The effect of blood pressure and cholesterol variability on the precision of Framingham cardiovascular risk estimation: a simulation study

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1 (2010) 24, & 2010 Macmillan Publishers Limited All rights reserved /10 ORIGINAL ARTICLE The effect of blood pressure and cholesterol variability on the precision of Framingham cardiovascular risk estimation: a simulation study Department of Public Health, Epidemiology and Biostatistics, University of Birmingham, Birmingham, UK This simulation study investigates the effects of withinindividual variability in estimated cardiovascular risk on categorization of patients as high risk. Published estimates of within-individual blood pressure and cholesterol variability were used to generate blood pressure and cholesterol levels for hypothetical subjects at a range of ages. These were used to calculate the estimated cardiovascular risk of each individual. The relationship between an individual s mean cardiovascular risk and within-individual coefficient of variation for cardiovascular risk was determined. Using the derived relationship, mean cardiovascular risk and withinindividual variation in risk was calculated for 5018 adults from a population health survey. From this, was determined their probability of being classified as high risk (420% 10-year cardiovascular risk) and the test characteristics of risk estimation at a range of ages. Within-individual variability in cardiovascular risk and potential for misclassification are both greater in lowerrisk populations. At age years, the positive predictive value of a diagnosis of high risk is 0.61 (95% confidence interval (CI): ), and at age years, it is 0.94 (95% CI: ). About 39% of adults under 45 years diagnosed as high risk are not at high risk. Cardiovascular risk assessment should be targeted at high-risk populations. (2010) 24, ; doi: /jhh ; published online 7 January 2010 Keywords: risk stratification; coronary heart disease; primary care; diagnosis; measurement error; screening Introduction Since it was first proposed in New Zealand in 1993, estimating cardiovascular risk has become an integral part of determining the eligibility for treatment with aspirin, antihypertensives or statins. 1 The Framingham risk equations remain the most widely used for this purpose. 2 For example, most UK guidelines recommend antihypertensive treatment for those whose blood pressures exceed 140/90 mm Hg if their 10-year cardiovascular risk is 420%. 3 5 Some guidelines recommend aspirin for those at 420% 10-year cardiovascular risk who are aged 450 years. 5 Lipid-lowering guidelines recommend treatment if the 10-year cardiovascular risk exceeds 20%. 5,6 Multivariable risk estimation is also part of the European guidelines, although using a different risk equation. 7,8 Further risk equations Correspondence: Dr, Department of Public Health, Epidemiology and Biostatistics, University of Birmingham, Edgbaston, Birmingham, West Midlands B15 2TT, UK. T.P.Marshall@bham.ac.uk Received 29 July 2009; revised 14 October 2009; accepted 6 December 2009; published online 7 January 2010 continue to be developed, usually using national data sources To date, the Framingham cardiovascular equation remains the most widely used method of assessing risk. This equation was derived from a large cohort study in the United States. It determines cumulative incidence (risk) of any vascular event in individuals free from cardiovascular disease, using as predictors: age, sex, systolic blood pressure, smoking status, total cholesterol level and high-density lipoprotein (HDL) cholesterol level, diabetic status and electrocardiographic evidence of left ventricular hypertrophy. 2 For an individual patient, the risk equation is derived from the average of two systolic blood pressures, a single total cholesterol level and a single HDL cholesterol level. Individualized cardiovascular risk estimation is therefore a diagnostic test for high risk of cardiovascular disease that has become a part of routine clinical practice. But little attention has been paid to the diagnostic test characteristics of estimating cardiovascular risk. There is an unacknowledged uncertainty in risk prediction. Individuals are assigned a precise risk of developing cardiovascular disease and treatment decisions are made accordingly, but the variables from which this probability

2 632 is calculated are subjected to chance variation. Age and sex can be determined with certainty, but there is a degree of uncertainty in the determination of smoking status, diabetic status, systolic blood pressure, total cholesterol level and HDL cholesterol level. For the categorical variables (diabetic and smoking status), this uncertainty is because of misclassification of individuals diabetic and smoking status. For the continuous variables this is because blood pressure and lipid levels are intrinsically variable within the same individual. The effect of this variation is to impart a degree of imprecision to any estimate of cardiovascular risk. By chance, the same individual will have different blood pressures and lipid levels from one consultation to the next and as a result estimated cardiovascular risk will also vary. The variability of blood pressure is well recognized and test characteristics have been determined for measurement of blood pressure and classification of individuals as hypertensive. 