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Letters to the Editor |
1 Pathology and Laboratory Medicine, University Medical Hospital Groningen, Groningen, The Netherlands
2 Roche Diagnostics GmbH, Mannheim, Germany
aAddress correspondence to this author at: University Medical Hospital Groningen, Department of Pathology and Laboratory Medicine, CMC-V, Room Y1.165, PO Box 30.001, 9700 RB Groningen, The Netherlands. E-mail m.r.fokkema{at}lc.umcg.nl.
To the Editor:
In 2004, Bruins et al. (1) published a report in which they used the approach of Harris and Yasaka (2) to determine the reference change values (RCVs) for B-type natriuretic peptide (BNP) and N-terminal proBNP (NT-proBNP). Week-to-week RCVs were 113% and 98%, respectively, meaning that concentrations had to increase or decrease by these percentages to be assessed as different from the previous measurement, with a 5% error probability for falsely assessing a change as significant. The clinical relevance of these large RCVs led to a lively discussion (3)(4)(5)(6) regarding RCV methodology. In response, we have developed some ideas for improving RCV calculation by addressing the skewness of the distribution.
The previous study used for the new approach investigated 43 patients with stable chronic heart failure by within-day, day-to-day, and week-to-week measurements of BNP (Abbott Diagnostics) and NT-proBNP (Elecsys® proBNP, Roche Diagnostics GmbH). For details, see the original report (1).
Natriuretic peptides are secreted in response to increased demand and may not be conceived to fluctuate around a physiologic (homeostatic) set point as do analytes that are regulated by physiologic processes. The assumption of gaussian-distributed measurements may not hold, and indeed, the (interindividual) distribution of natriuretic peptides shows a right-skewed shape. Whereas log-transformation is the recognized remedy for appropriate transformation, its use in the construction of RCVs was not proposed and also requires an intraindividual skewed distribution. Assessing the skewness can be accomplished by comparing the arithmetic mean and median: the mean is greater than the median for right-skewed distributions. The success of log-transformation, based on the raw data from the original report (1), was assessed by determining the percentage deviation from 1 of the week-to-week mean over the week-to-week median, before and after transformation. Mean deviations before and after transformation were 10.6% and –0.1% for BNP and 10.3% and 0.5% for NT-proBNP, respectively. These results suggest that a lognormal approach is preferable over a normal approach for BNP and NT-proBNP. Measurements follow a lognormal distribution if the logarithms of the measurements follow a gaussian distribution.
Mathematically, the lognormal distribution uses 2 parameters, µ and 
2, the mean and variance of the underlying gaussian distribution. The lognormal mean, SD, and the CV are determined by µ and 2:
In the following derivation of RCVs, only the total variation is considered [no split in subcomponents; for a comparison, see Ref. (7)]. A change between 2 consecutive (independent) measurements, x and y, is considered significant (with 5% error probability) when the difference,
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x z x , where z = 1.96. This follows from the gaussian distribution of the log-transformed measurements [compare with Iglesias et al. (8)]. By retransforming the difference and the interval borders to the original scale, we see that
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x }; exp{+1.96 x x }] to be significant. Because
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Turning this approach to practice requires an estimate 
of the parameter . A simple way can be based on aggregate data. Because the lognormal CV depends only on (see the scheme
), this yields = 
. Thus, can be obtained by inserting the untransformed population CV in this expression, and the derivation of RCVs can proceed as delineated above. The results are compiled in Table 1
. We note that an estimate of can also be based on the single serial measurements given in the original study (1), which lead to very similar RCVs. A statistical article discussing several options for RCVs in skewed distributions is in preparation.
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The lognormal RCVs possess better biological plausibility. Paradoxical values of decreases greater than 100% are eliminated. However, in view of monitoring applications, these RCVs are still rather high. The corrected lognormal RCVs refer to the commonly used 5% bidirectional statistical error. This RCV setup implies that 
5% of clinically stable patients show changes greater than the RCV (false positives). However, for the treatment of heart failure, false negatives present the major risk, and it is imperative that deterioration in a patient’s clinical condition is not missed so that appropriate clinical intervention can be initiated (9). The common probability "insurance" of 95% against false positives could be too high, and another value, 80%, would be clinically more appropriate to lower the false-negative rate. When 80% is used in the construction of RCVs, then NT-proBNP week-to-week lognormal RCVs narrow to 85% for increases and to –46% for decreases.
The important message we take from this analysis is that the skewness of the distribution requires adequate methods to deal with it to achieve clinically and biologically valid RCVs.
References
The following articles in journals at HighWire Press have cited this article:
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  F. S. Apple, A. H.B. Wu, A. S. Jaffe, M. Panteghini, R. H. Christenson, NACB COMMITTEE MEMBERS, R. H. Christenson, F. S. Apple, C. P. Cannon, G. Francis, et al. National Academy of Clinical Biochemistry and IFCC Committee for Standardization of Markers of Cardiac Damage Laboratory Medicine Practice Guidelines: Analytical Issues for Biomarkers of Heart Failure Circulation, July 31, 2007; 116(5): e95 - e98. [Full Text] [PDF]
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