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Technical Briefs |
1
Division of Human Nutrition and Epidemiology, Wageningen University, 6700 EV Wageningen, The Netherlands
2
Wageningen Centre for Food Sciences, 6703 GW Wageningen, The Netherlands
aaddress correspondence to this author at: Wageningen Centre for Food Sciences/Division of Human Nutrition and Epidemiology, Wageningen University, PO Box 8129, 6700 EV Wageningen, The Netherlands; fax 31-317-485369, e-mail Petra.Verhoef{at}Staff.NutEpi.WAU.nl
Many studies have shown that increased plasma concentrations of total homocysteine (tHcy) are associated with cardiovascular disease (1). Like most biological variables, plasma tHcy fluctuates within an individual around a long-term mean (2)(3). tHcy measurements often are based on a single blood sample. Taking the mean of two or more repeated measurements will reduce the error attributable to within-subject biological fluctuations and reflect more closely a person’s true mean tHcy value within a certain period. However, as the time interval between two repeated measurements becomes shorter, the values become more similar and the error reduction diminishes. In that case, the benefit of taking the mean of two measurements is not fully used. On the other hand, intervals that are too long (several weeks) may compromise the compliance of study participants and allow long-term seasonal changes (4)(5).
Several studies on the weekly and monthly biological variation, as
expressed by the CV, in plasma tHcy concentrations have been published
(Table 1
). From these studies, no conclusions can be drawn about the
optimal time interval between two repeated samples to obtain a
sufficiently precise estimate of the true tHcy concentration within a
predefined period. The optimal time interval is reached when the
interval-specific CV does not increase further with increasing time
intervals.
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The aim of this study was to determine how many days between two samplings within 1 week are needed to reach the maximum biological variation in tHcy. Our findings may be useful in studies involving estimates of an individual’s true mean concentration of tHcy.
The participants in this study were six male and nine female healthy volunteers, ages 19–46 years. Use of medication or dietary supplements known to affect Hcy or folate metabolism were contraindications for participation. We applied strict criteria related to folate metabolism because folate is a strong determinant of Hcy metabolism. All individuals screened were eligible. Volunteers agreed to participate by signing an informed consent form. The Medical Ethical Committee of the Wageningen University approved the study.
On 5 sequential days, 5 mL of venous blood was collected between 0800 and 1000 from fasting (9–11 h) volunteers. Each volunteer’s five visits occurred at the same time in the morning on each day. Participants had their blood collected in the same position, sitting or lying down, throughout the study. Samples were collected in EDTA-containing tubes. Plasma was separated within 30 min and stored at -80 °C until analysis.
Plasma tHcy concentrations were measured within 2 weeks after the end of the study on a HPLC with fluorescence detection at our laboratory (6)(7). All samples from one individual were analyzed in duplicate in one analytical run to avoid between-run analytical variation. The within-run analytical CV based on these samples was 4.1%. The between-run CV in this laboratory was known to be 6.0%.
The intercorrelation of tHcy values within individuals over time, i.e.,
the semivariance, was calculated for intervals of 1, 2, 3, and 4 days.
The semivariance, 
(d), is equal to one-half the average
squared difference in concentration between any two samples that are
d days apart; the sum of the squares is divided by twice the
number of pairs available at a specified interval (4). Thus,
it is an estimate of the conditional variance of the second
measurement, given the outcome of the first one. The formula for this
calculation is:
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If repeated measurements are more correlated when they are taken at
short time intervals than when they are far apart, a model such as the
one described in the Appendix can be applied. The
within-subject correlation coefficient (
) between two consecutive
measurements, which is called autocorrelation, affects the variance of
sums and differences of two consecutive measurements. For uncorrelated
measurements ( = 0), it is a well-known property that the
SE becomes smaller by a factor of 1/
= 0.71.
On the other hand, if the two measurements are completely
correlated, i.e., identical, then there is obviously no reduction of
variance at all. By plugging in some selected values of
and 
2 in the model and comparing the
resulting curve with the empirical data, we found that values for the
autocorrelation in the range of 0.5–0.8 were consistent with the data.
A gradual increase of SD in our data with increasing individual mean
values of tHcy measured over 5 consecutive days indicated that the
usual assumptions of normality and constant variance were violated. We
therefore performed a logarithmic transformation on tHcy. This made it
possible to express the variability as a CV. For small to moderate
values of the CV, i.e., up to 
20%, the (semi-)variance of 100
x ln(tHcy) provides a fair estimate of the squared CV, as can be
derived straightforward from the Taylor series: CV =
).
This is the more natural model to use when within-subject SDs are
proportional to the mean value of the variable, as appeared to be the
case in our data. All statistical analyses were performed with SAS
(Ver. 6.12 for Windows).