12 This analysis uses data on within-individual variability in blood pressure and cholesterol levels to determine the variability of estimated 10-year cardiovascular risk. It then applies this variability to a population of individuals whose cardiovascular risk is known, allowing us to determine the distribution of cardiovascular risks that we would expect to find in each individual. We can therefore determine the probability that cardiovascular risk estimation would classify an individual as high risk (X20% 10-year cardiovascular risk). From this we can determine the proportion of a population who would be classified as high risk and to calculate the test characteristics of a diagnosis of high risk. Materials and methods The analysis is conducted in two parts. The first part is a simulation study to estimate within-individual variability in cardiovascular risk resulting from variability in diagnostic measurements. The second part is a classification study, using the estimated variability in cardiovascular risk to determine the proportion of persons who would be diagnosed as high risk in a survey population in relation to their true (reference) high-risk status determined from cardiovascular risk factors recorded in the same survey. Simulation study: cardiovascular risk and within-individual variability in cardiovascular risk To determine the relationship between cardiovascular risk and within-individual variability in cardiovascular risk across a range of ages, 10-year cardiovascular risk was calculated for 18 hypothetical subjects: nine men and nine women aged 30, 35, 40, 45, 50, 55, 60, 65 and 70 years, all nonsmoking and all non-diabetic. Each subject was assumed to have an average systolic blood pressure, total cholesterol and HDL cholesterol level for a person of their age, gender, smoking status and diabetic status. Each was assigned true mean blood pressures, total cholesterol levels and HDL cholesterol levels. The true mean values were obtained from the Health Survey for England 1998 for men and women in the age bands 30 35, 35 44, 45 54, and years. 13 The process was repeated for 18 smokers of the same age and sex and for 18 diabetic subjects of the same age and sex, using the appropriate true mean blood pressures and cholesterol levels for smokers and diabetics. The extent of within-individual variation in blood pressure was determined from a recent secondary analysis of data from a large clinical trial in subjects with a history of transient ischaemic attack or minor stroke. Among patients treated with dual therapy (ACE inhibitor with a thiazide diuretic), this found within-individual measurements of systolic blood pressure to have a coefficient of variation (s.d. divided by the mean) of 7.3% in a population with an average systolic blood pressure of 133 mm Hg. 14 To reflect within-individual variation in measured blood pressure that would be observed in 500 clinic visits, a large number (500) of systolic blood pressures incorporating a degree of variability were generated for each individual. These systolic blood pressures were the sum of the average systolic blood pressure and variation from the average. This variation is the product of an error term and the average systolic blood pressure for that individual. Error terms were generated using Excel as a series of normally distributed random numbers with a mean of zero and an s.d. equal to the coefficient of variation for within-individual blood pressure variation. Pearson s correlation coefficients were calculated for each series of random numbers to confirm that each series of generated random numbers was truly independent. Each individual therefore had 500 normally distributed measured blood pressures, with a mean equal to their true mean blood pressure and an s.d. equal to the product of the coefficient of variation and their true mean blood pressure. Using the same method, 500 total cholesterols and 500 HDL cholesterols were generated, reflecting within-individual variation in total cholesterol and HDL cholesterol. The Framingham equation calculates cardiovascular risk from the ratio of total cholesterol to HDL cholesterol. A published estimate of within-individual (biological) variability of total cholesterol to HDL cholesterol ratio indicates that this has a coefficient of variation of 6.8%. 15 Risk factors were assumed to vary independently. Five hundred estimates of 10-year cardiovascular risk were calculated for each of the 18 subjects using one total cholesterol, one HDL cholesterol and the average of two systolic blood pressures. These represent 500 different 10-year cardiovascular risks that might be calculated on these individuals at 500 different clinic visits. For each individual, their

3 mean cardiovascular risk was determined and the distributional characteristics of their cardiovascular risk: the 5th and 95th percentiles, the s.d. and the coefficient of variation using the log antilog method. 15 The probability that each individual would be categorized as high risk (420% 10-year cardiovascular risk) was determined from the s.d. and true mean cardiovascular risk. Finally, the equation of a line of best fit for the relationship between cardiovascular risk and coefficient of variation of cardiovascular risk was determined in order to be able to calculate the coefficient of variation for a patient at any given level of cardiovascular risk. it is possible to determine the diagnostic test characteristics assessment for men and women of different ages. The sensitivity of cardiovascular risk assessment is the expected number of high-risk individuals correctly classified as high risk divided by the total number of truly high-risk individuals. The positive predictive value (PPV) of cardiovascular risk assessment is the number of truly high-risk individuals correctly classified