Within- and between-subject variation in commonly measured anthropometric and biochemical variables.
The present study examines the between-subject variation, within-subject day-to-day biological variation, and analytical variation of several metabolic variables commonly measured in biochemical and physiological studies in a group of resting, healthy individuals after an overnight fast, the condition in which most metabolic studies are performed. For several of these analytes, systematic studies of within-subject day-to-day variation have been performed (6), and we present our data for comparison as well as presenting new data for the others. We present other useful statistics derived from these measures of variation, including reference change values, indices of individuality ([I.sub.ind])  and numbers of determinations required to estimate underlying within-subject values.
Subjects and Methods
Six healthy male [mean (SD) age, 22.3 (1.3) years; mean (SD) body mass index, 23.6 (1.0) kg/[m.sup.2]] and six healthy female [mean (SD) age, 23.1 (1.7) years; mean (SD) body mass index, 21.8 (1.5) kg/[m.sup.2]] subjects were studied daily over a period of 12 consecutive days in all subjects. Two of the male subjects had an Asian-Indian background, and the remaining subjects were white Caucasian. Subjects with a history of any significant cardiac, respiratory, gastrointestinal, or urogenital illness were excluded. The study was approved by the Central Oxford Research Ethics Committee, and all subjects gave their informed consent. The participants were instructed to fast and to not smoke (one male and one female smoker) from 2200 h the previous day; they arrived at the laboratory at 0800 h. We asked the subjects to avoid any strenuous exercise after 2200 h the previous day until the blood tests were taken the following morning. The subjects' weight and percentage of body fat were assessed every morning. The percentage of body fat was assessed by bioimpedance analysis with a Holtain bioelectrical impedance meter (Holtain Ltd) using equations described previously (7). All measurements were made by a single observer (A.W.). A carmula was placed each morning retrogradely into a vein draining a heated hand to provide arterialized blood. On each day, three blood samples were taken at 5-min intervals for the measurement of insulin, C-peptide, glucose, nonesterified fatty acids (NEFAs), and glycerol. A single blood sample was taken daily for 3-hydroxybutyrate (3-OHB), lactate, triglycerides, and glucagon.
Laboratory analyses, including the determination of analytical coefficients of variation (CVs), were performed after storage at 4[degrees]C for the following variables: plasma glucose, NEFAs, lactate, triglycerides, glucagon, insulin, and C-peptide. For each subject, samples from the 12 days were analyzed fresh in separate assays for glucose, insulin, C-peptide, and NEFAs and triglycerides, and on the same assay for glycerol, lactate, and 3-OHB; inter- and intraassay CVs were used for analytical variation as appropriate. The analytical CVs quoted were obtained for general laboratory use and not determined as part of the current study. Interassay variation was assessed from 30 determinations, measured on separate days, and intraassay variation was assessed from 10 determinations, measured on a single assay. Intra- and interobserver variation for bioimpedance measurements were assessed from triplicate measurements by three observers on two subjects on a single day.
