1 Department of Internal Medicine II-Cardiology, University of Ulm Medical Center, Ulm, Germany.
2 MEDIS Institute, GSF-National Research Center for Environment and Health, Neuherberg, Germany.
3 Institute of Epidemiology, GSF-National Research Center for Environment and Health, Neuherberg, Germany.
4 Centre for Amyloidosis and Acute Phase Proteins, Department of Medicine, Royal Free and University College Medical School, London, United Kingdom.
Received for publication September 15, 2002; accepted for publication January 30, 2003.
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ABSTRACT |
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coronary disease; inflammation; predictive value of tests; proteins
Abbreviations: Abbreviations: CI, confidence interval; MONICA, Monitoring of Trends and Determinants in Cardiovascular Disease; VCa, analytical variance component; VCb, between-subject variance component; VCw, within-subject variance component.
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INTRODUCTION |
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C-reactive protein represents an exquisitely sensitive objective marker of inflammation, tissue damage, and infection. Its plasma half-life (19 hours) is rapid but identical under all conditions, in contrast to virtually all other major acute-phase reactants, so that the synthesis rate of C-reactive protein is the sole determinant of its plasma concentration (3). Excellent anti-C-reactive protein antibodies and a well-established World Health Organization international reference standard for C-reactive protein (4) are available so that precise, sensitive, and robust clinical serum/plasma assays can be readily undertaken (57). The measurement of C-reactive protein thus has many advantages for detection and monitoring of the acute-phase response in general and particularly in relation to atheroma and its complications.
In long-term observational epidemiologic studies, risk variables are usually measured once at "baseline" and then related to outcome. Most physiologic variables, however, are not stable over time but show a more or less pronounced diurnal, seasonal, and long-term variation. The potential for long-term variation is of great importance, since such variation may have considerable impact on the accuracy of risk prediction by particular analytes. Relatively little information is available about this aspect of even the conventional risk factors in adequately sized samples and over longer periods of time (8), and only a few studies have investigated the hemostatic parameters commonly used in epidemiologic studies (912). Because the acute-phase response is nonspecific, highly sensitive, and induced by a wide range of different processes, including most forms of tissue injury and infection, long-term variation might be expected to be even more important for markers of inflammation than for other biovariables that are subject to such common and wide-ranging effects. In particular, for C-reactive protein, which is extremely sensitive and shows a dynamic range of up to 10,000-fold in response to a variety of stimuli (13), this information is needed to assess the risk prediction associated with elevated values reliably.
The objectives of the present study were to investigate the repeatability of C-reactive protein measurements in a large sample of middle-aged men from the general population and to correct earlier estimates of the association of C-reactive protein and coronary heart disease for the measurement error in C-reactive protein. Repeatability was assessed recognizing three potential sources of variation in C-reactive protein, that is, the error of the measurement process itself (analytical variation), the variability of values in individual subjects (within-subjects variation), and the variability of values between individuals (between-subjects variation).
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MATERIALS AND METHODS |
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In 19871988, 852 subjects of this group participated in a reexamination (response rate, 91 percent) and submitted to the same protocol during the same time of the year (October through May). For 696 of these subjects, we were able to obtain a second set of complete C-reactive protein and covariable values. All C-reactive protein values were measured in triplicate on both measurement occasions. They were originally recorded as averages after elimination of the extreme value if the coefficient of variation was larger than 15 percent. For a systematic subsample of the initial study population (every other man, n = 469), however, we were able to recover the three individual C-reactive protein values of the first measurement occasion. The basic statistics of our variables in the various subgroups did not differ appreciably from those in the larger groups from which the subgroups were sampled.
Survey methods
Participants completed an identical standardized questionnaire in 19841985 and in 19871988, including medical history, lifestyle, and drug history. Blood pressure was measured after the interview (duration, approximately 30 minutes) by a random-zero sphygmomanometer (Hawksley & Sons, Ltd., West Sussex, United Kingdom) according to the recommendations of the American Heart Association. Body height (m), body weight (kg), body mass index (weight (kg)/height (m)2), smoking behavior, and alcohol consumption (g/day) were determined as described elsewhere (17). Leisure-time physical activity was assessed on a four-level graded scale for winter and summer (none, <1, 12, and >2 hours/week). The number of years of education was calculated from the highest level of formal education completed. The presence of diabetes was determined by history.
