CLIN. CHEM. 28/2, 294-300
(1982)
On IndividualReference IntervalsBased on a LongitudinalStudyof Plasma
Proteinsand Lipidsin HealthySubjects,and Their PossibleClinical
Application
Nlels Erlk Raun,1 Birger Broch Mglier,2 Uffe Back,1 and inger Gad3
In a longitudinal Study, we determined interindividual and
intra-individual variation in 20 plasma proteinsand lipids
and in other blood constituentsby analysisof variance.
Blood from 20 healthysubjectswas sampled monthly for
six months, a rigorousblood-sampling technique being
applied.The mean proportionof interindividual
variation
differedfor each blood constituent, ranging from 22 to
91 % of the total variation. The possible clinical application
of individual reference intervals of this homeostatic model
was demonstrated by the fact that they were exceeded in
individualcases of upper respiratory tract infection.
Concordance between individual
reference intervalsin
healthycontrolsand in patients-as exemplifiedintwo
chronic diseases, multiple sclerosis and chronic inactive
pyelonephritis-suggests
that the use of individual intervals in (chronic) disease is valid, even when derived from
healthy persons. Additionally, sex- and age-related differences were significant for some constituents.
AddItIonal Keyphrases: variation, inter- and intra-individual
analysis of variance
related differences
pye!onephritis
‘
clinical application
age- and sexchronic disease
multiple sclerosis
#{149}
Extensive use of repeated plasma-protein
analyses in
evaluating the course of immunologic diseases and the effects
of treatment is often unwarranted,
because interindividual
variation isso large (1). Furthermore,
automated
analysis (e.g.,
offers
the clinician
of data that are not immediately
nephelometric
applicable.
It
methods)
may thus be fruitful
to separate
a huge number
variation
uses of these
results.
Material and Methods
Subjects.
Twenty adults without any known diseases voluntarily participated
in monthly blood sampling for approximately six months. The subjects were mainly selected
from hospital-staff
and relatives of patients with multiple
sclerosis. The age range was 24 to 55 years (mean 39.6, median
39, SD 9.1 years) and included equal numbers of men and
women
(mean
ages, 38 and 41 years, respectively).
This group
was the control group.
or pyelonephritis
were
of 10 men and 10 women
with a definite diagnosis of multiple sclerosis (2). They were
comparable to the healthy persons with respect to sex and age
(mean 40.6, range 25-69 years). The mean age of the six
women with chronic inactive pyelonepbritis whom we studied
was 49 years (range 36-58 years).
Samples.
The subjects had blood sampled under uniform
conditions. All had been fasting for at least 6 h and had not
been exercising. After they had been sitting down for at least
10 miii, 120 mL of blood was drawn by syringe, with slight cuff
pressure. Sample-tubes
were filled in a fixed order and
brought
to the laboratory
within
30 mm.
Blood was sampled from three of the control persons and
three of the patients twice a week between 0800 and 1000
hours. At the first examination the urine was checked for albumin, blood, and glucose as well as for significant bacteriuria.
Blood was sampled from the subjects six times, with a fourweek interval between samplings
in the case of the controls.
In cases of controls who developed upper respiratory tract
infection, additional samples were taken as soon as possible
and repeated one, two, and four weeks after the outbreak of
infection.
Chemical methods. The serum specimens
were assayed for
total protein; albumin; orosomucoid; a1-antitrypsin;
haptoglobin; ceruloplasmin;
a2-macroglobulin;
immunoglobulins
IgG, IgA, and 1gM; and the Clq, Cis, C3, C3 (pro)activator,
C4, C5, and Cis inhibitor components of complement.
Total protein was determined by the biuret method (3).
The individual serum proteins were assayed by “rocket”
immunoelectrophoresis
interindividual
from intra-individual
variation, to determine
the “individual
reference interval.” This might facilitate the extraction of
information from data, both for therapeutic
and diagnostic
purposes.
We estimated inter- and intra-individual
variation
in 20
plasma proteins and serum lipids, and we demonstrate some
potential
Patients
with multiple
sclerosis
studied. The former group consisted
(4).
Antisera were obtained from Dako or Behringwerke
and
standards from Behringwerke (standard
human serum).
A pool of human donor serum was used for calibration
when
commercial standards were not available (i.e., for the complement components other than C3 and C4).