Blood samples were drawn into precooled heparinized syringes; a portion (100 [micro]L) was immediately deproteinized in 70 g/L perchloric acid, and the supernatant was stored at -20[degrees]C for later analysis of glycerol and 3-OHB concentrations (8). Fasting glucose was measured in plasma (fluoride/ oxalate) by the hexokinase method (Gluco-quant glucose; Boehringer Mannheim) on a discrete analyzer (Cobas MIRA; Roche Diagnostics) using a 5.56 mmol/L glucose calibrator (Sigma Chemical Co.). Immunoreactive insulin was measured in heparinized plasma by double antibody RIA with Sepharose attached to the second antibody for separation by decanting (PhRIA100; Pharmacia Ltd). The method was automated using a sample processor (IDS Star 700; Kemble Instrument Co., Ltd) and an automatic gamma counter (LKB-Wallac 1277 Gamma master; Wallac). There was 100% cross-reaction to intact proinsulin and cross-reaction with all split proinsulins in this RIA. C-peptide was measured in heparinized plasma by RIA (range, 0.02-3.3 nmol/L), using anti-human C-peptide guinea pig serum (Linco Human C-peptide RIA kit; Biogenesis Ltd). The C-peptide assay was automated as described for the insulin RIA. Glucagon was measured at the Department of Medicine, Royal Victoria Hospital, Belfast, Ireland, in heparinized plasma by RIA (range, 5-150 ng/L) using an antibody raised to porcine glucagon (NOVO Nordisk). The assay has been reported previously in detail (9). The antibody YY89 was used at a final dilution of 1:90 000, and YY89 reacts with the C-terminal region (C-GLI), which has been considered to be pancreas specific. The detection limit of the assay was 15 ng/L. No cross-reactivity has been noted with other gut and islet hormones. Plasma triglycerides were measured in plasma from potassium-EDTA-anticoagulated whole blood, using the GPO-PAP kit with Precimat glycerol calibrator (Boehringer Mannheim) on a centrifugal analyzer (Cobas FARA; Roche Diagnostics). The results were not corrected for free glycerol. Plasma NEFAs were measured in plasma from potassium-EDTA-anticoagulated blood by an enzymatic colorimetric method on a Cobas MIRA discrete analyzer (Roche Diagnostics). Plasma lactate was measured in plasma from potassium-fluoride/EDTA-anticoagulated blood using a Monotest lactate fully enzymatic U/V kit (cat. no. 149993; Boehringer Mannheim). Enzymatic methods for blood glycerol and 3-OHB were adapted to an IL Monarch centrifugal analyzer (Instrumentation Laboratory) as described previously (8).
Data were checked for normal or log-normal distribution using the Shapiro-Wilk test and are expressed as mean (SD) or geometric mean (SD range) as appropriate. The following variables were logarithmically transformed in subsequent analyses: triglycerides, NEFAs, insulin, C-peptide, glucagon, glycerol, 3-OHB, and lactate. Estimates of the overall mean (or geometric mean) value, the underlying between-subject variance, [V.sub.G], (i.e., excluding within-subject variance), and of the within subject variance, [V.sub.W] (between-day, biological plus analytical) were obtained using analysis of variance, with subject as a random effect, using PROC MIXED in SAS (SAS Institute). For analytes that were measured on three 5-min interval samples, only the first sample was used for comparability with analytes measured on one sample only. For normally distributed data, the between- and within-subject [CV.sub.S], [CV.sub.G] and [CV.sub.W] respectively, were calculated as the square root of the variance component estimate divided by the overall mean. For logged data, [CV.sub.G] and [CV.sub.W] were calculated as the square roots of the respective variance component estimates. [CV.sub.W] was further partitioned into within-subject biological variation, [CV.sub.I] and analytical variation, [CV.sub.A], using the equation:
[CV.sub.I] = [square root of ([CV.sub.W.sup.2] - [CV.sub.A.sup.2])]
The within-subject biological variation, [CV.sub.I], in fact can be further partitioned into the coefficients of "underlying" biological variation (denoted by [CV.sub.U]) and the variation occurring between separate samples (denoted by [CV.sub.S]). The latter will include biological pulsatility of plasma concentration, plus variation occurring from sample handling. For analytes measured on three samples taken at 5-min intervals on each day (i.e., glucose, insulin, C-peptide, NEFAs, and glycerol), this was calculated from the biological variation, [CV.sub.I], by fitting a second model using all three measurements in which the day was included as a random effect, nested within subjects. The [CV.sub.U] was calculated as the square root of the underlying biological variance component divided by the overall mean, or simply the square root of the underlying biological variance component if the data were log transformed. The between-sample CV, i.e., between successive 5-min samples, [CV.sub.S], was calculated using the equation:
[CV.sub.S] = [square root of ([CV.sub.I.sup.2] - [CV.sub.U.sup.2])]
In addition, we have also calculated the "critical differences", or reference change values required to detect a significant change in values within individuals at the 5% level of confidence. This latter uses the between-assay, [CV.sub.BA], rather than the within-assay, variation, together with [CV.sub.I], i.e., [CV.sub.I+BA] = [([CV.sub.BA.sup.2] + [CV.sub.I.sup.2]).sup.1/2] , to calculate the variation found in practice between samples taken on different occasions. The reference change values (10) at the 5% level were calculated as:
1.96 X [square root of 2] [CV.sub.I+BA] X the mean overall value
The "index of individuality" (10) for each analyte was determined as:
[I.sub.ind] = [CV.sub.I+BA]/[CV.sub.G]
which indicates the degree to which a single measurement in this population is able to distinguish unusual results in a subject. Arbitrary values are used to differentiate situations where a value determined in an individual may be assessed in terms of the population reference range ([I.sub.ind] >1.4) from those where the population reference interval is significantly greater than within-subject variation ([I.sub.ind] <0.6), and is therefore not useful for detecting unusual results in individuals. [Fraser and Harris (10) point out the semantic difficulty associated with this index getting smaller as individuality becomes greater, but we have followed common practice in this report.]
