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1 Department of Preventive Medicine and Biometrics, University of Colorado
Health Sciences Center, 4200 E Ninth Ave., B 119, Denver, CO 80262.
2 Department of Medicine, Dartmouth College, Hanover, NH.
3 Colorado Heart Imaging, Inc., Denver, CO.
4 Department of Medicine, University of Colorado Health Sciences Center, Denver,
CO 80262.
5 Barbara Davis Center for Childhood Diabetes, Denver, CO.
Received May 6, 2003;
accepted after revision November 6, 2003.
Supported by the National Heart, Lung, and Blood Institute (grant
RO1-HL61753); National Institutes of Health (grants M01 RR00051 and P30
DK57516); and Merck, Inc. (university program grant).
Abstract
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SUBJECTS AND METHODS. Electron beam CT was performed on 1,074 participants. Coronary calcium volume scores were repeated 5 min apart. Interscan variability was examined using Bland-Altman plots and homogeneity tests. Transformations of the Box-Cox family (including power, roots, and logarithm) were applied to calcium volume scores. The transformation that stabilized the variation in calcium volume scores was applied to progression of calcium volume scores in 109 subjects with diabetes.
RESULTS. The variability in calcium volume score increased as the level of coronary calcium increased (rho = 0.67, p < 0.001 for the relation between the absolute difference and the mean value of calcium volume scores). This heterogeneity was removed using the square root transformation of the calcium volume score (rho = 0.09, p < 0.15 for the relation between the absolute difference in the square root of the calcium volume score and the mean square root of the calcium volume score). This transformation was applied to calcium volume scores taken a mean of 2.7 years apart in 109 subjects with diabetes. A significant change in calcium volume score was defined as a difference between the square root–transformed to calcium volume scores greater than or equal to 2.5 mm3 (> 99th percentile of interscan variability). Significant progression was observed in 10% of the subjects. The square root of the calcium volume score corrected for the bias in progression of calcium volume because of the level of coronary calcium.
CONCLUSION. Using the square root of the calcium volume score stabilized interscan variability across the range of coronary calcium. Defining change in coronary calcium as greater than or equal to 2.5 mm3 of the difference in the square root–transformed calcium volume scores provided an estimate that was unbiased with respect to baseline coronary calcium. This analytic technique may facilitate investigations of the relevance of changes in coronary calcium to clinical outcomes and the use of changes in coronary calcium as a measure of the therapeutic impact on subclinical disease in clinical trials.
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Recent studies have shown that the extent of coronary calcium changes over time in some individuals [10–12], and larger scale epidemiologic studies of changes in coronary calcium are planned for the future [13]. Investigators are now using changes in coronary calcium as a measure of efficacy in clinical trials of lipid-lowering therapy [14, 15]. Most studies have used annualized percent change in coronary calcium volume as a measure of changes in coronary calcium. These studies have not fully accounted for the potential of interscan variability in determining significant changes in coronary calcium.
Interscan variability of coronary calcium has been clearly established. Technical factors can limit the extent of interscan variability— for example, setting the trigger time to 40% of the ECG R-R interval versus the conventional 80% trigger [16–18]. However, interscan variability cannot be completely eliminated. The use of a volumetric score compared to the Agatston score also reduces interscan variability [19, 20]. Of particular importance in the evaluation of changes in coronary calcium is the relation between interscan variability and the coronary calcium score [20–22]—that is, the relation between measurement variability and the actual amount of coronary calcium. Without accounting for the relation between interscan variability and the calcium score, a bias may be introduced in the evaluation of changes in coronary calcium. For instance, using the change in calcium score, progression would be overestimated in subjects with high baseline coronary calcium and underestimated in subjects with low coronary calcium. Using the percent change in coronary calcium would have the opposite effect.
Several statistical methods could be applied to this problem. One method uses transformations of the differences between two measures to stabilize the variance across all ranges of the measures [23], whereas an alternate method uses a regression technique to account for potential nonuniform differences between two measurement techniques [24]. When the latter method is applied to duplicate measures of coronary calcium area, it shows that the variance increases as mean coronary calcium area increases in a symmetric fashion [21]. This tendency indicates a uniform pattern of interscan variability with respect to calcium score. This study identifies transformations of coronary calcium volume that lead to a score with variability that is uniform with respect to the actual value of coronary calcium. In addition, it obtains a criterion for defining significant changes in coronary calcium over time. This analytic strategy should be applied to other populations and other scoring techniques for coronary calcium to determine the generalizability of the specific transformations and the criterion identified in this report. Using this general methodology, however, an unbiased estimate of significant progression or regression of coronary calcium across a wide range of coronary calcium scores can be obtained.
