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American Journal of Epidemiology Advance Access originally published online on November 20, 2006
American Journal of Epidemiology 2007 165(4):398-409; doi:10.1093/aje/kwk021
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American Journal of Epidemiology Copyright © 2006 by the Johns Hopkins Bloomberg School of Public Health All rights reserved; printed in U.S.A.

ORIGINAL CONTRIBUTIONS

Effects of Past and Recent Blood Pressure and Cholesterol Level on Coronary Heart Disease and Stroke Mortality, Accounting for Measurement Error

Hendriek C. Boshuizen1, Mariapaola Lanti2, Alessandro Menotti2, Joanna Moschandreas3, Hanna Tolonen4, Aulikki Nissinen4, Srecko Nedeljkovic5, Anthony Kafatos3 and Daan Kromhout1,6

1 National Institute for Public Health and the Environment, Bilthoven, the Netherlands
2 Association for Cardiac Research, Rome, Italy
3 Department of Preventive Medicine and Nutrition Clinic, Medical School, University of Crete, Heraklion, Crete, Greece
4 Department of Health Promotion and Chronic Disease Prevention, National Public Health Institute, Helsinki, Finland
5 Institute for Cardiovascular Diseases, Clinical Center of Serbia, Beograd, Serbia-Montenegro
6 Division of Human Nutrition, Wageningen University, Wageningen, the Netherlands

Correspondence to Dr. Hendriek C. Boshuizen, Expertise Centre for Methodology and Information Services, National Institute for Public Health and the Environment (RIVM), P.O. Box 1, 3720 BA Bilthoven, the Netherlands (e-mail: hendriek.boshuizen{at}rivm.nl).

Received for publication July 12, 2005. Accepted for publication July 11, 2006.


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 References
 
The authors aimed to quantify the effects of current systolic blood pressure (SBP) and serum total cholesterol on the risk of mortality in comparison with SBP or serum cholesterol 25 years previously, taking measurement error into account. The authors reanalyzed 35-year follow-up data on mortality due to coronary heart disease and stroke among subjects aged 65 years or more from nine cohorts of the Seven Countries Study. The two-step method of Tsiatis et al. (J Am Stat Assoc 1995;90:27–37) was used to adjust for regression dilution bias, and results were compared with those obtained using more commonly applied methods of adjustment for regression dilution bias. It was found that the commonly used univariate adjustment for regression dilution bias overestimates the effects of both SBP and cholesterol compared with multivariate methods. Also, the two-step method makes better use of the information available, resulting in smaller confidence intervals. Results comparing recent and past exposure indicated that past SBP is more important than recent SBP in terms of its effect on coronary heart disease mortality, while both recent and past values seem to be important for effects of cholesterol on coronary heart disease mortality and effects of SBP on stroke mortality. Associations between serum cholesterol concentration and risk of stroke mortality are weak.

blood pressure; cerebrovascular accident; cholesterol; coronary disease; epidemiologic methods

Abbreviations: ICD-8, International Classification of Diseases, Eighth Revision; SBP, systolic blood pressure


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 References
 
Many studies have shown that high blood pressure and serum cholesterol are related to cardiovascular disease risk. However, it is not clear whether recent or past exposure is more important. Pathophysiologic knowledge supports both direct effects of serum cholesterol and blood pressure on cardiovascular function and plaque rupture and long-term effects via the relation of these variables with atherosclerosis. Clinical trials of blood-pressure-lowering medication show that most of the reduction in coronary heart disease occurs during the first year of treatment, while maximal reduction of strokes occurs only after approximately 5 years (1). In clinical trials of statins, maximum reductions in coronary heart disease and stroke are reached only after approximately 5 years (2, 3). However, follow-up in most trials is not much longer than 5 years, so information on longer-term benefits is often absent.