Laboratory procedures
Nonfasting blood samples were drawn from an antecubital vein of the seated participant according to the recommendations of the International Committee for Standardization in Haematology. Only short-term venous stasis and minimal suction were applied. Serum samples from all subjects at the baseline examination in 19841985 and during the survey in 19871988 were immediately put on ice and then stored at 70°C until analysis.
Serum concentrations of C-reactive protein were measured in triplicate in a high-sensitivity immunoradiometric assay using monospecific polyclonal and monoclonal antibodies produced by immunization with highly purified C-reactive protein (7). C-reactive protein was heavily skewed but appeared to be almost perfectly approximated by a lognormal distribution, such that the lognormal transformation of C-reactive protein (mg/liter) was used throughout. Serum total cholesterol and high density lipoprotein cholesterol were measured by routine enzymatic methods. High density lipoprotein cholesterol was measured on serum after precipitation with manganese chloride and phosphotungstate.
Statistical methods
All computations were performed in Windows NT 4 (Microsoft Corporation, Redmond, Washington), with the software products SAS (SAS Institute, Inc., Cary, North Carolina), S-PLUS (Mathsoft, Inc., Seattle, Washington), and WinBUGS (18); the graphics were made with SAS software.
Variation
Variation was analyzed from concepts described by Fleiss (19), Bland and Altman (20), and Fraser and Harris (21). Basically, we computed estimates of the three variance components implied by the data, a nested structure of subjects (936 "levels"), measurement occasions (two levels for 696 subjects, one level for the rest), and replicates (three levels for 469 subjects at occasion 1, one level for the rest), assuming the traditional nested normal random-effects model. For the computations, we used the SAS MIXED procedure (restricted maximum-likelihood method, RANDOM statement), weighting an observation by the number of values represented by that observation (single replicate value or average of replicates). The three variance components are designated VCb (between subjects), VCw (within subjects), and VCa (analytical). For evaluating the within-subject variation, we used the 95 percent repeatability coefficient advocated by Bland and Altman (20) and computed as 1.96 x x (VCw + VCa)1/2. This coefficient (also called the critical difference (22) or the reference change value (23)) represents, when back-transformed by taking antilogs, for 95 percent of the subjects the upper limit of the ratio of the larger to the smaller of the measurements on two separate specimens of a single subject. A 95 percent confidence interval was obtained from the covariance matrix of the variance components. The intraclass correlation coefficient of reliability (reliability coefficient) was used to characterize the repeatability of measurements for comparing subjects or groups of subjects. It was computed as the VCb/(VCb + VCw + VCa) ratio (18) with an approximate 95 percent confidence interval (24, 25).
For evaluation of the analytical variation (the error of the measurement process itself), analogous coefficients were computed as 1.96 x x VCa1/2 (95 percent repeatability coefficient) and as (VCb + VCw)/(VCb + VCw + VCa) (reliability coefficient).
The number of measurements required to achieve a given reliability was computed with the Spearman-Brown prophecy formula (19). A variable was treated as being measurement error free if its reliability coefficient exceeded 0.75, following the recommendation of Fleiss (19). To assess the measurement error for the other variables, we estimated the reliability coefficient in an analogous way treating categorical variables as ordinal.
Association between C-reactive protein and coronary heart disease
The association of C-reactive protein and coronary heart disease had previously been analyzed with the Cox regression model (16). To correct the earlier results for the measurement error in C-reactive protein and the covariables, we repeated the analysis, utilizing the measurements at the second measurement occasion where available. The most used tool for measurement error correction is a structural approach with regression calibration (26). The independent variables were C-reactive protein (lognormal mg/liter) and the following covariables: the continuous covariables age (years), body mass index (kg/m2), total cholesterol (mmol/liter), high density lipoprotein cholesterol (mmol/liter), and systolic blood pressure and diastolic blood pressure (mmHg). The categorical covariables were smoking status (never smoked, former smoker, current smoker), alcohol consumption (men: 0, <40, 40 g/day; women: 0, <20,
20 g/day), years of schooling (<8, <11, >11 years), winter and summer leisure time physical activity (none, <1, 12, and >2 hours/week), and diabetes by history (no, yes). The continuous covariables were at least rather symmetrical such that they were used on their original scale. The dependent variable was again time to incidence of a first major coronary heart disease event. A subject was considered censored when he had died from another cause, when he had left the study area, or when the observation period had ended. The independent variables were C-reactive protein (lognormal mg/liter) and the covariables listed above. As a preliminary covariable check, the possibility of seasonal variation in C-reactive protein was investigated by fitting a sinusoidal curve with a period of 1 year to the data (details of the analysis method can be found elsewhere (27)). We reduced the number of covariables by the same forward-stepping procedure as before, at each step adding that variable that changed the absolute value of the C-reactive protein coefficient in the Cox regression the most and by at least 10 percent when added to the variables already in the model (28). Age was forced into the regression from the beginning. The categorical variables, recognizing their ordinal character, were treated as continuous variables. All variables were used with their linear terms. In this stepping process, the repeat measurements were utilized with the method of regression calibration by linear approximation of the calibration function (28). The final estimates of the regression models of interest were then obtained by Bayesian inference using Markov chain Monte Carlo methods (29), assuming the classic measurement model and "uninformative" priors.