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Electron Beam CT
High-resolution unenhanced images at end-diastole at 100-msec exposure time
with 3-mm slices were obtained using a C-150 Ultrafast CT scanner (Imatron). A
standard acquisition protocol was used. Scanning started near the lower margin
of the bifurcation of the main pulmonary artery. Breath was held for
approximately 45 sec. ECG triggering was at 80% of the R-R interval. Thirty to
40 contiguous 3-mm slices were acquired. The threshold for coronary calcium
was set at a CT density of 130 H in at least 3 pixels (an area > 0.51
mm2). A region of interest was encircled in each coronary artery
and a computer-driven measurement of the lesion area and its maximum density
was recorded. A coronary calcium volume score was obtained by multiplying the
pixel area by the section thickness, and a total volume score was derived by
the sum of all lesion volumes in cubic millimeters. An Agatston score was
obtained by multiplying the pixel area by a density score (1, 130–199 H;
2, 200–299 H; 3, 300–399 H; and 4, > 399 H) and summing all
lesion scores. A second independent electron beam CT scan was obtained from
each participant after a 5-min rest.
Statistical Analysis
Bland-Altman plots [23] and
Spearman's rank correlations were obtained for the absolute value of the
difference and the mean value of the calcium volume scores for scan pairs.
Superimposed on the Bland-Altman plot was the estimate of the mean value of
the absolute difference as a function of the mean calcium volume scores using
the nonparametric regression and smoothing splines (a piecewise cubic
polynomial that is continuous with respect to slope and curvature
[25]) with the degrees of
freedom set at 5. If the variance is homogeneous (i.e., the amount of
variability is not associated with the underlying score), the Spearman's rank
correlation will not be significantly different than zero and the slope of the
nonparametric regression line will not be significantly different than zero.
Results of the analyses of the absolute difference compared to the mean of the
two calcium volume scores taken 5 min apart are presented as Spearman's rank
correlations (rho) and p values for the relationship. Transformations
of calcium volume scores from among the Box-Cox family
[x(r – 1) / r and log(x)]
were considered for their ability to stabilize estimates of the variance
across the ranges of coronary calcium. Transformations were not used to
normalize the distribution of calcium volume scores. The Box-Cox family is a
class of transformation that includes all powers (e.g., roots such as the
square root, and squares, cubes) and the logarithm.
The square root transformation, which met the criteria for stable variance with respect to coronary calcium, was applied to the sample of pilot study participants (n = 109) with electron beam CT scans taken 2.7 years apart. The difference in the square root of the mean of two calcium volume scores taken 5 min apart at follow-up and the baseline square root calcium volume score was calculated. Significant progression of calcium volume score was defined as a difference of greater than 2.5 mm3 between baseline and follow-up. This value was greater than the 99th percentile of the difference in the square root of two measurements of calcium volume scores taken 5 min apart from the 1,074 subjects used to assess the variability in calcium volume scores.
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The variation in the calcium volume scores from two scans taken 5 min apart was dependent on the mean calcium volume score for the pair. As the level of coronary calcium increased, the interscan variation increased (Fig. 2). Significant positive correlation existed between the absolute value of the difference and the mean level of calcium volume scores (rho = 0.67, p < 0.001 for nonzero calcium volume scores). In other words, the variability in calcium volume scores for a person with high coronary calcium was larger than the variability in calcium volume scores for a person with low coronary calcium.
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The natural logarithm transformation of calcium volume scores altered the relation between the variation and the mean value of calcium volume scores; however, this transformation did not remove the dependence of the variation and the mean values of calcium volume scores (rho = –0.66, p < 0.0001) (Fig. 3). The cube root transformation of calcium volume scores also provided a significant negative relation between the variation and the mean of the calcium volume scores (rho = –0.27, p < 0.001) (Fig. 4). The transformation that minimized the relation between the variation and the mean of calcium volume scores was the calcium volume score to the 0.45 power (rho = 0.00, p = 0.97) (Fig. 5). Square root transformations of calcium volume scores also removed the relation between the variation and the mean of calcium volume scores (rho = 0.09, p < 0.15) (Fig. 6). Thus, the variability in the square root of calcium volume scores did not depend on the amount of coronary calcium. By using the square root transformation of calcium volume scores, an unbiased comparison of changes in coronary calcium over time could be made across the range of calcium volume scores.
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The cumulative probability plot for the absolute value of differences in square root calcium volume scores for scan pairs is shown in Figure 7. A value of 2.2 mm3 for the difference in the square root of the calcium volume score represents the 99th percentile. Using a cutoff point of 2.5 mm3, no subjects had differences in the square root–transformed calcium volume scores greater than 2.5 mm3 from the two scans taken 5 min apart.
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The square root transformation of calcium volume scores was applied to 109 subjects with diabetes who underwent two electron beam CT examinations a mean of 2.7 years apart. Using a conservative definition for progression of coronary calcium as a change of 2.5 mm3 in the square root of the calcium volume score, we found that 10% of the subjects had a significant change (progression) in coronary calcium over this 2.7-year period as determined by electron beam CT. Alternate methods for assessing subclinical disease were not performed in these subjects. Predictors of progression of coronary calcium in these patients with diabetes have recently been published [26]. No difference was apparent in the proportion of subjects with progression of coronary calcium across the range of coronary calcium scores.