Three volunteers were not fasting on the first day but completed the rest of the study. Data from these volunteers were reported as missing on the first day. The plasma tHcy concentrations in the 15 volunteers throughout the 5 days were 4.2–20.9 µmol/L with a mean of 9.2 (SD, 2.8) µmol/L.
The relationship between CV and sampling interval is shown in Fig. 1
. The values of the semivariance for the different time
intervals of 1, 2, 3, and 4 days, based on ln(tHcy) values and
expressed as a CV, were 7.9%, 12%, 13%, and 13%, respectively, with
corresponding numbers of observation pairs per interval of 57, 42, 27,
and 12, respectively. The CV at the time interval of 0 days refers to
the analytical variation for duplicates of a single sample, i.e., the
within-run analytical CV, which was 4.1% in our study. As Fig. 1
shows, the CV increased monotonically at a decreasing rate when the
interval increased from 0 to 4 days. This confirms that measurements on
consecutive days were correlated. Beyond the time interval of 2 days,
the CV increased very little.
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Thus, sampling on consecutive days reduces the benefit of taking the
mean of two measurements as a means of improving precision. For
uncorrelated measurements, the error would be reduced by a factor of
0.71 when duplicate samples are taken. We estimated that the
autocorrelation for consecutive days was 0.6 in this study. Therefore,
the error was reduced only by a factor 
= 0.89 for a 1-day interval
and 0.83 or 0.78 for a 2- or 3-day interval, respectively. For a 4-day
interval, the error was reduced by a factor of 0.75 and thus almost
reached the full error reduction of a factor of 0.71 that would
be achieved if no autocorrelation were present.
This study showed that the CV calculated from the semivariances of two repeated tHcy measurements increases with an increasing sampling interval of 1–4 days. This implicates the presence of autocorrelation of repeated tHcy measurements on short time intervals. The variation hardly increased between intervals of 2–4 days. We therefore suggest that serial blood measurements of tHcy to assess a person’s true mean average should be made at least 2 days apart.
Thirup and Ekelund (8) also examined the day-to-day
variation of plasma tHcy on 5 consecutive days, but calculated only one
CV instead of interval-specific CVs. They reported a mean
within-subject biological CV of 13% (8). We calculated that
the within-subject biological variation in our study was 12% at the
4-day interval, which is close to their finding. Studies that used
weekly through monthly sampling strategies found lower values for the
biological CV for plasma tHcy (Table 1
).
We used the method as described by Rotterdam et al. (5) for assessing the optimal time interval in days between repeated cholesterol measurements. Like these authors, we examined the biological variability as a function of time between repeated blood measurements, expressed as a semivariance. An attractive feature of this approach is that it presents different CVs at various time intervals, rather than just one CV.
Because of the presence of autocorrelation, the extent to which the error of the mean can be reduced increases with the time interval between two repeated tHcy measurements. We found that a 4-day interval yields almost the full benefit that can be achieved without the presence of autocorrelation.
In conclusion, this study shows that when the mean of two repeated tHcy determinations is calculated to enhance precision, the measurements should be taken at least 2 or, even better, 3 or 4 days apart to optimize error reduction.
Appendix 1
If xt is
a random variate with
E(xt) =
µ,
Var(xt)
= 2, and
Covar(xt,
xt+d) =
2d for
d = 0, 1, 2, ... , then is called the
autocorrelation. For this model, the variance of the sum and the
difference of two values are:
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Acknowledgments
We thank the volunteers for their participation in the study. We also thank the personnel of the division of Human Nutrition and Epidemiology of the Wageningen University who helped us with the study. We would especially like to thank Professor Clive West for scientific advice. The study was supported by the Wageningen Centre for Food Sciences (WCFS).
References
The following articles in journals at HighWire Press have cited this article:
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  G. Soletormos, A. Semjonow, P. E.C. Sibley, R. Lamerz, P. H. Petersen, W. Albrecht, P. Bialk, M. Gion, F. Junker, H.-P. Schmid, et al. Biological Variation of Total Prostate-Specific Antigen: A Survey of Published Estimates and Consequences for Clinical Practice Clin. Chem., August 1, 2005; 51(8): 1342 - 1351. [Abstract] [Full Text] [PDF]
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 M. P Hannon-Fletcher, N. C Armstrong, J. M Scott, K. Pentieva, I. Bradbury, M. Ward, J. Strain, A. A Dunn, A. M Molloy, M. A Kerr, et al. Determining bioavailability of food folates in a controlled intervention study Am. J. Clinical Nutrition, October 1, 2004; 80(4): 911 - 918. [Abstract] [Full Text] [PDF]
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A. Melse-Boonstra, C. E West, M. B Katan, F. J Kok, and P. Verhoef Bioavailability of heptaglutamyl relative to monoglutamyl folic acid in healthy adults Am. J. Clinical Nutrition, March 1, 2004; 79(3): 424 - 429. [Abstract] [Full Text] [PDF]
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