To date, guidelines for the prescription of blood-pressure- and cholesterol-lowering drugs restrict prescription mostly to patients with a high absolute risk of cardiovascular disease, which implies that these drugs will be prescribed mostly at older ages. If long-term effects are important, an extra benefit could be gained from prescribing these drugs at younger ages to persons expected to have a high absolute risk in old age.

Measurements of both blood pressure and serum cholesterol show considerable intraindividual variation. This "measurement error," including both imperfections of measurement instruments or protocols and biologic fluctuations, causes regression dilution bias (4–6). In order to make realistic estimates of potential treatment effects, regression dilution must be taken into account.

The difference between two measurements taken several years apart, however, could be due not only to measurement error but also to long-term changes. To date, most studies correcting for measurement error have implicitly assumed that the exposure of interest is the average exposure during the study period and that all deviations are due to measurement error rather than real change (7–14). In that case, two measurements spaced apart during any arbitrary time period can be used to estimate the amount of "error" in a single measurement, which then is used to adjust for regression dilution bias (5). In more recent studies, however, investigators have recognized that the correlation between two blood pressure or cholesterol measurements decreases with the time interval between them (15, 16) and have defined a moment or period of "true exposure" (typically 5 years or 0–10 years before the at-risk moment) (4), implicitly assuming that exposure at other times has no effect on disease occurrence (15, 16).

We are interested in effects of present exposure as compared with past exposure, and this can only be studied by comparing subjects with different exposure trajectories. Adjustment for measurement error in this situation requires a statistical model that separates the difference between two measurements taken at different times into a real difference and a measurement error component. Tsiatis et al. (17) proposed a relatively simple two-step procedure for adjusting for measurement error which first models individual exposure trajectories (step 1) and then uses predicted values from these models in the disease model (step 2) to estimate relative risks adjusted for measurement error. In this method, the "real" exposure is determined by the choice of exposure model in the first step.

We used this method to reanalyze data from the 35-year follow-up of nine cohorts from the Seven Countries Study, investigating the effects of recently measured blood pressure and cholesterol as compared with measurements taken 25 years previously on coronary heart disease and stroke mortality in elderly subjects (ages 65 years or older), with and without adjusting for measurement error. Since this method is relatively new, we supplemented these analyses with a comparison of this method with a more traditional method of adjustment for regression dilution.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 APPENDIX
 References
 
Population and follow-up
We used the 35-year follow-up data from nine of the original 16 cohorts included in the Seven Countries Study (18, 19), comprising five European countries: Finland (Eastern and Western), the Netherlands (Zutphen), Greece (Crete), Italy (Crevalcore and Montegiorgio), and Serbia (Zrenjanin, Velika Krsna, Belgrade). In these cohorts, 6,518 men aged 40–59 years were enrolled between 1958 and 1964 (the baseline year, year 0, varied between cohorts). Repeat measurement rounds were organized in years 5 and 10 in all cohorts, in year 17 in the Netherlands, in year 25 in all countries except Greece, in year 30 in all countries except Serbia, and in year 35 in all countries except Greece. Mortality follow-up was carried out until 35 years after baseline, with only nine subjects being lost to follow-up. Causes of death were based on information obtained from death certificates, hospital and medical records, interviews with physicians, and relatives of the deceased, with the exception of years 25–35 in Italy and Greece and years 15–35 in Finland, where official causes of death were used. Final causes of death were assigned according to the International Classification of Diseases, Eighth Revision (ICD-8), by a single reviewer (A. M.), following defined criteria. In the presence of multiple causes of death, the following hierarchy was used: violent causes, cancer in advanced stages, coronary heart disease, and stroke. The endpoints used in the current analysis were coronary heart disease (ICD-8 codes 410–414 and A795 (sudden coronary death)) and stroke (ICD-8 codes 430–438).

