals at high risk of disease is rarely recommended on the basis of a single measurement. Repeated measurements are obtained from subjects with high initial readings, and treatment is offered only to those with persistently high levels. Often, the readings display “regression to the mean”, whereby an initially extreme observation tends to become less abnormal with replication. Regression to the mean is part of a more general phenomenon of misclassification of individuals, which impairs the performance of any criteria chosen to define a “high-risk” group using an imprecisely measured characteristic [5]. A further consequence of measurement error is dilution (or “attenuation”) of the association between risk factor and disease, so that the doseresponse gradient for measured values is less steep than for true levels of the risk factor [5,6]. The precise nature of these effects depends upon the form of the measurement errors, the shape of the distribution of true values, and the
nature of their relationship to the disease outcome. There may be uncertainty concerning each of these. Predicting the consequences of imprecise measurements becomes mathematically complex except for a few specific circumstances [7J The most tractable case is where the risk factor is normally distributed with measurement errors which are also normally distributed with mean zero and variance independent of the true level of the characteristic. In these circumstances, when the dependent variable is a mean (or proportion) [7], or the logarithm of a person-time incidence rate [8], and is linearly related to true levels of a risk factor, the dose-response relationship to measured values is also linear, and the degree of attenuation of the slope is equal to the coefficient of reliability for the measurement (Fig. 1). There is some evidence that these conditions are approximated by, respectively, cholesterol and coronary heart disease, and blood pressure and stroke. Clinical trials [9-131 suggest that these specific associations of risk factor and disease are fairly rapidly reversible if levels of the risk factor are modified. We shall use these examples to illustrate the possible effect of imprecise risk factor assessment upon the benefits of “high-risk” and “population-based” strategies for prevention of cardiovascular disease. In formulating policy [13], these benefits need to be balanced against costs and risks, but these will not be considered further in this paper.
LEVEL OF RISK FACTOR Fig. 1. Dose-response relationship and distribution of true levels (solid lines) and measured levels (batched lines) of a hypothetical normally distributed risk factor, measured with reliability coefficient 0.5. The shaded area denotes the position within the measured risk factor distribution of subjects with levels in the top decile of the true distribution.
Measurement Error and Evaluation of Preventive Strategies METHODS
Single measurements of diastolic blood pressure (phase 4) and capillary blood cholesterol were included in a medical examination of male Whitehall civil servants during 1967-1969 [14]. Mortality during follow-up to 31 January 1987 was analysed in relation to risk factors measured at entry. The relationship between 18-year cumulative mortality from coronary heart disease (ICDS codes 410-414) and cholesterol level was modelled by an iteratively weighted linear regression, using weights inversely proportional to the variances of the fitted proportions. Stroke mortality (ICD8 430438) was modelled as an exponential function of diastolic blood pressure, adjusting for age at risk by proportional hazards regression. Each risk function (dose-response relationship) was then applied to a hypothetical population with a normal distribution of the relevant risk factor. The mean and variance of the distribution was adjusted in each case to the mean and variance of the corresponding distribution in the Whitehall study. Additive normal measurement errors of constant variance were assumed to apply for each risk factor. The error variance was chosen, in turn, to correspond to different levels of reliability, defined as the ratio of the true to the measured variance of a characteristic [7]. The dose-response relationship of cumulative coronary mortality to true cholesterol level was derived by dividing the linear regression coefficient for measured cholesterol by the reliability [7, 151. Prentice [8] has suggested that a similar procedure can be used to correct proportional hazards coefficients for attenuation. We confirmed by simulation that this approximation holds, even for reliability coefficients as low as 0.25. Accordingly, the association between the logarithm of the instantaneous (person-time) stroke mortality rate and true diastolic blood pressure was assumed to be linear, with a slope estimated by the coefficient from the proportional hazards model for the measured values divided by the reliability of blood pressure measurement. For each value of reliability, and each true level of the risk factor, the probability was calculated of the corresponding measured value falling within the top 10% and the top 25% of the measured risk factor distribution (Fig. 1). It was assumed for simplicity that the aim of a