We also estimated, for each analyte, the number of repeat measurements (on different days) that would be required to estimate a subject's underlying homeostatic set point to within [+ or -] 15% with 80% confidence using the formula of Fraser and Harris (10). This calculation depends only on the overall within-subject variation ([CV.sub.I+BA])
BETWEEN- AND WITHIN-SUBJECT AND ANALYTICAL VARIATION
The between- and within-subject biological and analytical [CV.sub.S], [CV.sub.G], [CV.sub.I], and [CV.sub.A], respectively, are reported in Table 1. The analytical variation is generally low and accounts for <7% of the total variance in all variables (data not shown).
BETWEEN- AND WITHIN-DAY VARIATION
Table 2 shows the underlying biological and between-sample [CV.sub.S], [CV.sub.U] and [CV.sub.S] , respectively, for the five analytes that were measured three times at 5-min intervals on each day. The underlying biological variation is greater than the between-sample variation in all cases.
Table 3 shows reference values for significant changes within-subjects at the 5% level, individuality indices for each variable, and the number of measurements that would be required to estimate the homeostatic set point to within [+ or -] 15% with 80% confidence. As would be expected, weight and percentage of body fat show the greatest individuality and require only a single measurement to estimate the true value. Of the biochemical variables, glucose and glucagon show the lowest individuality indices, at 0.7 and 0.8. A single glucose measurement is sufficient to estimate the true value, but the larger within-subject CV of glucagon means that four measurements are required to estimate the set point to within [+ or -] 15%. Triglycerides (3), C-peptide (4), and insulin (5) require only a modest number of samples, whereas the remaining analytes have large within-subject biological CVs, high individuality indices, and require larger numbers of measurements for accurate estimation of their homeostatic set points.
This study demonstrates a diversity in the range of day-to-day variation of different anthropometric and metabolic variables in any individual. As expected, the anthropometric variables weight and percentage of body fat show the lowest individuality indices and require the smallest number of samples to measure precisely. The metabolic variables examined exhibit greater fluctuation, varying from the relatively stable glucose and glucagon to the highly variable NEFAs and 3-OHB. Such variability will incorporate several components, such as assay variability, variation in experimental technique, and true biological variability (2-5).
We compared our data for between- and within-subject biological variation with previously published studies in healthy subjects using the compilation of Sebastian-Gambaro et al. (6). Our data for glucose are comparable with the median values from previous studies ([CV.sub.G] = 7.8%; [CV.sub.I] = 6.1%), which ranged from 1 day to 1 year in duration. For insulin and triglycerides, although we report lower between-subject [CV.sub.S], possibly reflecting our more uniform selection of subjects, we found within-subject [CV.sub.S] similar to those in previous studies ([CV.sub.I] = 21% and 22%, respectively). Our within-subject CV for C-peptide was somewhat larger than that reported previously, but our within-subject CVS for lactate was similar (9.3% and 27%). We present new data for reference for NEFAs, 3-OHB, glycerol, and glucagon. Although the biological variability of glucagon compares with the other pancreatic islet peptides, that of the three analytes relating to fatty acid metabolism is considerably greater than all other variables measured in this study and almost all serum concentrations reported by Sebastian-Gambaro et al. (6).