Measurements
Blood pressure was recorded by a physician or nurse at the end of the physical examination. It was recorded as the average of two measurements taken 1 minute apart with a calibrated mercury sphygmomanometer, usually while the subject lay in the supine position. Blood pressure measurements from year 17 (the Netherlands) were excluded because they were insufficiently standardized. Information on the use of antihypertensive drugs was collected only during the 25-, 30-, and 35-year examinations in Finland, the Netherlands, and Italy. Total cholesterol was measured in a nonfasting blood sample according to the Abell-Kendall method, as modified by Anderson and Keys (20), in standardized laboratories. Current smoking of one or more cigarettes per day was assessed with a standardized questionnaire (19). The presence of cardiovascular disease was established by combining history data with information from clinical records. Diabetes was defined as receiving medical treatment for diabetes.

Statistical analysis
We used the two-stage approach introduced by Tsiatis et al. (17) to adjust for measurement error (illustrated in figure 1). An example SAS code (SAS Institute, Inc., Cary, North Carolina) can be downloaded from the website of the Netherlands National Institute for Public Health and the Environment (www.rivm.nl/sasmacros).


Figure 1
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  		FIGURE 1. Schematic representation of the analysis, illustrated using a hypothetical example of a male subject with 35 years of follow-up who is aged 44 years at baseline and dies at age 78 years. The drawn curve in the exposure model is the fitted population average systolic blood pressure (SBP) of men born in 1916; the dashed line represents the empirical Bayesian (EB) estimate of the SBP trajectory of the hypothetical subject from a random-intercept model (parallel to the population average); and the dotted line represents the EB estimate of the SBP trajectory of the hypothetical subject from a random-slope model.

 
In the first step, the exposure data are modeled as a function of age and calendar time, using a random-effects model. From this model, an empirical Bayesian predicted value of exposure at any age can be calculated for each person. An empirical Bayesian estimate is a weighted average of the (modeled) population mean value and the estimate based on measurements taken on the subject himself. The empirical Bayesian estimate is thus "shrunken" in the direction of the population mean value. Shrinkage is larger when the individual estimate is less precise (i.e., has more measurement error).

In the second step, the empirical Bayesian estimates are entered as exposures in the disease model. Since empirical Bayesian estimates are shrunken towards the population mean (compared with measured data), they have a lower variance than measured data. Using empirical Bayesian estimates in the Cox model instead of measured values implies that the same differences in mortality have to be explained with less variance in exposure, resulting in higher hazard ratios per unit of exposure. If the exposure model is a random-intercept model without covariates, using the empirical Bayesian estimate is similar to using a Cox model with average exposure during follow-up as the exposure variable and applying a "classical" attenuation coefficient (5, 21) to adjust for regression dilution bias.

Step 1: the exposure model.
In our data set, only relatively simple exposure models could be fitted, because we had at most six measurements per subject. We analyzed systolic blood pressure (SBP) as the blood pressure variable, since in most cases this described our data as well as or better than models using diastolic blood pressure in combination with pulse pressure. We assumed linear effects of exposure on the log scale, consistent with results of meta-analyses (12, 13, 22). In all models, we used serum cholesterol and SBP as a single multivariate outcome, thus including the correlation between them in the model; neglecting this correlation can bias analyses that adjust for measurement error (5). Models were fitted separately for each cohort using SAS PROC MIXED.

In the first and simplest model, the random effect for each individual comprised a constant difference from the age- and calendar-time-specific population average values (see figure 1), fitted by including third-order polynomials for age and calendar time in the fixed part of the model:

Formula (1)
where Xij is the vector of outcomes (SBP and cholesterol) in round j for individual i, a = age – 50 in round j, y = calendar year – 70 in round j, the ß's are vectors of regression coefficients, {Sigma}{varepsilon} is a 2 x 2 covariance matrix with unequal diagonal elements and zero off-diagonal elements, and {Sigma}ß is the (unstructured) 2 x 2 covariance matrix of the random effects. This covariance structure implies that the true values of SBP and cholesterol are correlated but their measurement errors are independent. In this model, ranking of individuals within the population is stable throughout life. Without the covariates a and y, the model would adjust for regression dilution bias in a similar way as applying attenuation matrices (5).