All determinations
were made in duplicate. The serum
specimens
were also assayed for total lipids, a1- and -lipoprotein, total cholesterol, triglyceride, and creatinine. Total
lipids were determined by colorimetry, with Fat Red 7B as
reagent (unpublished
method by E. Raabo).4
The method was calibrated by use of a pooled specimen of
human serum, the total lipids of which were determined grevimetrically.
The a1- and f3-lipoproteins
were assayed by rocket immunoelectrophoresis
as above, with human
serum pool and
3-lipoprotein
standard
serum (Behringwerke)
as standards.
Total cholesterol was determined enzymically (Calbiochem
Cholesterol
one-vial
pack, cat. no. 15989) with glycerol as
standard.
Neurological
Department,
Kommunehospitalet,
magsgade 5, 1399 Copenhagen K, Denmark.
2Nephrological
Department,
Hvidovre Hospital,
1
Oster
Fan-
Creatinine was determined
on the Jaff#{233}
reaction.
by a mechanized
assay based
Copenhagen,
Denmark.
‘Department
of Clinical
Chemistry,
Kommunehospitalet,
penhagen,
Denmark.
Received March 4, 1981; accepted Oct. 26, 1981.
294
CLINICAL CHEMISTRY. Vol. 28, No. 2, 1982
CoRaabo, E., Personal communication (Department of Clinical
Chemistry, Holbmk Amts Sygehus, DK 4300 Holbak, Denmark).
Statistical
methods.
probability
on only
distribution
positive
values.
Most variables exhibit an asymmetric
(positive skewness) because they take
Logarithmic transformation
will often
reduce this skewness and may result in a nearly normal distribution.
A square-root
transformation
will have the same
effect, but to a lesser degree. Additionally, such transformations may have a stabilizing
effect on variances.
When the
arithmetic
mean value is calculated
on log-transformed
variables, the antilog taken afterwards
is actually the geo-
metric mean of the untransformed
variable (5a). The approximation to the normal distribution is examined by probit
analyses of the original data, and by logarithmic and squareroot transposed scales, and the best-fitting transformation
is
chosen for further use.
Variation in results of biochemical
tests originates from (a)
biological differences between individuals,
(b) day-to-day
variation
in values for each individual, (c) the blood-collecting
procedure,
and (d) anlytical
variation (handling of blood
samples,
instrumental
order
(8). Analytical
is seen
in diseased
sclerosis
patients.
variation
was minimized
by
bringing the samples to the laboratory for centrifugation
without delay. Both intra- and inter-batch
variation were
decreased
by parallel running of samples on each electrophoretic plate. Because a total of 120 samples from 20 control
persons were analyzed in almost 50 batches, inter-batch
variance cannot be estimated. Intra-batch variation was also
deceased by averaging the values from duplicate assays.
Intra-individual variation
is in this investigation co-mingled
with the analytical components of variation and so is called
“residual variation.”
The effect of interindividual
variation was estimated by
one-way analysis of variance (ANOVA) (9), with persons regarded as a random effect (see Appendix).
Components of variance were estimated from tables of expected mean squares (lOa). Comparisons
between healthy
state and infectious state (fixed effect) was done by twoway-ANOVA, mixed-model,
and mean values were corrected
for the second main factor, individual
persons. Comparisons
between sexes were done by a two-way-ANOVA, nested design.
We estimated
the effect of age by linear regression
analysis.
To eliminate
possible bias by trend during the six-month
observation
period, we always performed
an analysis of covariance of time concomitantly
with ANOVA.
All analyses were done by means of SPSS computer
programs at the Computer
Center of the University
of Copenhagen (11).
Results
Interindividual
variation.
Table 1 shows the mean, range,
and median for each of the measured variables. Mean values
and medians correspond well for all except lysozyme. Interindividual variation is given as a percentage of the total variation when significance was found (p 0.01). The magnitude
of the mean interindividual
variation for each analyte varied
from 22% to 91%. Immunoglobulins and acute-phase reactants
showed high interundividual variation. Greater variability was
observed for complement
components.
Plasma lipids also
showed a high interindividual
variation.
Splitting of total variation into interindividual
variation
and a residual variation can be expressed as the proportion
between the standard deviation and the mean value-i.e.,
the
persons,
as exemplified
by the multiple
Sex- and age-related
differences.
Interindividual variances
were compared for men and women by an F test. Significantly
higher interindividual variances were found for fibrinogen and
creatinine in women. The mean values for fibrinogen were
identical
for both sexes, but highly significant
differences
were
found in the case of creatunine and hemoglobin (Table 2).