Assay noise with modern biochemical methods is, in general, small in relation to other sources of variation, and this was confirmed by our study. Within-day sample-to-sample variation can be significant, as is seen in tests in which multiple samples are taken on the same day. In some cases, this may represent underlying biological fluctuation, such as for plasma insulin, where 13-min oscillations in plasma concentration occur (11). In other cases, the source of the variation is less easy to identify, but may include residual effects of the stress of cannulation, duration of venous stasis (although in the present study all samples were taken from unoccluded "arterialized" veins), contamination of cannula samples with flush fluids, or postsampling degradation.
In the present study, additional day-to-day biological variation was greater than within-day biological variation for each of the five analytes for which repeat samples were taken each day. Diurnal patterns in blood concentrations of metabolites (5,12), including progressive changes that can occur with prolongation of fasting (13), could masquerade as day-to-day variation if the sampling time is not carefully controlled. Differences in the conditions of sampling, such as exertion in the period preceding the blood sample (2,14, 15), could be misinterpreted as underlying biological fluctuations. In the present study, however, the timing of sampling and the duration of fasting were controlled, and undue exertion before sampling was avoided. The residual variation that was observed is likely to represent less immediate environmental influences, such as effects of the previous day's food intake or exercise, or fluctuations from other poorly characterized sources. All biological systems are subject to variation, which is usually under homeostatic control even if the complexity of inputs makes interpretation difficult.
The importance of the within-subject variation when interpreting results can be assessed by comparison with the variation observed between subjects in a group of "normal" individuals. The ratio of the within- to between-subject CVs is termed the individuality index (10) and indicates the degree to which one individual can be distinguished from another by a single measurement in the present population. As expected, weight and percentage of body fat showed low individuality indices, although their within-subject variation was not insignificant even over the course of the 12 days of the study, especially for percentage of body fat. The variation in the individuality of important metabolites and hormones, however, was appreciable, ranging from glucose and glucagon, with indices of 0.7 and 0.8, to NEFAs and 3-OHB, with indices of 1.4 and 1.5, indicating that the day-to-day variation within individuals was markedly greater than the underlying variation between individuals. For most of these variables, however, it would not be wise to attempt to distinguish between individuals in this population on the basis of a single day's measurement, and it would be preferable to use the mean of repeated samples taken on different days.
When using metabolic variables as risk factors or covariates in physiological and metabolic studies, e.g., in relation to the power to distinguish between different interventions or to determine relationships between variables, it is the precision of the measurement as an estimate of the underlying "true" value or homeostatic set point that is of interest. This depends only on the within-subject variation (biological and analytical), and we have used this to assess the number of repeat samples on different days that would be required to estimate the set point to within [+ or -] 15% with 80% confidence. For several important metabolic variables, such as plasma NEFAs and 3-OHB and, to a lesser extent, insulin and C-peptide concentrations, a measurement taken in a healthy individual on a single day is clearly insufficient to estimate their true values with even moderate accuracy. For glucose, a single measurement will suffice, but we have not similarly studied the variation in subjects with increased glucose concentrations.
For those analytes for which we took three samples each day, the total within-day variation (i.e., biological plus analytical) was somewhat smaller than the between-day variation. This means that taking the mean of three samples on the same day confers little advantage in determining an individual's homeostatic set point. To estimate the set point to within [+ or -] 15% with 80% confidence, as above, would make no difference to the number of sampling days required for glucose and C-peptide and would save only a single sampling day for insulin and NEFAs (data not shown). Only for glycerol, where the combined within-day variation is of a similar magnitude to the between-day variation, is there a noticeable advantage, reducing the number of samples required by over one-third, from 10 to 6. Within the normal range, it is much more advantageous to use the mean of repeated single samples taken on different days because this would reduce the overall within-subject variation.
In summary, in this study of biological variability in anthropomorphic and metabolic variables on consecutive days in healthy subjects, we present new data relating to glucagon and three components of fatty acid metabolism and confirm previous measures for components of glucose metabolism. These data are important for the assessment of individual subjects and the design of studies involving these variables. The within-subject variation of the fatty acid-related metabolites is greater than most analytes reported previously in blood. The source of this variation and the interrelationships between these and other metabolically linked variables on a within-subject, day-to-day basis remain to be determined.