1189
policy of screening and treatment would be to identify the individuals above a cut-off defined as the 90th percentile of the true risk factor distribution. Three “high-risk” strategies were then compared. In the first, all subjects in the top decile of the true distribution would be identified and offered treatment, regardless of their initial measurement. This approach maximizes the yield of screening but would involve repeated measurements on a large proportion of the population. In the second approach, only those with risk factor levels in the top 25% of the measured distribution would be followed up with repeated measurements, and treatment offered to those above the 90th percentile of the true distribution. The third strategy is similar, except that only the top 10% of the measured distribution would be asked to return for repeated measurements. The overall impact of each of these three “high-risk” strategies on mortality was estimated for various degrees of risk factor modification among those offered treatment, assuming that the whole population was covered by the screening programme and that risk factor reduction resulted in complete reversal of the corresponding disease risks. These public health effects were compared with the hypothetical result of various degrees of shift in the distribution of the risk factor throughout the population (the “population-based” approach), again assuming complete reversibility of the association between risk factor and disease. The particular findings derived from this cohort of middle-aged men will not necessarily apply to other populations or other combinations of risk factors and disease. However, the principles of the approach are generalizable. RESULTS
Distributions and risk functions for measured risk factors
Figures 2 and 3 show the distribution of plasma cholesterol and phase 4 diastolic blood pressure as measured among men aged 40-59 years at entry to the Whitehall study. These were based on 15,406 men with cholesterol measurements and 16,008 men with a recording of diastolic blood pressure. The distributions were unimodal with slight positive skew, but were not as highly skewed as a log-normal distribution. The corresponding normal distributions which have been used for subsequent simulation are superimposed.
1190
ROSE DAWD STRACIUN and GEOFFREY
2
3
4
5
7
6
8
9
PLASMA CHOLESTEROL (xtmol/l) Fig. 2. Distribution of measured plasma cholesterol levels among 15,406 Whitehall men aged 40-59 at entry (bars), and ll-year coronary heart disease mortality (squares) by level of measured cholesterol. The normal distribution and linear risk function assumed in subsequent analyses are superimposed.
Figure 2 also shows the relationship between measured cholesterol and cumulative 18-year coronary heart disease mortality among men aged 40-59 at entry. Overall, 1143 men died of coronary heart disease during follow-up. The risk function was approximately linear (x2 for goodness of fit = 24.4, df = 18), with a slope corresponding to an increase in 18-year mortality of 15.7 per 1000 men per mmol/l increase in cholesterol. Inclusion of a quadratic term for cholesterol did not significantly
40
50
60
70
80
DIASTOLIC
90
improve
the
fit
of
the
model
(x2 = 1.39,
df = 1).
The excess risk associated with raised cholesterol was fairly constant at different ages, favouring an additive model, rather than the more usual assumption of a multiplicative relationship. The regression coefficients for men aged 40-49, 50-54 and 55-59 at entry were, respectively, 13.8, 15.3 and 19.2 per 1000 increase in 18-year mortality per mmol/l increase in cholesterol. These should be compared with
100
110
BLOOD PRESSURE
120
130
140
(mIig)
Fig. 3. Distribution of measured diastolic blood pressure levels among 16,008 Whitehall men aged 4&59 at entry (bars), and 18-year stroke mortality (squares) by level of measured blood pressure. The normal distribution and exponential risk function assumed in subsequent analyses are superimposed.