To investigate the effect of recent exposure versus past exposure, a model is needed in which the ranking of subjects on exposure changes with time. The simplest model for this is one where the individual deviations from the population average change linearly with age (linear model; see dotted line in figure 1):

Formula (2)
Next to model 2, we used a polynomial model, which provided the best fit as judged by the log-likelihood:

Formula (3)
From models 2 and 3, we calculated exposure at two different ages and entered them simultaneously in the Cox model (figure 1). We illustrate this in table 1 by presenting measured and fitted Xij values from models 1 and 2 for an example subject. We also give the mean population values (values for ß0i = 0 and ß1i = 0) to illustrate the shrinkage towards this value. From the linear model (model 2), it is also possible to obtain an empirical Bayesian estimate of the rate of change (ß1i) for each person.


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  		TABLE 1. Example of measured values and empirical Bayesian values calculated for serum total cholesterol level (mmol/liter) for an arbitrarily chosen participant aged 44 years in 1960, Seven Countries Study, 1958–1999

 
Since SBP and cholesterol trajectories in persons who survive might differ from those in persons who have already died, Tsiatis et al. (17) prescribed that the exposure model be refitted for each risk set separately ("risk set" is defined below). Andersen and Liestol (23) suggested that this is often unnecessary. We tried both approaches and observed little difference in results, even when using all-cause mortality as the endpoint. Therefore, only a single exposure model was fitted to the data.

Step 2: the Cox survival model.
In each Cox model fitted, age was used as the time scale, with the age of entry set at 65 years. When using age as the time scale, the exposure of each person who experiences an event is compared with the exposure of all persons from the same cohort who are in follow-up at that age (hereafter called "current age"). This group of (usually) one case and many controls is called the risk set.

Comparison of adjustment methods.
We performed the following analyses to compare adjustment methods:

  1. Without adjustment for regression dilution bias, using exposure at baseline.
  2. Corrected for regression dilution using an attenuation factor (univariate analysis) or attenuation matrix (multivariate analysis), referred to herein as "classical adjustment." Adjustment was based on two repeated measurements (21) spaced 10 years apart, since this is close to half of the average time from baseline to event in our data (24.5 years for coronary heart disease and 24.6 years for stroke).
  3. Correction for regression dilution using the average of the empirical Bayesian estimates of exposure between baseline and current age from exposure model 1.
In the absence of both measurement error and changes over time, baseline exposure would be equal to average exposure, so all analyses would yield identical results.

For analysis 2, confidence intervals for the multivariate case were calculated using 250 bootstraps. For analysis 3, Tsiatis et al. (17) suggested bootstrapping for calculation of confidence intervals. However, because running times for the software were extensive, we used an approximate method (see Appendix).

Analyses comparing exposures at a single moment in time.
We performed the following analyses, aiming to model 1) exposure at the current age and 2) exposure 25 years before the current age:

4. Exposure as last measured, 1) at the current age and 2) 25 years before the current age.
5. Empirical Bayesian estimates of exposure 1) at the current age and 2) 25 years before the current age from exposure model 2 (linear model). Exposure 25 years previously was calculated only when this moment fell after baseline, so this analysis comprised only years 25–35 of follow-up.
6. As above in point 5 but from exposure model 3 (polynomial model).

Analyses simultaneously modeling exposures at two moments in time.
We repeated analyses 4–6 while simultaneously entering the exposures at two different moments in time into the model (analyses 7–9). In these models, the correlation between point estimates from direct measurements taken at two moments in time was acceptable (<0.6). However, the correlation was high for empirical Bayesian estimates at two moments in time from a linear model (~0.9) and appreciable for those from the polynomial model (approximately 0.6 for SBP and 0.8 for cholesterol).

In analysis 10, we analyzed the empirical Bayesian estimate of current exposure from the linear model together with the change in exposure (ß1i) from this model. Here the correlation between both regression coefficients ranged from 0.4 for cholesterol to 0.8 for SBP.