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ADJI WIDJAJA,  RICHARD J. MORRIS  JONATHAN C. LEVY,  * KEITH N. FRAYN  SUSAN E. MANLEY,  and ROBERT C. TURNER 
 Department of Clinical Endocrinology, Hannover Medical School, 30625 Hannover, Germany.
 Diabetes Research Laboratories and  Oxford Lipid Metabolism Groupwdef, Radcliffe Infirmary, Woodstock Road, Oxford OX2 6HE, UK.
 Nonstandard abbreviations: lina, index of individuality; NEFA, nonesterified fatty acid; 3-OHB, 3-hydroxybutyrate; CVO, between-subject CV; CVw, within-subject CV; CVI, within-subject biological variation; CVu, underlying biological variation; and CVs, variation between samples.
* Author for correspondence. Fax 0044-1865-723884; e-mail jonathan.levy@ drl.ox.ac.uk.
Received January 14, 1999; accepted January 29, 1999.
Table 1. Between- and within-subject biological CVs and analytical CV of body composition, intermediary metabolites, and related hormones Biological CV Overall mean or Analyte geometric mean [CV.sub.G] Body weight, kg 66.5 12% Body fat, % 24.2 29% Glucose, mmol/L 4.94 7.5% Insulin, (c) pmol/L 52.2 26% C-peptide, (c) nmol/L 0.39 26% Glucagon, (c) ng/L 52.5 28% Triglycerides, (c) mmol/L 0.61 20% NEFAs, (c) [micro]mol/L 376 32% Lactate, (c) mmol/L 0.88 29% Glycerol, (c) pmol/L 48.1 44% 3-OHB, (c) [micro]mol/L 42.5 41% Biological CV Analyte [CV.sub.I] [CV.sub.A] Body weight, kg 0.9% Negligible Body fat, % 10% 1.7% (a) Glucose, mmol/L 4.8% 2.4% (a) Insulin, (c) pmol/L 26% 6.6% (a) C-peptide, (c) nmol/L 24% 3.8% (a) Glucagon, (c) ng/L 19% 5.5% (a) Triglycerides, (c) mmol/L 21% 1.6% (a) NEFAs, (c) [micro]mol/L 45% 4.1% (a) Lactate, (c) mmol/L 31% 1.6% (a) Glycerol, (c) pmol/L 36% 4.1% (a) 3-OHB, (c) [micro]mol/L 61% 6.1% (a) (a,b), CV (a) within- or (b) between-assay as appropriate. (c) After log transformation. Table 2. Partition of the biological CVs into [CV.sub.u] and [CV.sub.s] sample variation for intermediary metabolites and related hormones measured daily with three samples at 5-min intervals. Analyte [CV.sub.u] [CV.sub.s] Glucose 4.1% 1.6% Insulin (a) 23% 10% C-peptide (a) 23% 6.3% NEFAS (a) 43% 8.7% Glycerol (a) 26% 24% (a) After log transformation. Table 3. Reference change values, individuality indices, and numbers of samples (on different days) required to estimate the underlying homeostatic set point. Number of samples required to estimate the underlying Reference change [I.sub.ind] homeostatic Analyte values (a) (b) set point (c) Body weight 1.6 kg 0.08 1 Body fat 6.80% 0.3 1 Glucose 0.7 mmol/L 0.7 1 Insulin 39 pmol/L 1.0 5 C-peptide 0.26 nmol/L 0.9 4 Glucagon 32 ng/L 0.8 4 Triglycerides 0.36 mmol/L 1.1 3 NEFAs 475 [micro]mol/L 1.4 15 Lactate 0.80 mmol/L 1.1 8 Glycerol 49 [micro]mol/L 0.8 10 3-0HB 72 [micro]mol/L 1.5 27 (a) Significant differences between days within individuals at 5% level. (b)Population reference intervals to detect unusual values: useful if [I.sub.ind] >1.4 and not useful if [I.sub.nd) <0.6. (c) To within [+ or -] 15% with 80% confidence. Estimates for greater precision or confidence are much increased.
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|Title Annotation:||General Clinical Chemistry|
|Author:||Widjaja, Adji; Morris, Richard J.; Levy, Jonathan C.; Frayn, Keith N.; Manley, Susan E.; Turner, Rob|
|Date:||Apr 1, 1999|
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