Measurement Error and Evaluation of Preventive Strategies
the very different observed risks for men with average cholesterol in these age-groups: 42 per 1000,86 per 1000 and 124 per 1000, respectively. Men aged 60-64 at entry have been excluded because the coefficient for cholesterol in this group was substantially greater (32.7 per 1000 per mmol/l increase). Within the age-range 40-59 at entry, measured cholesterol was almost independent of age, blood pressure and cigarette smoking, so its additive relationship to coronary heart disease was assumed to be free of substantial confounding effects. Figure 3 shows the relationship between measured diastolic blood pressure and 18-year stroke mortality rates among men aged 40-59 at entry. The risk function, based on 183 deaths from stroke, was approximately exponential (x2 for goodness of fit = 12.0, df = 8) and appeared to be a multiplicative function of age-specific rates. A proportional hazards model was therefore fitted to adjust for age at risk and confirmed that the assumption of a log-linear relationship
1191
to measured diastolic blood pressure was appropriate (x2 for quadratic term = 1.02, df = 1). The proportional hazards regression coefficient was 0.435 per 10mmHg increase in measured diastolic blood pressure, this varying little with age within the range 40-59 at entry (test for x2 = 1.39, age-blood pressure interaction: df = 1). As with cholesterol, the coefficient for men aged 60-64 at entry was substantially different (0.319 per 10 mmHg) and this group was excluded from the analysis. Comparison of strategies for reduction of plasma cholesterol
Table 1 shows, for different degrees of reliability of cholesterol measurement, the distribution of cholesterol levels and the strength of the relationship between cholesterol and coronary heart disease mortality. The standard deviation of the true distribution is less than that of the measured distribution (Fig. 1) and the cut-off points defining the top and
Table 1. Effect of measurement error on the relationship between plasma cholesterol and fatal coronary heart disease Corrected for measurement error with reliability coefficient of: As measured
0.75
0.50
0.25
5.15 1.06 3.78 6.51
5.15 0.87 4.04 6.26
5.15 0.61 4.36 5.94
Distribution of plasma cholesterol (mmoljl)
Mean Standard deviation 10th percentile 90th percentile Dose-response
5.15 1.23 3.57 6.72
relationship with coronary heart disease
Overall 18-year CHD mortality (per 1000 men) CHD mortality difference (per 1000 men) per mmol/l increase in plasma cholesterol Ill-year CHD mortality (per 1000) in bottom decile Population attributable CHD mortality (per lOOO)* Proportion of attributable mortality in top decilet “High-risk”
0.5 mmol/l 0.75 mmol/l 1.Ommol/l
74.2 31.4
74.2 62.8
40.0 34.2 19.4%
34.7 39.5 19.4%
25.8 48.4 19.4%
5.8 68.4 19.4%
1.05 1.57 2.09
1.57 2.36 3.14
3.14 4.71 6.28
0.78 1.18 1.57
strategy 2: Identtfy and treat all from true top docile in top 25% of measured distribution
Proportion of true decile identified Reduction (per 1000) in 18-year CHD mortality per 1.Ommol/l reduction of cholesterol with treatment$ “High-risk”
74.2 20.9
strategy 1: bienttfy and treat all in top decile of true distribution
Reduction (per 1000) in ll-year CHD mortality assuming reduction of cholesterol with treatment3 of: “High-risk”
74.2 15.7
(100%)
89.9%
75.0%
62.8%
1.57
1.88
2.36
3.94
strategy 3: Identtfy and treat all from true top decile in top 10% of measured distribution
Proportion of true top decile identified Reduction (per 1000) in ll-year CHD mortality per 1.Ommol/l reduction of cholesterol with treatmentt “Population-based”
(100%)
62.9%
46.5%
38.4%
1.57
1.31
1.46
2.41
1.57 3.14 7.85
3.14 6.28 15.70
strategy: Shift entire distribution of cholesterol levels downward by ltfestyle change
Reduction (per 1000) in 18-year CHD _ ._ mortality . _ .assuming reduction of all cholesterol levels by:
0.05 mmol/l 0.1 mmol/l 0.25 mmol/l
0.78 1.57 3.92
1.05 2.09 5.23
*18-year CHD mortality in the whole population minus 18-year CHD mortality in the lowest decile. tProportion of population attributable mortality occurring among men in the top decile. SAverage reduction among all those offered treatment (taking into account acceptance and compliance). CE +4,11-E
1192
DAVID S~CHAN