If the relative risk of the event under study changes with age, the proportional hazards assumption is not satisfied when age is used as the time scale. Therefore, we added interaction terms between current age and all statistically significant effects. In models containing only exposure at a single moment in time, the interaction of current age with SBP was statistically significant in most models. Therefore, we retained this interaction term in all models, and we present relative risks of events for SBP at age 75 years (approximately the mean age during follow-up). The interaction between coronary heart disease and diabetes also reached statistical significance and was retained. When entering SBP at two different moments in time simultaneously into the model, for stroke (but not for coronary heart disease) the interaction of current age with the most recent exposure was generally statistically significant and was therefore retained in the models.

We stratified all analyses by cohort to prevent confounding by ecologic effects.

In fully adjusted models, we further adjusted the results for body mass index (weight (kg)/height (m)2; last measured), smoking status (last measured), number of cigarettes currently smoked per day (≤19 or ≥20; last measured), diabetes (last measured), the presence of cardiovascular disease at age 65 years, use of antihypertensive drugs (last measured), and family history of cardiovascular disease (reported at baseline). We present relative risks for differences of 1 mmol/liter in total cholesterol and 20 mmHg in SBP (both 84 percent of the total population standard deviation in year 25).


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 APPENDIX
 References
 
At baseline (year 0), average blood pressures and serum total cholesterol levels were highest in Northern Europe and lowest in Serbia (table 2). At age 65 years (5–25 years later), these differences were much smaller, as levels had risen considerably in Serbia but not in Northern Europe.


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  		TABLE 2. Characteristics of the study population after 35 years of follow-up, Seven Countries Study, 1958–1999

 
First we compared the results of the two-step approach with those of the classical method for adjustment for regression dilution bias (table 3). Both SBP and serum total cholesterol had a clear effect on coronary heart disease risk. For stroke, the effect of SBP was strong, but the effect of cholesterol was weak and mostly not statistically significant. In all of these models, the relative risk for SBP declined with age because of the interaction between SBP and age (see figure 2 for an example). The tables present relative risks at age 75 years.


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  		TABLE 3. Relative risk of coronary heart disease mortality and stroke mortality according to systolic blood pressure and serum total cholesterol level, comparing unadjusted results with results obtained using different methods of adjustment for regression dilution bias, Seven Countries Study, 1958–1999

 

Figure 2
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  		FIGURE 2. Relative risk (RR) of coronary heart disease mortality (top) and stroke mortality (bottom) per 20-mmHg difference in systolic blood pressure (average value during the study period, adjusted for measurement error) as a function of age, Seven Countries Study, 1958–1999. Dotted lines, 95% confidence interval.

 
Adjusting for measurement error univariately with the classical method (5) yielded higher adjusted relative risks than the two-step method, which used empirical Bayesian estimates from a multivariate model. Multivariate adjustment with the classical method (fully adjusted model) gave relative risks similar to those of the two-step method but with marginally wider confidence intervals.

When we repeated these analyses by geographic area (results not shown), we saw similar effects in all areas, but in this case the confidence intervals from the two-step method were appreciably narrower than those from the classical method.

Comparing the effect of recent exposure with exposure 25 years previously (table 4), the effects of exposure measured 25 years previously on risk of coronary heart disease or stroke mortality were stronger than those of more recent exposure. Employing the two-step method (analyses 5 and 6) yielded similar results. Repeating these analyses using only the follow-up from years 25–35 (not shown) produced similar outcomes. Small differences between results using the linear exposure model versus the polynomial model were seen for recent exposure.