as high risk divided by the total sum of probabilities of being classified as high risk. The specificity of cardiovascular risk assessment is the expected number of individuals correctly classified as not at high risk divided by the total number not at high risk. 633 Classification study: misclassification as high risk in a population of adults To determine the effects of cardiovascular risk misclassification on a population, a sample population was selected from the Health Survey for England The analysis was confined to persons in whom the Framingham risk equation is valid, those aged years and free from cardiovascular disease. Of individuals in the survey, 5018 have blood pressure and cholesterol measurements, are free from cardiovascular disease and aged years. Risk factor data for each of the 5018 individuals were entered into Excel and the 10-year cardiovascular risk was calculated. This is regarded as the true (reference) cardiovascular risk. The test cardiovascular risk is the result that would be obtained as a result of cardiovascular risk estimation. Test cardiovascular risks will form a distribution around the true mean cardiovascular risk. Using the relationship between individual risk and the coefficient of variation derived from the modelling exercise described above, the coefficient of variation and s.d. of each individual s test cardiovascular risk was determined. By knowing the s.d. and true (reference) mean cardiovascular risk, it is possible to determine the probability that any single individual would be classified as high risk (420% 10-year cardiovascular risk) using the normal distribution function in Excel. Across a population, the sum of all individuals probabilities of being classified as high risk is numerically equal to the total number of individuals that we would expect to be classified as high risk following assessment. For example, if 100 individuals each have a probability of 0.05 of being classified as high risk, we would expect 5 to be misclassified if all were assessed. The sum of probabilities of being classified as high risk in all low-risk individuals (mean 10-year cardiovascular risk o20%) is numerically equal to the expected number of false positives that would be found in low-risk individuals. The sum of probabilities of being classified as high risk in all high-risk individuals is numerically equal to the expected number of true positives that would be found in high-risk individuals. From this Sensitivity analysis The relationship between variability and mean systolic blood pressure is not precisely described, but coefficient of variation may be greater in those with higher blood pressures. 17 Data in the same paper suggest that an individual s coefficient of variation increases by B for every mm Hg increase in their mean systolic blood pressure. A sensitivity analysis was carried out by adjusting the coefficient of variation of cardiovascular risk by for every mm Hg that an individual s systolic blood pressure differs from the population mean from which the coefficient of variation was derived (133 mm Hg). This somewhat exaggerates the likely effect of increasing variability of higher blood pressures. Results Simulation study According to the Framingham equation, average 10-year cardiovascular risk for a 70-year-old nonsmoking, non-diabetic woman with average blood pressure and cholesterol levels is 19.1%. The 5th and 95th percentiles of her 10-year cardiovascular risk are 15.7 and 23.3%. On 35.6% of occasions she will be found to be at 420% 10-year cardiovascular risk. Average 10-year cardiovascular risk for a 55- year-old non-smoking, non-diabetic man with average blood pressure and cholesterol levels is 16.4% with 5th and 95th percentiles of 13.3 and 20.2%, respectively. On 4.4% of occasions he will be found to be at 420% 10-year cardiovascular risk (Tables 1 3, Figure 1). The distribution of cardiovascular risks in a 55-year-old male non-diabetic, non-smoker is shown in Figure 2. Measured by the coefficient of variation, the variability of 10-year cardiovascular risk is greater than the variability of either blood pressure or cholesterol levels. Variability is greater at lower mean cardiovascular risk and therefore greater in younger than in older adults. Across the relevant range of ages, the relationship between coefficient of variation of 10-year cardiovascular risk and average

4 634 Table 1 Distributional characteristics of 500 simulated 10-year cardiovascular risks in nine male and nine female non-diabetic, non-smokers Age (years) 10-year cardiovascular risk Percentage of 10-year cardiovascular risk estimates 420% Mean 95th percentile 5th percentile Median s.d. Coefficient of variation Males: non-diabetic, non-smokers Females: non-diabetic, non-smokers Table 2 Distributional characteristics of 500 simulated 10-year cardiovascular risks in nine male and nine female non-diabetic smokers Age (years) 10-year cardiovascular risk Percentage of 10-year cardiovascular risk estimates 420% Mean 95th percentile 5th percentile Median s.d. Coefficient of variation Males: diabetic, non-smokers Females: diabetic, non-smokers cardiovascular risk closely follows an inverse loglinear relationship. The relationship is slightly different for non-diabetic non-smokers (coefficient of variation: Log n (average cardiovascular risk) þ ; r 2 ¼ 0.994), but very similar for both smokers and diabetics (coefficient of variation for diabetics or smokers: Log n (average cardiovascular risk) þ ; r 2 ¼ 0.997). It is therefore possible to determine the coefficient of variation of 10-year cardiovascular risk for any individual.