bottom deciles therefore vary with the level of reliability assumed for the cholesterol measurement. The true dose-response gradient is steeper than it appears in the measured data, leading to underestimation of the proportion of deaths statistically attributable to raised cholesterol (population attributable mortality), unless correction is made for measurement error. Table 1 also shows, for each level of reliability, the estimated effects of the three “high-risk” strategies and various “populationbased” shifts upon cumulative 18-year mortality from coronary heart disease. The most effective “high-risk” strategy involves identifying all men in - the top decile of the distribution of true cholesterol. Measurement error results in underestimation, using observed data, of the attributable mortality in this group. However, the proportion of all the attributable deaths which occur in the top decile is unaffected by measurement error. Table 1 shows the reductions in coronary heart disease mortality that might be expected in the population as a whole, as a result of reductions in cholesterol levels of 0.5, 0.75 and 1.0 mmol/l (approximately 7, 11 and 15%, respectively) among the men in the top decile of risk who were all identified and offered treatment (“high-risk” strategy 1). The equivalent calculations for “high-risk” strategies 2 and 3 in Table 1 take into account the failure to detect all the men truly at high risk, when repeated measurements are restricted to a subgroup of the population. If 25% of men were followed up with repeated measurements, then this loss of sensitivity is more than offset by the steeper gradient of the risk function. However, if only 10% have repeated cholesterol measurements, then the public health benefits are slightly less than predicted from measured data, unless reliability is low. These reductions associated with policies of screening and treatment may be compared to the effect of a small decline in the cholesterol levels throughout the population, assuming a corresponding reduction in disease risks. Survey measurements suggest that the public health benefits of a “population-based” strategy that led to a 0.1 mmol/l (approximately 2%) decrease in cholesterol in all men would be comparable to a screen-and-treat policy that identified all individuals in the top decile of plasma cholesterol and achieved a reduction in their cholesterol levels of 1.0 mmol/l. As far as the optimal “high-risk” strategy is concerned,
and GEOFFIWROSE
this comparison is unaffected by measurement error, since the benefits of different degrees of cholesterol reduction are additive and independent of the level before modification. However, the relative effectiveness of the less sensitive policies of selective follow-up (“high-risk” strategies 2 and 3) is less than suggested by measured data. Comparison of strategies for reduction of blood pressure
Table 2 shows similar findings for the relationship between diastolic blood pressure and fatal stroke. The outcome here has been expressed as the hypothetical proportion of men dying of stroke during the 18 years of follow-up, in the absence of changes in mortality from other causes. Calculations based on observed data, without adjustment for measurement error, underestimate the strength of the association more seriously here than for cholesterol and heart disease, because the dose-response relationship rather than linear. The is exponential attributable mortality for men truly at high risk is greater than it appears in measured data, even when expressed as a proportion of the population attributable mortality (Table 2). The greater concentration of attributable mortality among men with high levels of blood pressure implies relatively greater potential benefits from the policy of screening and treatment. Thus, even if the sensitivity of the screening programme is limited, the benefits of the “highrisk” approach are greater than they appear in observed data, particularly when the reliability of measurement is low (Table 2). The estimates for the policies of selective follow-up make allowance for the fact that men with extremely high values are more likely to be detected as abnormal at initial screening than men with blood pressures just above the 90th percentile. These men at extremely high risk stand to benefit more, in absolute terms, from a constant proportional reduction in risk as a result of treatment. The relative effectiveness of the optimal “high-risk” strategy and the “populationbased” approach varies with the reliability of measurement, in contrast to the position for cholesterol and coronary heart disease. Thus, the most effective screen-and-treat policy which identified all men at high risk and achieved a 5 mmHg reduction in their diastolic blood pressure would be matched by the effects of a