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The square root transformation of calcium volume scores was applied to a
study of changes in coronary calcium in a small pilot study of subjects with
diabetes (n = 109). Using conservative criteria for defining
significant changes in square root calcium volume score (a difference 
2.5
mm3, > 99th percentile for the interscan variability of
replicate pairs of scans 5 min apart), we found that 10% of subjects showed
progression in coronary calcium over a 2.7-year period. With this cutoff
point, no false-positive changes in calcium volume scores were detected (e.g.,
in no subjects did the difference in the square root of the calcium volume
scores from scans 5 min apart fall outside of this value). Application of
specific cutoff points for determining significant changes in calcium volume
scores may depend on the population studied. The criteria for determining
significant changes should be established a priori, but may be different
between studies depending on the study design and the objectives.
Evidence is accumulating for the idea that coronary calcium is a marker for the presence of subclinical atherosclerosis. Coronary calcium has been shown to reflect the presence and extent of atherosclerosis as measured by more invasive techniques such as angiography [1, 2]. A meta-analysis of 16 studies (n = 3,683) indicates that the presence of coronary calcium is associated with increased prevalence of coronary disease [4]. Of particular importance is that the presence of coronary calcium predicts subsequent cardiovascular disease events [6], even in asymptomatic individuals [5, 7, 8]. However, the use of coronary calcium in prognostic models for patients with coronary disease when other known risk factors are included continues to be debated [4, 9].
Various scoring procedures have been applied to the measurement of coronary calcium. The historical standard is the Agatston score. Because of the stepwise nature of the weighting factor, the analysis of changes in the Agatston score may not accurately reflect changes in coronary calcium. The calcium volume score, which does not use a weighting factor, has been used to assess changes in coronary calcium. More recently, the measurement of coronary calcium mass using a cardiac CT phantom has been applied to the measurement of coronary calcium [27]. Two recent studies have addressed the issue of variability using these different techniques. One showed less variability with the coronary calcium mass compared to the calcium volume or the Agatston score [28], and the other showed no significant difference in variability between these methods [29]. As pointed out by Rumberger and Kaufman [29], these technologies are evolving and strategies for analyses should remain flexible. The method described in this article for assessing changes in calcium volume score could be applied to other scoring procedures, such as coronary calcium mass, in which the measurement variability may be dependent on the level of the measurement.
To our knowledge, few reports have investigated whether changes in coronary calcium are associated with coronary disease events. One study of 817 asymptomatic individuals with coronary calcium measured twice with an average interval of 2.2 ± 1.3 years showed that among those 45 subjects with subsequent coronary events, coronary calcium volume progression was significantly greater [30]. In a second study, among 225 individuals with a calcium score of greater than 20 who underwent repeated scanning 1–7 years later, those with coronary events (n = 30) had an annualized increase in coronary calcium of 35%, versus 22% in those without events (p < 0.05) [31].
Several studies have looked at predictors of short-term changes in coronary calcium. Conventional cardiovascular disease risk factors, hypertension and diabetes, were associated with progression of coronary calcium in one study [32] but not in others [10]. In a cohort of premenopausal women, high-density lipoprotein cholesterol and plasma triglyceride were associated with progression of coronary calcium [12]. Two studies have reported differences in progression of coronary calcium with lipid-lowering therapy [10, 14]. The clinical significance of changes in coronary calcium over time remains to be clearly established.
Criteria for evaluating changes in coronary calcium are problematic because interscan variability is related to the coronary calcium score. When evaluating interscan variability of percent changes in coronary calcium volume, the interscan variability is greater at lower calcium volumes [20–22]. Greater interscan variability is apparent at high calcium volumes by using change in raw calcium volume score (Fig. 2). Bielak et al. [21] applied a linear regression technique to determine the 95% limits of agreement and showed that variability increased symmetrically as the coronary calcium area increased.
Given this uniform pattern of variance, we examined several transformations of calcium volume score including roots, powers, and the logarithm (i.e., the Box-Cox family) in an attempt to stabilize the interscan variability across a range of calcium volume scores. The calcium volume score to the 0.45 power provided the most stable interscan variance across the range of coronary calcium levels in this population. A conceptually simpler square root transformation also provided an estimate of interscan variability that was not different across the range of calcium volume scores in this population of 1,074 subjects (rho = 0.09, p < 0.15). An unbiased estimate of changes in coronary calcium volume over time can be determined by using this transformation of calcium volume score.
The exact nature of the transformation and cutoff points for identifying changes in coronary calcium may be different in different populations. Regardless, stabilizing the interscan variability over the range of coronary calcium will be important in investigations of changes in coronary calcium. This article provides a model for analysis of changes in coronary calcium volume that is not biased with respect to baseline coronary calcium score. Future studies should apply an appropriate analytic strategy to ensure that the results of changes in coronary calcium over time are not influenced by differential interscan variability.
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