Significant covariation (p = 0.005) between age and some
analytes
variation).
Usually, most of the total variation can be attributed
to
interindividual
differences. The biological day-to-day intraindividual variation may be decreased by control of such
variables as diet, exercise, time of sample collection, and interval of resting and posture before venipuncture
(6, 7). The
blood-collection procedure was made uniform by using slight
cuff pressure
and syringe suction, and filling the sample tubes
in a fixed
coefficient.
These values are given in Figure la. It
is seen that most of the variables show a higher interindividual
variation than residual variation. Total variation
coefficients
for most of the plasma proteins and plasma lipids range between 15% and 30%,as indicated by the area between the two
circular lines.
Immunoglobulins
A and M showed a high interindividual
variation coefficient as compared with immunoglobulin
G.
Figure lb illustrates that comparable splitting of variances
variation
were observed.
Haptoglobun,
fibrinogen,
Cia,
fl-li-
poprotein, total lipids, total cholesterol, and number of leukocytes increased with age. Albumin, a2-macroglobulin,
and
IgA decreased with age.
Individual
reference interval. The possible clinical application of ANOVA in clinical data as shown in Figure la is
visualized in Figures 2 and 3. Extraction of interundividual
variation as explained above is applied on serial values for one
of the acute-phase reactants (orosomucoid, or cr1-acid glycoprotein)
in the individual subject. Figure 2 shows that results
for both healthy persons and patients with a chronic inactive
disease (exemplified by chronic pyelonephritis)
vary within
the individual reference interval (mean ±2SDjnia ,ersonai), the
standard
deviation having been estimated only from data on
healthy subjects. For a total of 37 blood samples from six pyelonephritis patients, two values for orosomucoid (-‘5%) exceeded individual reference limits. As compared with healthy
women, the pyelonephritis
patients had generally higher interindividual
variances, but significantly so only for IgG and
fi-lipoprotein.
Figure
3 shows our values for three otherwise healthy persons during nonspecific upper respiratory
tract infections.
The
resulting abnormally
increased values for the individual
subjects may often still fall within the range for a normal
population.
Discussion
Our purpose was to evaluate
individual
reference
intervals.
the possible applicability
We were not interested
of
in
evaluating the different sources of analytical variation, because these have been amply studied by several investigators,
but we did try to minimize
both pre-instrumental
variation
and analytical variation by using a standardized
blood-sampling procedure
and by making two determinations
on each
blood sample. The reasons for a strict procedure during blood
sampling have been emphasized by Statland et al. (8), who
showed that during 30 s of blood collection there was about
1% increase in the concentrations
of total protein, albumin,
total lipids, and cholesterol. Also, prolonged tourniquet application (3 miii) caused a significant increase of about 5% in
the same constituents.
Variations from these sources have
been reduced in our study as described above. Furthermore,
it has been shown that exercise and posture influence values
for proteins and protein-bound elements by about 5% of mean
values
(6). This variation
seems
to have been nearly eliminated in this study.
In a vertical study Weeke
crossed immunoelectrophoresis
studied
19 plasma
proteins
with
The mean values in his
study are mostly comparable with our mean values obtained
in a longitudinal study. To conform with the normal distri(12a).
CLINICAL CHEMISTRY, Vol. 28, No. 2, 1982
295
Table 1. Basic StatistIcs and Interindividual VarIation on Blood and Plasma ConstItuents
Persons
Unit
n
Trsn.for-
-
Mean5
250
rn+ 2SD
Median
Range
Interindividual.
mation
Total
protein
gIL
In 20 Healthy
variatioub,
116
log
Albumin
Umol./L.
116
-
588
72.7
Orosomucoid
umol/L
116
log
l5.11
61.
82
519
657
9.8
2l..14
72.8
585
15.6
37
TO
51
5
33
15.6
01-Antitryp.in
mol/L
116
log
51
Haptoglobin
ljmol/L
116
sqrt
16.1
Ceruloplasmin
j”ol/L
116
log
1.88
1.2
?ibrinogen
ao1/L
116
-
9.11
I.l
02-Macroglobulin
3.0
1.81.
111.7
63-63.5
49
515-667
33
9.5-21.
TO
39-76
70
7-1.2
85
0.5-3.8
9.0
31.
3-19.5
1.6
ijmol/L
116
-
2.77
1.2
11.3
2.79
l.2l.6
91
Clq
a.u.