1193
Measurement Error and Evaluation of Preventive Strategies Table 2. Effect of measurement error on the relationship between diastolic blood pressure and fatal stroke
Corrected for measurement error with reliability coefficient OE
Distribution
relationship
strategy
I: ldenttfy
84.1 13.5 66.8 101.4
84.1 11.7 69.2 99.1
84.1 9.5 71.9 96.4
84.1 6.8 75.5 92.8
11.44 1.79 1.81 9.63 37.4%
11.44 2.39 0.56 10.88 51.8%
11.44 5.70 0.006 11.43 89.7%
0.51 0.95 1.33
1.11 2.01 2.73
3.62 5.96 7.48
89.9%
75.0%
62.8%
0.91
1.70
5.34
11.44 1.55 3.05 8.39 31.5%
strategy
2.5 mmHg 5 mmHg 7.5 mmHg
strategy
(100%) 0.57
3: Identify and treat all from true top &cile in top 10% of measured distribution
Proportion of true top decile identified Reduction (per 1000) in Is-year stroke mortality for 5 mmHg reduction of DBP with treatment$ “Population-based”
0.30 0.57 0.82
2: Identtfy and treat all from true top docile in top 25% of measured distribution
Proportion of true top decile identified Reduction (per 1000) in Is-year stroke mortality for 5 mmHg reduction of DBP with treatmentt “High-risk”
0.25
and treat all in top decile of true distribution
Reduction (per 1000) in 18-year stroke mortality assuming reduction of DBP with treatmentz of: “High-risk”
0.50
with fatal stroke
Overall 18-year stroke mortality (per 1000 men) Stroke mortality ratio per 10 mmHg increase in DBP Is-year stroke mortality (per 1000 men) in bottom decile Population attributable stroke mortality (per lOOO)* Proportion of attributable mortality in top decilet “High-risk”
0.15
of phase 4 diastolic blood pressure (mmHg)
Mean Standard deviation 10th percentile 90th percentile Dose-response
As measured
strategy:
Shtft entire distribution
Reduction (per 1000) in ll-year stroke mortality assuming reduction of all diastolic pressures by:
(loo%)
62.9%
46.5%
38.4%
0.57
0.69
1.20
3.21
0.95 1.83 2.63 4.04
1.83 3.36 4.65 6.65
of blood pressure downward by ltfestyle change
1 mmHg 2 mmHg 3 mmHg 5 mmHg
0.49 0.95 1.40 2.24
0.64 1.25 1.83 2.88
l18-year stroke mortality in the whole population minus Is-year stroke mortality in the lowest decile. tproportion of population attributable mortality occurring among men in the top decile. fAverage reduction among all those offered treatment (taking into account acceptance and compliance).
downward shift of the whole blood pressure distribution of 1.2 mmHg (taking the measured data at face value), 1.5 mmHg (assuming reliability to be 0.75) or 2.2 mmHg (assuming reliability to be 0.5). Confidence limits for the estimates
The 95% confidence interval for the coefficient relating coronary heart disease mortality to measured cholesterol was 15.70 f 4.08 per 1000 men per mmol/l increase. Confidence limits for the estimates in Table 1 may therefore be derived from the published figures plus or minus 26%. The 95% confidence interval for the proportional hazards coefficient relating stroke mortality (on a logarithmic scale) to measured diastolic blood pressure is 0.435 + 0.084 per 10 mmHg increase. Approximate confidence limits for the estimates in Table 2 may therefore be derived from the published figures plus or minus 9% (e”.OW - 1).
A similar approach may be used with estimates of risk functions derived from other studies. For instance, the estimate used by MacMahon et al. [6] from pooled data relating measured diastolic blood pressure to stroke incidence lies close to (but below) the upper 95% confidence interval quoted above. Allowance for versibility
coverage,
compliance
and re-
The impact of preventive programmes is limited by incomplete coverage, poor acceptance of and compliance with treatment, and lack of reversibility of the relationship between risk factor and disease [16]. The estimates of benefit presented in the tables are based upon the average reduction in levels of each risk factor achieved among those offered treatment. This reduction reflects both the effectiveness of the treatment and the level of acceptance and compliance among truly high-risk men identified by screening.