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  		TABLE 4. Relative risk of coronary heart disease and stroke mortality according to systolic blood pressure and serum total cholesterol level at a single moment in time, Seven Countries Study, 1958–1999

 
When exposures at two moments in time were entered into the model simultaneously, past and current cholesterol values from direct measurements had equal influences on coronary heart disease mortality (table 5), while with the two-step method, past exposure was more important. For SBP, all analyses showed that the effect on coronary heart disease mortality was mostly related to past SBP. The analysis using current value and rate of change showed a statistically significant effect of the current value only. In this model, the relative risk for the current value represents the relative risk for the current value given that change is the same, so it represents the distance between two parallel blood pressure trajectories over a lifetime, rather than current SBP only. Although they were not statistically significant, results indicated that with similar current SBPs, coming from lower past values protects against coronary heart disease mortality. This effect was less strong for cholesterol. For stroke mortality (table 6), the results were less clear but also indicated a more important role of past SBP and maybe even past cholesterol than recent SBP/cholesterol.


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  		TABLE 5. Relative risk of coronary heart disease mortality when systolic blood pressure and serum total cholesterol level measured at two moments in time are simultaneously entered into the model, Seven Countries Study, 1958–1999

 

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  		TABLE 6. Relative risk of stroke mortality when systolic blood pressure and serum total cholesterol level measured at two moments in time are simultaneously entered into the model, Seven Countries Study, 1958–1999

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
APPENDIX
 References
 
In this study, we examined the importance of past exposure to high blood pressure and serum cholesterol relative to that of recent exposure, both using data as measured and after adjustment for regression dilution bias. For coronary heart disease mortality, we observed stronger effects of past SBP than of recent SBP, while both past and recent SBP influenced stroke mortality. Both past and recent serum cholesterol level influenced coronary heart disease mortality, while there was no clear evidence of an association between stroke mortality and past or recent cholesterol.

In a few previous studies, researchers simultaneously entered both previous and later blood pressure into a single model (24), but they did not adjust for regression dilution bias (25–27). These investigators all observed additional effects of past blood pressure when taking recent blood pressure into account, although past exposure did not always have stronger effects as it did in our observations.

More investigators have approached the problem by examining the effect of changes in blood pressure. Most of them (28–34), but not all (35), have observed, like us, higher risks for changes that are compatible with higher life-average SBP. This direction of effects, however, could also result from regression to the mean. We used an empirical Bayesian estimate for rate of change so regression to the mean could not influence our results.

To study the effects of timing of exposure, we used Cox models with age as the time axis, relating events at the current age to exposure in the past. Until now, the Seven Countries Study has mainly been analyzed using follow-up time from baseline as the time axis. Menotti et al. (29) analyzed the same data on SBP with that approach and concluded that the effect of baseline SBP declined during follow-up, confirming results of similar analyses in other studies (36). Our model shows that this decline is due to the aging of the population rather than the lengthening of the period between measurement and effect.

We ignored the occurrence of nonfatal cardiovascular conditions during follow-up and only adjusted for the presence of such conditions at the start of follow-up (age 65 years). Since the presence of a cardiovascular condition at age 65 years is influenced by blood pressure or cholesterol levels earlier in life, this adjustment might have weakened the effect observed for earlier SBP or cholesterol levels. However, results were similar without this adjustment. Another limitation of our study is that information on treatment of hypertension was only partly available, and no information was available on treatment of hypercholesterolemia. In addition, since high SBP 25 years previously (in the 1960s) was mostly untreated, this could have contributed to the strong effect observed for past SBP, as treatment might mask effects of recent SBP.

Because we used a relatively new method to adjust for regression dilution bias, we first compared it with a method that is more commonly used on similar data. Both methods produced similar results when applied to SBP and cholesterol simultaneously (i.e., multivariately), but the new method provided slightly narrower confidence intervals, since it uses more of the available information. However, classical univariate adjustment overestimated the effects of SBP and cholesterol in comparison with multivariate adjustment. Knuiman et al. (5) observed underestimation but also concluded that applying univariate adjustments in multiple-covariate situations is not recommended. Several meta-analyses (12, 13, 16, 37) of blood pressure and/or cholesterol used univariate adjustments. Moreover, in a recent meta-analysis, Lewington et al. (16) assumed that effects of SBP are exclusively due to SBP 0–10 years before the at-risk moment. When this assumption is not true, as was suggested by our findings, overadjustment results. Therefore, although high blood pressure is an important risk factor for cardiovascular disease, its effect might be smaller than was suggested by this meta-analysis.