116
log
0.88
0.59
1.31
0.83
0.6-1.53
n.e.
Cli
a.u.
116
log
0.96
0.66
1.39
0.911
0.56-1.59
C3
au.
116
log
0.98
0.69
1.41
0.97
0.59-1.51.
57
a.u.
116
log
0.91.
0.62
1.141
0.93
0.511-1.7
211
71
C3 pro
activetor
1.6
Cl.
au.
116
.qrt
0.78
0.1.1
1.26
0.73
0.35-1.52
C5
a.u.
116
log
0.93
0.59
1.1.8
0.89
0.5-1.9
a.u.
115
og
1.02
0.56
1.86
0.96
0.1.8-2.33
7.1415.Is
n.e.
0.25-2.8
86
Cli
inhibitor
10.5
22
70
lgO
gIL
116
log
IgA
g/L
116
aqrt
1.18
0.37
2.14
1.25
1gM
g/L
116
log
0.55
0.22
1.35
0.50
0.2-1.75
mg/L
116
-
3.2
0.1
6.3
2.8
1-8
Lysozyme
10.6
7.7
111.6
86
n.e.
s.u.
116
uqrt
1.01.
0.55
1.68
1.05
0.11-1.72
a...
8-Lipoprotein
g/L
116
-
5.67
3.0
8.1.
5.59
2.9
-9.6
69
Total
g/L.
115
log
5.1
7.66
5.3-19.8
70
..1
7.6
3.53
4.0-9.0
86
0.38
3.35
1.10
01-Lipoprotein
Ci,ulriterul
mmol/L
115
1g
7.81.
5.5G
Triglyceride
meal/I.
116
log
1.13
Cretinine
umol/L
110
-
Hemoglobin
m.ol/L
lOT
-
109/L
lipid
Leukocyte.
lOll
log
pct
101
sqrt
pct
101
-
F.osinophilocyte.
pet
101
#{149}qrt
Lymphocytes
pot
101
#{149}qrt
Monocytea
pct
101
#{149}qrt
Neutrophilocytes,
12.0
86.7
8.86
66
7.2
10.5
5.55
3
10
0
6
36
76
58
107
87.9
8.75
5.15
0.19-14.99
62-106
61
53
7.011
73
2.7-14
68
1.0
%
0-9
a.i.
rod-shaped.
Neutrophilocyte.,
56.1.
56
2978
.egm.nt-shap.d
1.95
3l.,3
3.1
0
9
2.0
013
1.1
17
58
311.3
13-611
1.7
0
13
3.0
0-16
n.e.
‘(and mean of 20 personswith approx. sixblood sampleseach. b interindividualvariation as percentage of total variation. n = Total number of observations.
m = estimated mean value, SD = standard deviation. a.u. = arbitrary ttilt.
st = square root. n.s. = nonsignificant at p = 0.01 level.
Table 2. Estimated Mean Values for and Interindlvidual Variation In Some Plasma Proteins of 10 Men
and 10 Age-Matched Women
Woman
n=59
AJiatyt.
UnIt
Albumin
a2-Macroglobulln
1gM
Triglycerides
Creatinine
Hemoglobin
Fibrinogen
LmoI/L
LmoI/L
g/L
mmol/L
mol/L
mmol/L
imol/L
Mean
599
2.38
0.44
1.42
93.5
9.4
(9.4)
n-si
Intsr.var.,
%
(31)
(95)
(91)
(61)
<1
(65)
23
Mean
577
3.17
0.68
0.90
80.3
8.3
(9.4)
Inter.var., %
(23)
(81)
(85)
(78)
26
(48)
55
p
0.05
0.02
0.05
0.05
0.001
0.001
n.s.
Results for about six blood sample, per person. Mien vakies are wel*ed for vying n..ti*ers of Individualexaminations. Nimibers in parentheses are not significantly
different (p
296
-
0.05). Only creatlnlne and flbrlnogen have sex-related different lnterlndMdual variation.
CUNICAL
CHEMISTRY,
Vol. 28, No. 2, 1982
.,o..,
AIipI,
b
i.nO,.
.
ffoptoglobin
#{149}
a
#{149}
I5A
Tr(g(yo,rid.,
#{149}
.
#{149}
Hoptoglobin
SM
.