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DAVIDSTRACIUNand Georwus
The estimates assume that the screening programme or population-based strategy covers the whole population and that relationships between the risk factors and mortality outcomes are wholly and rapidly reversible when risk factors are modified. These assumptions are unrealistically optimistic, but the benefits accruing under different conditions can easily be obtained by multiplying the results in the tables by the likely coverage and by the presumed degree of reversibility. DISCUSSION
Attenuation of dose-response
relationships
The dilution of associations and attenuation of regression coefficients by errors of measurement in the independent variable have long been recognized by statisticians [5,7, 15, 161and have recently been discussed more widely in an epidemiological context [6, 18, 191. Few longitudinal studies, however, have obtained the replicate measurements required to demonstrate this phenomenon in relation to disease incidence. Gardner and Heady [5] quote an example from a study of London busmen. The proportional increase in IO-year incidence of coronary heart disease was 19% per 10 mmHg increase in casual systolic blood pressure but 26% per 10 mmHg increase in the average of six blood pressure readings (which may be taken as a good approximation to true systolic blood pressure). More recently, MacMahon et al. [6] have used replicate measurements of diastolic blood pressure in the Framingham cohort to estimate the degree of attenuation of the log-linear association of diastolic blood pressure with coronary heart disease and stroke in pooled longitudinal data. They suggest a larger degree of attenuation than in the study of busmen: the proportional increase in age-adjusted coronary heart disease incidence being 19% per 6 mmHg increase in measured diastolic blood pressure but 32% per 6 mmHg increase in true diastolic pressure (recalculated from Ref. [6]). Reliability of risk factor measurement
We have made simplifying assumptions about the shape of the true risk factor distributions, the nature of the measurement errors and the mathematical form of the dose-response relationships. We have not made any assumptions about the magnitude of the errors, which influence the reliability of the measurement. These are likely to vary according to attention
Row
to protocol, technical advances, and the period of time over which a single measurement is taken to represent true level of a risk factor. The assumption of additive normal errors of constant variance may be questioned. In the Lipid Research Clinics study [20] and the Medical Research Council Mild Hypertension Trial [21], within-subject variability of cholesterol was greater in men with high measured levels, suggesting that the error variance might be proportional to the true value. This could account for part of the positive skew in the measured distribution seen here (Fig. 2) and elsewhere [21,22], but would tend to invalidate our simple procedure for correcting the slope of the dose-response relationship. The coefficient of variation over a 2-3 month period in the Lipid Research Clinics study was 8% [20], and over a 12-month period in the MRC Mild Hypertension Trial was 7% [21]. These are consistent with smaller studies under controlled dietary conditions [23]. Using this estimate, the short-term reliability of cholesterol measurement in the Whitehall study would be approximately 0.9. However, if a single measurement is to be taken as representative of a period of several years, the reliability is likely to be lower. In a large Swedish study [24], the reliability of cholesterol measurement at 6-week intervals was 0.74, but at an interval of 2 years this fell to 0.66. The early work of Armitage et al. [17] suggested a within-subject standard deviation of about 6 mmHg for diastolic blood pressures measured annually over 4 years. This would imply a reliability of 0.80 for the distribution of measured values in the Whitehall study. The factor used by MacMahon et al. [6] to adjust for attenuation was 1.6, implying a reliability of 0.625 (= l/l .6). Prentice [8] derived a reliability of 0.36 for survey measurements of diastolic blood pressure in women. These wide discrepancies highlight the uncertainties involved in making quantitative adjustments of observed data for presumed measurement error in the absence of better information on within-person variability over a period of months and years. Cholesterol and coronary heart disease
The adoption of an additive, rather than a multiplicative model to describe the relationship between cholesterol and coronary heart disease is supported by data from the Pooling Project Research Group [25] and the Multiple Risk Factor Intervention Trial [26,27] showing that
Measurement Error and Evaluation of Preventive Strategies