RESULTS
Distribution of C-reactive protein
Figure 1 shows the distribution of the baseline triplicate C-reactive protein values, plotted against a standard normal distribution (Q-Q plot), using a logarithmic scale for C-reactive protein. The data points closely approximate a straight line with no apparent outliers, such that a normal distribution may be assumed for log-transformed C-reactive protein. The same conclusion was reached when adjusting C-reactive protein for the covariables and on the other two levels of measurement (within and between subjects). One can see that the minimum of C-reactive protein was 0.05 mg/liter, which was the lower detection limit of the assay used. The maximum was 70 mg/liter, and the 99th percentile was 25 mg/liter. A value of more than 3 mg/liter was reached by 32.2 percent of the values, and a value of more than 10 mg/liter was reached by 3.6 percent.
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The next block with three rows of data reports the analogous indices for the within-subject variation quantifying the repeatability of a subjects expected C-reactive protein value over time (usual value, homeostatic set point). The 95 percent repeatability coefficient (critical difference) was 8.40 (95 percent confidence interval (CI): 7.55, 9.46), meaning that for 95 percent of the subjects, the ratio of the larger to the smaller of two C-reactive protein determinations on different blood samples of a single subject is likely to be smaller than anywhere between 7.55 and 9.46. The reliability coefficient was 0.54, representing only moderate reliability. Therefore, for the assessment of the association between C-reactive protein and coronary heart disease, a correction for the fluctuation of C-reactive protein should be considered. As seen in the last row of table 1, a value of 3 (95 percent CI: 3, 4) determinations on separate specimens of a single subject is required to achieve at least the reliability of total cholesterol of 0.75 in our data estimated by the Spearman-Brown prophecy formula.
For the covariables, only the average of the triplicate measurements was available for analysis, such that the within-subjects variation was confounded with the analytical variation. Table 2 reports reliability coefficients for both the continuous and the categorical variables, the latter all being ordinal variables allowing continuous analyses. The coefficients ranged from 0.54 for alcohol consumption and summer leisure time physical activity to 0.93 for body mass index. The sizes of the reliability coefficients suggest that in regression analyses at least body mass index and smoking status may be treated as measurement error free.
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DISCUSSION |
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Problems of comparison of our results with those of the literature
Comparison of our variation results with published results turned out to be difficult for a number of reasons. One reason is the apparent lack of agreement on what statistics to report; for example, whereas Bland and Altman (20) strongly recommend the repeatability coefficient, Fleiss (19) makes extensive use of the classic reliability coefficient to which Bland and Altman are somewhat opposed (30). However, it seems that both coefficients are justified in their own right, the repeatability coefficient relating to measurements taken on a single individual and the reliability coefficient relating to the comparison of measurements on different individuals. Still others recommend using the repeatability coefficient, not basing it on the variance components obtained from analysis of variance computations, as do Bland and Altman, but on the variance components divided by the total mean (31), this way producing a "relative critical difference." Comparability is also impaired by many authors doing analyses for the untransformed values when the assumptions implied by the methods of analysis are not even approximately met. Lognormal C-reactive protein can almost perfectly be approximated by a normal distribution, such that most results obtained from the untransformed values are not comparable to those obtained from the transformed values.
Analytical variation
The measurement error of the assay was extremely small compared with within-subjects variation, the variability of C-reactive protein values free of assay measurement error within subjects. As an "acceptable goal," the analytical variation, expressed as the standard deviation ( ), should be less than 50 percent of the biologic within-subjects standard deviation (21), 25 percent being considered "optimal" (23). Our analysis yielded 10 percent, which is of the same magnitude as reported by Clark and Fraser (32) using a less sensitive assay (7 percent, computed from their "components of variation" for the untransformed C-reactive protein values). Our reliability coefficient of 1.00 was at its possible maximum. These results suggest that there is very little measurement error in the measurement device. Thus, the method used seems suitable for both clinical and scientific applications, even with a single determination.