5 Table 3 Distributional characteristics of 500 simulated 10-year cardiovascular risks in nine male and nine female diabetic non-smokers 635 Age (years) 10-year cardiovascular risk Percentage of 10-year cardiovascular risk estimates 420% Mean 95th percentile 5th percentile Median s.d. Coefficient of variation Males: diabetic, non-smokers Females: diabetic, non-smokers Source: see text. Ten-year CVD risk 40% 35% 30% 25% 20% 15% 10% 5% Age and intra-individual variation in ten-year CVD risk Average (men) 95th percentile (men) 5th percentile (men) Average (women) 95th percentile (women) 5th percentile (women) 0% Age (years) Figure 1 The relationship between age and intra-individual variation in 10-year cardiovascular risk in non-smoking, nondiabetics with cholesterol levels and blood pressures. Frequency % 10% Distribution of CVD risks 15% 20% CVD risk (10 year) Figure 2 Distribution of 10-year cardiovascular risks in a 55-year-old male diabetic non-smoker. 25% Using this relationship, s.d. values were calculated for persons with a range of 10-year cardiovascular risks and from these s.d. values were derived the probabilities that 10-year cardiovascular risk would be found to exceed 20%. (Table 4) In a non-diabetic non-smoker, a risk of 15.0% has a 95% confidence interval (CI) (or prediction interval) from 10.9 to 19.1% and has a small probability (P ¼ 0.008) of exceeding 20%. In a nondiabetic non-smoker, a risk of 15% estimated risk has an almost identical 95% CI and a probability of of exceeding 20%. Classification study Altogether, 25.7% (590 of 2292) of men and 8.3% (226 of 2726) of women aged years without cardiovascular disease in the Health Survey for England 2003 are at high risk (420% 10-year cardiovascular risk) according to the Framingham risk model. Both the sensitivity and PPV of cardiovascular risk assessment increase with age and are higher in men than women (Table 5). In men and women combined, at ages years sensitivity is 0.89 (95% CI: ) and PPV 0.61 (95% CI: ), whereas at ages years sensitivity

6 636 is 0.92 (95% CI: ) and PPV 0.94 (95% CI: ). As the survey included no persons under 35 years at high risk, it is not possible to determine the test characteristics for this age; however, sensitivity and PPV are likely to be very low. Sensitivity analysis Allowing for greater variability of blood pressure and of cardiovascular risk estimates in persons with higher mean blood pressures has almost no effect on the test characteristics of cardiovascular risk assessment. Discussion Cardiovascular risk estimation in individuals is subjected to diagnostic error in the same way as Table 4 Estimated precision of 10-year cardiovascular risk estimates Estimated average 10-year cardiovascular risk 95% confidence intervals Lower Upper Probability of being at 420% 10-year cardiovascular risk Source: see text. any method of categorization. Variability in estimated cardiovascular risk is greater than variability of either blood pressure or cholesterol levels. In age groups with a low prevalence of high risk, risk estimation misclassifies significant numbers of individuals but is more reliable in populations with a higher prevalence of high risk. A previous modelling study found a very similar CI for estimated coronary risk of among diabetic patients to be 15% (95% CI %). 18 The findings are likely to be similar with any multivariable risk equation using similar variable risk factors and in any population with a similar distribution of those risk factors. A model is dependent on its underlying assumptions. The assumption that blood pressure and cholesterol levels vary independently is probably reasonable. Within-individual variability of systolic blood pressure may be greater than that was assumed for this analysis. An individual patient data meta-analysis of clinical trials of blood pressure treatment found the coefficient of variation to be 9.9% (Additional information from Musini V, personal communication). 19 This degree of variability would increase the extent of misclassification. Most of the variability in risk is the result of variation in measured blood pressure and the classification study regards the survey blood pressure as individuals true mean blood pressures. However, they include both within-individual and between-individual variations. The true distribution of blood pressures is therefore somewhat narrower than that used here. Although it is possible to adjust the distribution of blood pressures in the survey to take account of within-individual variation, this would alter the relationship between blood pressure Table 5 Test characteristics of cardiovascular risk assessment in persons aged years Age (years) 10-year cardiovascular risk (true) Sum of probabilities of being classified as at 420% 10-year cardiovascular risk Sensitivity Specificity PPV Prevalence 10-year cardiovascular risk (true) o20% X20% o20% X20% Men Total Women Total Abbreviation: PPV, positive predictive value. Source: See text.