#{149}
Iriglyo.rkla
S
&
#{149}Ceroiopfo.n,n
8
&
C Cf
S
3
S
t
S
S
I)
.5
I
C
‘
10’
10
10
C..ff,.n,
of
ooriotion
R..i#{225}oI(per
Co.ffic.nr
30
20
of oO(OtO
R..ooI
p.,
o.,,’
Fig. 1. a. Comparison in healthy subjects between interindividual and residual variation by coefficients of variation for 21 plasma
constituents and hemoglobin. b. Comparison, In multiple sclerosis patients, between interindividual and residual variation by coefficients of variation for 22 plasma constituents and hemoglobin
“Residual” variation Includes Intraindividual variationand both analytical and pre-lnstrumental
variation
pmol/l.,..
IndvduaI
normal rong.s
80-
Orosomucojd
7060-
Pt’4 patient
40-
50-
403020-
mo1/L
Population
normal
range
patient
Control
person
30-
Population
rtorrnol
range
Individual
normal
ranges
20-
100-
I
123456
10-
I
sane
Fig. 2. Variability of orosomucold (Ct i-acid glycoprotein) during
approximately
sixmonths,as shown for threepersons
Mean values and IndIvidual normal ranges constructed from ANOVA of Table 1.
The range for the control person Is smaller than the population reference Interval.
The two patients with chronic Inactive pyeloneptirltls (P? have hlly Increased
mean ‘values but remaIn generally within Individual ranges constructed from
analyses for healthy persons. As the logarithm of the observed values was applied to all estimations to yield a normal distribution, all reference values are
calculated as exonentlal ftxictlons of mean values ±250, and hence Individual
normal ranges are of differentmagnitude
days
FIg. 3. VarIability oforosomucoid (a1-acld glycoprotein)
during
nonspecific upper respiratory tract Infection in three otherwise
0
5 1’O 15 20 25 30 35
healthy persons
Individual normal ranges for the healthy state are shown. In some Instances
concentratIons of orosomucold In plasma do not exceed the population upper
95% limit but are still abnormally hi for the Individual person
CLINICALCHEMISTRY,
Vol. 28, No. 2, 1982
297
bution, we used the same transformation
of data that Weeke
did. However, he only used a log transformation,
while we have
used either log or square-root
transformations.
This enabled
us to obtain practically
normal distributions,
as illustrated
in
similar values for mean and median. Nevertheless,
gaussian
statistics
have been applied
in several studies on untransformed data (7, 13, 14).
In the present material, total protein, albumin, and (to a less
degree) a2-macroglobulin,
/3-lipoprotein, and lysozyme, all
of which have ranges well beyond 1, were little sensitive to
either log-transformation
or square-root transformation.
We
found sex-related differences in albumin, a2-macroglobulin,
and 1gM, as also found by Weeke. ‘We only found significant
sex-related different variances in creatinine and fibrinogen
(cf. Williams et al., 1) because of the limited number of persons in our study. This is even more marked in the comparison
between 10 healthy women and six pyelonephritis
patients.
For comparison of variances, adherence to normality is also
more crucial than for mean values.
The results shown in Table 2 indicate
that sex-specific
normal ranges might be useful for at least a2-macroglobulin,
1gM, triglycerides, and creatinine (and hemoglobin).
However,
when the stability of the individual,
expressed
as percentage
of interindividual
to total variation
(Table 1), is taken into
account, the utility of this stratification
may be questioned.
Applying the method of Harris, a sex-related classification
seems reasonable for creatinine (and hemoglobin) but not for
the other constituents,
although differences between mean
values are large and of statistical significance (15).
The tendency for plasma protein concentrations
to change
with age, as reported by Weeke (12b), is also seen in the
present material. However, the difference in number of
subjects studied explains why we found significant changes
in fewer proteins than did Weeke. One exception
was found;
Weeke observed a slight increase in IgA with age, while we
found a relatively great decrease.
On comparing the coefficients of variation (interindividual
vs residual variation in a plot diagram, Figure 1), it is apparent
that most plasma proteins have a higher interindividual
variation than residual variation (mostly intra-individual
variation). Several phase reactants have been determined.
From the values for the coefficients of variation, haptoglobin
seems the most appropriate,
but it varies greatly in diseased
persons,
primarily
owing to hemolysis.
From our data we
suggest that orosomucoid is the best phase reactant to follow,
and this conclusion is in agreement
with other investigators.