excess risks remain more constant than relative risks when the effect of cholesterol is considered in different age-groups. However, neither model fits perfectly, and variation in the excess risk associated with a given level of cholesterol has been suggested as a basis for selective screening [28]. The MRFIT study showed an upwardly concave relationship between 6-year mortality from coronary heart disease and serum cholesterol [26]. However, cumulative mortality over a longer period of follow-up may be expected to more closely approximate the linear pattern assumed here, because increased all-cause mortality limits the period of risk among subject with higher levels. The approximately linear relationship between coronary heart disease mortality and measured cholesterol makes the “populationbased” strategy of prevention highly effective by comparison with the “high-risk” approach. This difference is reinforced by the practical problems of identifying all subjects truly at high risk (Table 1). Randomized trials of drug treatment for hyperlipidaemia have achieved reductions of between 8 and 13% in total cholesterol in the intervention group [29]. Although these comparisons with a placebotreated group may underestimate the reductions that are possible when pharmacological treatment is supplemented by dietary advice, compliance is likely to be lower in clinical practice. Furthermore, it is unlikely that all those who are offered treatment will accept it. These factors will limit the average degree of cholesterol reduction that can be achieved among the high-risk individuals identified by screening and follow-up. On the most optimistic assumption that all men with cholesterol levels above the true 90th percentile could be identified and treated, our calculations suggest that the resulting decrease in coronary heart disease mortality could be matched by the effect of a general downward shift of cholesterol levels by as little as l-2%. A similar conclusion can be reached from observed data. Estimation of the actual magnitude of such effects, however, depends upon the level of reliability assumed for the cholesterol measurements (Table 1). Blood pressure and stroke
The association between measured diastolic blood pressure and fatal stroke was close to log-linear, as reported by others [6]. This exponential dose-response relationship tends to
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make the “high-risk” approach more effective, because a greater proportion of the attributable cases are found among those with high measured values than is the case with a linear association. Opportunistic measurement of blood pressure is also better suited than cholesterol screening to obtaining repeated measurements on large sections of the population, which are required to identify all those with high true values. Randomized trials of pharmacological treatment for mild hypertension have achieved a mean reduction of 6.4 mmHg in diastolic blood pressure among the attenders [9]. The effect of treatment in clinical practice is likely to be closer to 5 mmHg. If the reliability of blood pressure measurement is in the range 0X5-0.8, as suggested above, then the most effective policy of screening and treatment could probably be matched by the preventive effect of a general downward shift of less than 2 mmHg. This is less than the change in diastolic blood pressure apparently resulting from migration between the north and south of Britain [30], and within the range that can be expected from modest dietary modifications can be expected from modest dietary modifications throughout a whole population [31,32]. Thus, even for this example which is well suited to a policy of screening and treatment, a “population-based” strategy of prevention could pay unexpectedly large dividends. CONCLUSIONS
Our analyses are intended to be illustrative rather than authoritative. A number of important assumptions have been made, not all of which may be justified. We have also shown that quantitative results may be extremely sensitive to these assumptions and to local circumstances. We hope that our simulations will encourage others to explore the nature and effects of measurement error in greater detail than was possible here. Nevertheless, these two specific examples illustrate general principles of broader relevance to public health. The results will be particularly applicable to situations where the distribution of a imprecisely measured risk factor, occupational or environmental exposure is approximately normal and a linear or log-linear dose-response relationship can be assumed. In an earlier discussion of preventive strategies [l], it was argued that small but widespread lifestyle changes, from which each
DAVIDS~CHAN and GEOFPREY ROSE
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individual gains little, may cumulate to produce substantial improvements in public health. We have shown here that the attributable (excess) risk among those with high levels of a risk factor is underestimated unless the dose-response relationship is corrected for measurement error. The potential benefits of small changes in levels of an imprecisely measured risk factor are also underestimated by uncorrected survey data. The relative effectiveness of different strategies may or may not be reliably indicated by unadjusted estimates based on epidemiological studies. The “high-risk” and “population-based” approaches to prevention are not mutually exclusive. Where risk factors are measured with error, each strategy is potentially more effective than it appears at first sight. However, misclassification of individuals may limit the effectiveness of a policy of screening to identify a subgroup at high risk.
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