7 and cardiovascular risk, complicating the calculation of cardiovascular risk. This analysis also ignores misclassification of smoking and diabetic status as sources of error. Both sources of misclassification would increase the variability of estimated cardiovascular risk. Their findings have a number of practical implications. It is possible to obtain more precise estimates of blood pressure and cholesterol levels by averaging multiple measurements. However, existing risk-prediction equations are derived from risk factor measurements that incorporate a degree of measurement error. They underestimate the relationship between a subject s perfectly measured risk factors and their risk of cardiovascular disease. This is called regression dilution bias. Therefore, using more precisely measured risk factors to calculate risk requires a recalibrated risk-prediction equation. Otherwise the equation will underestimate risk in patients with higher than average risk factor values and overestimate risk in patients with lower than average risk factor values. But there is no accepted method for recalibrating a multivariable statistical model. The fact that risk cannot be known precisely does not obviate the need to take clinical decisions, but greater weight could be given to patients preferences for treatment than to whether patients meet precise risk threshold levels. Risk information can be presented to patients in a way they can understand. 20 If the 55-year-old man in Figure 2 would choose treatment for 10-year risk reduction of 43%, we can advise him that it is likely that a drug offering a relative risk reduction of 0.25 will achieve at least this effect. Because it varies, repeated risk estimation will show regression to the mean high-risk patients will tend to have lower risks on reassessment that may change their apparent eligibility for treatment. But the change in risk is spurious and clinicians should avoid recalculating risk until the right answer is obtained. This is analogous to the situation with blood pressure, in which repeated measurement can be used to misclassify patients as eligible for treatment. 21,22 It is misleading to recalculate a patient s cardiovascular risk following intervention to estimate the benefits to an individual patient because changes in measured cardiovascular risk are affected by chance and by regression to the mean in addition to the effects of intervention. Diagnosis of high cardiovascular risk is most accurate when applied to a population with a high prevalence of high risk. Cardiovascular risk assessment in persons aged o45 years will misclassify many as high risk. Universal cardiovascular risk assessment is planned for all adults aged years in the United Kingdom. 23 The likelihood of frequent misclassification of those in low-risk populations, in common with both the economics and practical evidence, argues against the universal cardiovascular risk factor assessment and for targeting those who are most likely to be at high risk. 23,24 Age and sex are strong predictors of cardiovascular risk and subject to little measurement error. Preselecting patients who are most likely to be at high risk on the basis of age and sex would greatly reduce misclassification. Clinicians should be aware that an estimated 10- year cardiovascular risk of 20% can be regarded as having a 95% CI from 13 to 27%. A diagnosis of high risk is most likely to be reliable in a population with a high prevalence of high risk. Cardiovascular assessment in young adults will commonly result in misdiagnosis of high risk. What is known about this topic K Blood pressure and cholesterol levels are known to vary from day to day within individual patients. This has the potential to affect categorization of patients as high risk. What this study adds K This paper determines the effects of risk factor variation on calculated cardiovascular risk. It also provides quantitative estimates of the probability that patients at a range of ages will be misdiagnosed as high risk. Conflict of interest The author declares no conflict of interest. Acknowledgements I thank Rebecca Taylor for commenting on an earlier draft of this paper. Tom Marshall obtained the data, carried out the analysis and wrote the paper. References 1 Jackson R, Barham P, Maling T, MacMahon S, Bills J, Birch B et al. The management of raised blood pressure in New Zealand. Br Med J 1993; 307: Anderson KM, Odell PM, Silson PWF, Kannel WB. Cardiovascular disease risk profiles. 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