IgA, 1gM,
haptoglobin, and plasma triglycerides have high
coefficients of variation, which means that there are great
individual
differences
and that
intra-individual
variation
is
low exept for triglycerides.
When more than a single measurement
of some plasma
constituent has been obtained, the population-based
normal
range may be abandoned in favor of individual-based
normal
ranges. Harris has shown that if, for some constituent, interindividual
variation
constitutes
more than 75% of the total
variation,
then, for an individual
whose mean value and
standard
deviation
are equal to those of his group, the population-based
95% reference
interval will include no less than
99.99% of his distribution
of values (16). Thus these limits are
quite insensitive
to most practically
arising deviations.
This
applies
to haptoglobin,
a2-macroglobulin,
IgA, 1gM, and
cholesterol; but also for interindividual
variation of 50%, the
conventional standard deviation is at least 40% larger than the
average individual standard deviation. Only when interindividual variation constitutes less than about 35% do conventional limits become more trustworthy.
This is the case for only a few plasma constituents (cf. Table
1).
Interindividual
variation,
expressed as the coefficient of
298
CLINICAL CHEMISTRY, Vol. 28, No. 2, 1982
variation
Winkel
(CV) in this study,
conforms
very well with that of
et al. for total lipids, cholesterol,
and creatinine;
however, they found smaller CVs for total protein and albumin, maybe because they examined
only young men (17).
Interindividual
CVs for ai-antitrypsin,
IgA, and 1gM are of
the same magnitude here as those of Statland et al., while we
found a smaller CV for orosomucoid, haptoglobin, IgG, C3,
C4, cholesterol,
and triglycerides,
a2-macroglobulin.
They examined
days within 10 days (13).
and a greater
CV for
14 persons on six separate
The residual variation estimated here was a little smaller
than the corresponding
“apparent
personal variation” of
Cotlove et al. for total protein, albumin, and cholesterol (18).
For IgG, IgA, and 1gM, residual variation was also comparable
with the intra-personal
variation of Butts et al. (14) on
applying the diffusion technique of Mancini, while our CV for
C3 was twice as high. The subjects of their study were tested
weekly, on the average four times.
Winkel et al. (17, 19) demonstrated
that the intra-individual variation from month to month is comparable with that
of day to day (two- to three-day interval) for healthy subjects,
while
within-day
variation
in plasma
proteins
is generally
modest.
Intra-individual
CV, compared with the analytical CV, has
been found of comparable magnitude for total protein, albumin, and cholesterol (17, 18), but smaller for creatinine
and
greater for total lipids. Moreover, they were of comparable
size
in a1-antitrypsin,
a2-macroglobulin,
IgG, IgA, 1gM, C3, and
C4, but intra-individual
CV was greater in haptoglobin
and
orosomucoid
(13). In protein components
where the total
analytical
variation
exceeds the intra-individual
variation,
physiological
changes in the individual may be obscured. More
precise
chemical
techniques
are
rigorous blood-sampling
the ratio of variations.
As mentioned, these components of variation are not separated in this study and results may not be valid here because
of different chemical methods as well as laboratory routine.
The potential uses of individual reference intervals require
that diseased persons behave like normal persons with respect
to reference
intervals.
We have in the present paper suggested
that patients
methods
necessary
with chronic
and
to improve
pyelonephritis
behave
persons except for having different-mostly
values
for plasma
proteins
(Figure
like normal
increased-mean
2). Furthermore,
the CVs
for both inter-individual
variation and residual variation for
normal controls and patients with multiple sclerosis are
comparable
(Figure 1, a and b). The mean values for these
patients
are similar to those for control persons, in contrast
to pyelonephritic
patients.5’6 These results indicate that sick
persons react similarly to control persons and that individual
reference intervals could be used.
Harris proposed a method for determining abnormal individual deviations after only two or three repetitive blood
samples, by applying weighted averages. This demands estimation of the analytical variations as well as the biological
variation involved in shifts between successive observations
(and may initially be replaced by the intra-individual
variation) (15,21,22).
We have not estimated the analytical variation; hence, the
model used here can be described as a state of homeostasis
(individual mean value) with physiological fluctuations over
time (cf. Figures 2 and 3). Although this model describes well
5Raun, N. E., and Broch-M#{216}ller,
B., Normality of plasma proteins
and lipids in a longitudinal study of multiple sclerosis patients. To
be published.
6Broch-Mdller, B., and Raun, N. E., Plasma proteins in chronic
pyelonephritis:
Intra-individual
variation.