Within-subject variation
The 95 percent repeatability coefficient for C-reactive protein was 8.40 (95 percent CI: 7.55, 9.46), which indicates considerable variation. The reliability coefficient of 0.54 was only of moderate size.
A number of studies have evaluated the biologic within-subject variance, mostly in smaller samples using various assays over either short periods of time (5, 9, 32) or medium time (12). Of these, only one presented analyses comparable to ours, at least with respect to the fact that they used lognormal-transformed C-reactive protein values (9). However, the within-subject variability was a little higher than ours, and the reliability coefficient of 0.86 for the healthy volunteers was considerably so because of the very large between-subjects variance component.
Two studies have reported on the long-term variability of high-sensitivity C-reactive protein. Ridker et al. (33), using data from 214 patients of the placebo group in the Cholesterol and Recurrent Events trial, found an acceptable correlation for lognormal-transformed C-reactive protein levels over 5 years with an age-adjusted correlation coefficient of 0.60 (p < 0.001), which is comparable to our age-adjusted reliability coefficient of 0.52. In a population-based study from Japan (34), 388 apparently healthy subjects had repeat measurements of C-reactive protein after a 5-year interval. For the 104 men, again for the lognormal-transformed C-reactive protein values, the correlation coefficient was 0.37 (95 percent CI: 0.19, 0.53), indicating moderate reliability. Thus, the variation of C-reactive protein found in our study, as measured by the reliability coefficient, compares with that reported in two other long-term studies.
If C-reactive protein measurements are used for cardiovascular risk assessment, based on our reliability estimates, three serial determinations (with a single assay measurement in each) should be done to achieve a reliability of 0.75, the reliability we found for total cholesterol, which still represents the standard in the clinical situation to which a new risk marker should be compared. Similar results had been obtained by Ockene et al. (35) when they applied the Spearman-Brown prophecy formula to their data. The reliability coefficient computed by the intraclass coefficient was 0.66 compared with our repeatability coefficient of 0.54. It would increase to 0.79 for two specimens and to 0.85 for three specimens. Since the reliability coefficient of total cholesterol in their data reached a value of 0.82, only a number of three or more specimens for the measurement of C-reactive protein would achieve a higher reliability for C-reactive protein than for total cholesterol.
Correction of the association of C-reactive protein with coronary heart disease for measurement error
Eleven prospective studies in apparently healthy men and women reported on the risk of increased C-reactive protein on future coronary heart disease. These subjects were followed for up to 12 years, and studies comprised a total of 2,557 cases. Results were remarkably consistent and showed an almost twofold increased risk if the top third of the C-reactive protein distribution was compared with the bottom third (2). In all of these studies, risk prediction was based on a single ("baseline") measurement. This increased risk associated with elevated C-reactive protein values was similar to that of classic risk factors.
We corrected the hazard ratios for C-reactive protein in the prediction of coronary heart disease obtained in our earlier analysis (16) for the variability of C-reactive protein over time. The corrected hazard ratios were considerably larger than the uncorrected ones. Although this may not be true universally (36), in the case of C-reactive protein, where there are only little variation over time in stable subjects free of disease and various unspecific, mainly environmental stimuli (37, 38), the true association between C-reactive protein and coronary heart disease is subject to considerable underestimation if no correction for the sources of such variability of C-reactive protein is made. In case there is a true change in the individuals habitual C-reactive protein over time, this certainly would correspond to a real change in coronary heart disease risk, and the correction would not be valid. Another issue relates to the additional adjustment of other biologic factors for measurement error (table 2). Better classification of traditional risk factors might have improved their predictive ability and thus may have resulted in significant associations with C-reactive protein, with the need to adjust for them and the potential consequence of attenuation of the initial association between C-reactive protein and coronary heart disease.
In summary, C-reactive protein measured by a high-sensitivity immunoradiometric assay showed extremely low analytical variation but a considerable within-subject variation over time. Cardiovascular risk prediction with C-reactive protein can be improved by taking this into account.
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ACKNOWLEDGMENTS |
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The authors thank Gerlinde Trischler for excellent technical assistance and Jens Baumert for critical comments on the revised draft of the manuscript.
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NOTES |
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REFERENCES |
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