The two-step method used here is not the only available method with which to adjust for measurement error. Andersen and Liestol (23) compared several methods by simulation. They observed that the method used here outperformed the others, but they also concluded that the method of Tsiatis and Davidian (38) (not included in their simulations), which fits a joint measurement error/disease model, seems preferable (23). However, in contrast to that method, the two-step method can be applied using standard software. It uses available information better than the classical method of adjustment for regression dilution bias, is more flexible, and can be applied to model exposure at multiple moments in time. A disadvantage, however, is that modeling exposures as multivariate outcomes in a mixed model is only feasible when the number of inaccurately measured exposures is low. Accurately measured stable factors, however, could be incorporated in the fixed part of the model.

Using the two-step method, one needs to choose from many possible models for exposure trajectories. In our study, we could only estimate simple exposure trajectories for each individual. Using two different models, a random-slope model and a more complex polynomial model gave slightly different results, showing the influence of the choice of exposure model, but nevertheless yielded the same conclusions.

In summary, the two-step method yielded smaller confidence intervals than classical methods in the analyses by region, where data were sparse. Classical univariate analyses, in our data, overadjusted for regression dilution bias. From these analyses, we conclude that increased past SBP and increased recent SBP both seem to be associated with increased risk of coronary heart disease mortality, with the risk not being significantly associated with recent SBP once past SBP has been accounted for. Past and recent high SBP both increase the risk of stroke mortality, and both past and recent high serum cholesterol level increase the risk of coronary heart disease mortality.


   APPENDIX
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
References
 
Quick Bootstrapped Confidence Intervals
Study subjects were resampled 10 times. These 10 samples were used to fit 10 exposure models. Empirical Bayesian estimates were calculated from these models for the subjects in the bootstrap sample. For subjects not in the particular bootstrap sample, only the fixed part of the model was available and the random part was randomly drawn from the exposure models on one of the other bootstrap samples. Using these 10 sets of empirical Bayesian estimates, 10 Cox models were fitted. Assuming independence of the errors in the empirical Bayesian estimates and the errors in the coefficients of a single Cox model (ßi), the standard error (SE) of the average coefficient of the 10 Cox models (ß) can be estimated as

Formula
where n is the number of bootstrap samples. The same formula is used in multiple imputation, and therefore SAS PROC MIANALYZE can be used to calculate confidence intervals for ß. The first term in the formula reflects the uncertainty due to the limited information on mortality (<800 cases) in the Cox model and the second term the uncertainty due to the exposure model (approximately 19,000 systolic blood pressure and cholesterol measurements). Since the latter term is much smaller than the first, 10 bootstrap samples were ample for estimation of SEß. Although our method of calculating empirical Bayesian estimates for subjects not in the bootstrap sample is somewhat ad hoc, this affects mainly the second term, which is small compared with the first term.


   ACKNOWLEDGMENTS
 
This work was funded by the European Union (contract QLK6-CT-2000-00211) and the Dutch Ministry of Health, Welfare and Sport.

Conflict of interest: none declared.


   References
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 References
 

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RE: "EFFECTS OF PAST AND RECENT BLOOD PRESSURE AND CHOLESTEROL LEVEL ON CORONARY HEART DISEASE AND STROKE MORTALITY, ACCOUNTING FOR MEASUREMENT ERROR"
Am. J. Epidemiol., February 15, 2008; 167(4): 502 - 503.
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H. C. Boshuizen, M. Lanti, A. Menotti, J. Moschandreas, H. Tolonen, A. Nissinen, S. Nedeljkovic, A. Kafatos, and D. Kromhout
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Am. J. Epidemiol., February 15, 2008; 167(4): 503 - 504.
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