To be published.
the state of normality or of a chronic, mostly inactive disease,
it may be less sensitive in the case of rapid non-random clinical
changes with few relevant prior observations. It must be emphasized that the model of Harris implies that intra-individual
variation is not too small as compared with analytical variation, a presumption
that is not always met.
Whether the model we used in this study or the random
walk model is preferred-depending
on type of disease and
study (15, 21)-the
practical applicability of individual reference intervals requires use of both automated
chemical
analysis (e.g., nephelometry)
and computerized
cumulation
and printouts
of results.
These
systems
offer the possibility,
whenever repeated blood samples are analyzed, to exchange
population-based
reference intervals with individual normal
ranges and to evaluate if changes as a result of remedial procedures or the natural history of the disease present are statistically significant, but sincere considerations
about the
clinician’s use of clinical results and the concept of normality
are a prerequisite.
We are much indebted to Mrs. Edda Ravn and the other technologists who performed the analyses. We also thank Mrs. Birte Pfeiffer
and her fellow secretaries who organized the appointments and prepared the manuscript. We express our gratitude to the persons who
voluntarily participated in the fastings and blood-drawings
for several
months.
Appendix
ANO
VA-analysis
of variance:
This
statistical
procedure
allows us to decide whether claimed differences
between
subgroups express real differences between sub-populations
or if these are only random samples
from a common population. Significance
of difference(s) between mean values of the
subgroups is tested by comparing the variance between these
mean values and the average variance within the subgroups
(9). If observations follow a normal distribution and variances
in subgroups
are comparable,
the mean sum of squares obtained may be compared by F statistics. The test is not unduly
sensitive to moderate
departures
from normality
(5b).
A scheme for interindividual
look like this:
Source
of
variation
and residual
Variation,
sum of
squares,
SS
Degrees
of
freedom,
df
variation
may
mean of
2
Individual
i
1
-
SS
=
--
-
Residual
i(n
Total
in-i
-
1)
1
-
s
‘
=
F
______
SSr
SSr
i(n-i)
=
The residual variance, s, which includes intra-individual
variation, is the single-observation
variance and is used for
determinations
of individual reference intervals. This procedure can easily be extended to more than one factor: some
of these may be “crossed,” giving rise to possible interaction
effects, e.g., individual person and state of health (infection,
non-infection), while others are “nested,” i.e., members of one
variable are not selected independently of other variables (e.g.,
individual persons within sexes) (lOb). Some factors may be
regarded
as “fixed,”
i.e., with a fixed number
of levels,
such
as sex and disease group, while other factors are called “random” when the levels are chosen at random (e.g., individual
persons
within
a group,
where
these
particular
persons
Source of
variation
mean sum
of squares, EMS
Expected
df
u.r.t.i.
u
Individual
u.r.t.i. X mdiv.
i
-
(u
r + no
1
1
-
1) X
i + ni4
F
ratio
F
F
F
-
a + nur?
r + no’
(i-i)
Residual
Total
ui(n-1)
uin -
1
It may be seen that the mean sum of squares from the effect
of u.r.t.i., cI, shall be tested against the interaction effect of
u.r.t.i. and individual and not be compared with the residual
variance.
The coefficients of variation for interindividual and residual
variations (Figure 1) are SD divided by the mean value in
untransformed
variables. In scale-transformed
variables
where mean value (m) and standard
deviation (s) have been
estimated,
approximation
of prescaled CV is 2s/m, when
square-root transformation
has been applied, and (e’ - e’)/2
when loge transformation
has been applied.
References
1. Williams, G. Z., Widdowson, G. M., and Penton, J., Individual
character of variation in time-series studies of healthy people II.
Differences in values for clinical analytes in serum among demographic groups, by age and sex. Clin. Chem. 24,313-320(1978).
2. McAlpine, D., Lumsden, C. E., and Acheson, E. B., Multiple
Sclerosis: A Reappraisal. Livingstone Ltd., London, 1972, pp 197223.
Sci. Publications,
F
SS, MS
ANOVA be:
3. Beisenherz, et aL, Reindarstellung von Enzymen. Z. Naturforsch.
86,576 (1953).
4. Laurell, C.-B., Electrophoretic
and electro-immuno-chemical
analysis of proteins. Scand. J. Clin. Lab. Invest. 29, suppl. 124,21-37
(1972).
5. Armitage, P., Statistical Methods in Medical Research, Blackwell
Variance
ratio,
Variance,
not be so important
but only whether persons in general have
individual ranges). The statistical model, whether called fixed
or random or mixed model (both types included) may become
rather complex when several factors are involved. A simple
set of rules for which the mean sum of squares are to be compared, may be used (lOc). For example, the effect of nonspecific upper respiratory
tract infection (u.r.t.i.), a fixed variable
with u = 2 levels crossed with healthy subjects, random effect
with i levels and an average of n replications,
will in a two-way
may
Oxford, 1974, pp
a) 350-355, b) 189-197.
6. Statland, B. E., Winkel, P., and Bokelund, H., Factors contributing
to intraindividual
variation of serum constituents:
2. Effects of exercise and diet on variation of serum constituents in healthy subjects.
Clin. Chem. 19, 1380-1383 (1973).
7. Bokelund, H., Winkel, P., and Statland, B. E., 3. Use of randomized
duplicate serum specimens to evaluate sources of analytical error.
Clin. Chem. 20, 1507-1512 (1974).
8. Statland, B. E., Bokelund, H., and Winkel, P., 4. Effects of posture
and tourniquet application on variation of serum constituents in
healthy controls. Clin. Chem. 20, 1513-1519 (1974).
9. Wonnacott, T. H., and Wonnacott, R. J., Introductory Statistics,
2nd ed., John Wiley & Sons, Inc., New York, NY, 1972, pp 214246.
10. Hicks, C. R., Fundamental
Concepts in the Design of Experiments, 2nd ed., Holt, Rinehart and Winston, New York, NY, 1973,
pp a) 38-42, b) 188-198, c) 173-182.
11. Nie, N. H., Hull, C. H., Jenkins, J. G., et al., SPSS Statistical
Package for the Social Sciences. McGraw-Hill Book Co., New York,
NY, 1975.
12. Weeke, B., Humane serumproteiner
identificeret og kvantiteret
med Laurell’s immunelektroforeser-metodologiske
og kliniske me-
toder. Thesis, Copenhagen, 1973, pp a) 39-41, b) 173-179.
13. Statland, B. E., Winkel, P., and Killingsworth, L. M., 6. Physio-
CLINICALCHEMISTRY,
Vol. 28,No. 2,
1982
299
logical day-to-day variation in concentrations of 10 specific proteins
in sera of healthy subjects. Clin. Chem. 22, 1635-1638 (1976).
14. Butts, W. C., James, G.E., and Kuehnemann, M., Intra-individual
variation in the concentrations
of IgG, IgA, 1gM, and complement
component C3 in serum of a normal adult population. Clin. Chem.
23,511-514 (1977).
15. Harris, E. K., Some theory of reference values. I. Stratified (categorized) normal ranges and a method for following an individual’s
clinical laboratory values. Clin. Chem. 21, 1457-1464 (1975).
16. Harris, E. K., Effects of intra- and interindividual variation on
the appropriate use of normal ranges. Clin. Chem. 20, 1535-1542
(1974).
17. Winkel, P., Statland, B. E., and Bokelund, H., 5. Short-term
day-to-day and within-hour variation of serum constituents in healthy
subjects. Clin. Chem. 20, 1520-1527 (1974).
18. Cotlove, E., Harris, E. K., and Williams, G. A., Biological and
300
CLINICAL CHEMISTRY, Vol. 28, No. 2, 1982
analytical components of variation in long-term studies of serum
constituents
in normal subjects. Ill Physiological and medical implications. Clin. Chem. 16, 1028-1032 (1970).
19. Morrison, B., Shankin, A., McLelland, A., et al., Intra-individual
variation in commonly analyzed serum constituents. Clin. Chem. 25,
1799-1805 (1979).
20. Harris, E. K., Kanofsky, P., Shakarji, G., and Cotlove, E., Biological and analytical components of variation in long-term studies
of serum constituents
in normal subjects. II Estimating biological
components of variation. Clin. Chem. 16, 1022-1027 (1970).
21. Harris, E. K., Some theory of reference values. II. Comparison
of some statistical models of intraindividual variation in blood constituents. Clin. Chem. 22, 1343-1350 (1976).
Harris, E. K., Cooil, B. K., Shakarji, G., and Williams, G. Z., On
the use of statistical models of within-person variation in long-term
studies of healthy individuals. Clin. Chem. 26, 383-391 (1980).
22.