TABLE I
STUDIES OF SODIUM CONTENT OF SERUM
Authors Age of Subjects
Mean
Sodium
(meq/l, serum)
S.D.
Bernstein8 Adults 145 3.5
variability in individuals with time, but
they are limited to newborns, and
labora-tony error cannot be determined from the
material given.
Because none of these references fulfills
the criteria outlined above, it was consid-ened desirable to collect data which would
allow calculation of:
1) Variation between individuals.
2) Variation of sodium in serum with
time in individual normal children past the neonatal period.
This work was supported in part by a grant (A-2536) from the National Institute of Arthritis and
Meta-bolic Diseases of the National Institutes of Health. Dr. Bergstrom was a Markle Scholar.
ADDRESS: (W.H.B.) 766 Irving Avenue, Syracuse 10, New York.
597
PEDIATRICS, April 1961
LIMITS
OF
VARIABILITY
OF
CONCENTRATION
OF
SODIUM
IN
SERUM
OF
NORMAL
CHILDREN
John B. Joseph, M.D., M.P.H., and William H. Bergstrom, M.D.
State University of New York, Upstate Medical Center
W
ITII the information presently avail-able, any single value for the concen-tration of sodium in serum encountered din-ically can be classified as normal orabnor-ma! with reasonable confidence. However,
it is often difficult to evaluate changes from
day to day in an individual patient, and to
decide whether any two values differ by
chance, as a result of disease, or in response
to treatment. Although normal averages are
readily available for various age groups, the extent to which a healthy individual may
vary from time to time has not been
satis-factonily defined. The difference between individuals in a group at any one time,
ex-pressed as the standard deviation for the
group, does not necessarily correspond to
the difference to be expected between sue-cessive samples in the same subject.
Defini-tion of variability with time in the same in-dividual, as well as group variability,
re-quires the collection of serial samples in a
suitably large group of subjects. Also, cal-culation of laboratory error and apprecia-tion of its contribution to observed van-ability requires duplicate analyses for each individual on each occasion.
Data available for sodium in serum
in-elude several groups of individual
deter-minations on normal subjects with averages
and standard deviations for each group8
(
Table I). In a few studies laboratory error has also been calculated, using replicate determinations from single serumsam-311 10 This approach does not include
that part of sampling error that may occur during the collection and handling of
speci-mens prior to their arrival in the laboratory. Gottfnied’s data11 do permit calculation of
Bruch and MeCune’
Newborns 145 4.I
McCance
and Youne
Christian
et al.3
Newborns
Newborns
144
I5
1 1 .4
5.3
Overman et al.4
Corsa et al.5
1 nio to ‘2 yr (6 groups)
1 tao to 15 yr
139-14’2
l4-I43
LI-4.3
-Gyllensward and
Joseph-son6
Newborn to adult (10 groups)
19-I39 5 .1-10.7
Elliott and Holley7
3) Laboratory error, including specimen
collection and analysis.
SUBJECTS AND METHODS
Subjects were healthy active children rang. ing in age from 1 month to 16 years, seen at the dispensary or at a local home for children. Blood was collected by finger puncture in 2-mm glass tubes. Two tubes were filled on each of two occasions, the time interval being from 1 to 3 weeks. There were thus two sets of duplicates for each subject. Each tube contained sufficient serum for a separate analysis, making a total of four values for each subject. The tubes were centrifuged within 3 hours and the
serum-con-taming portion of the tube was cut off,
stop-pered and refrigerated until used.
Sodium was measured by internal-standard flame photometry using a Baird Associates pho-tometer. Serum was diluted 1:500 (0.1 ml to 50 ml) and the final concentration of lithium sulfate in standards and unknown was .01 molar. All determinations were made by the same individual. At intervals throughout the period of study, analyses were performed on aliquots of a single serum sample collected ini-tially for the purpose of quality control. All
sam-pies were collected and analyzed during the
months of July and August of 1959.
RESULTS
There were 59 subjects, from whom 118
sets of duplicate sera were obtained. The resulting 236 analyses are shown in Table II. The over-all concentration of sodium in
serum was 146 meq/1. Analysis of variance according to the model implied in Table
III indicated:
1) Laboratory error was
±2.5 meq/l, (±-v’6.42).
2) Variation with time in the same
in-dividual, apart from laboratory error, was
/(26.45 - 6.43)
3.2me/l(±4/ 2
3) The variation between any two single
successive analyses in any individual (standard deviation) was found to be
±4.0 meq/l. This figure comprises
the individual variation with time and
the laboratory error shown separately above,
(± ,/2.52+3.22).
4) There was no significant difference be-tween individuals. Analyses of the quality control serum, sampled at in-tervals throughout the study, had a
standard deviation of ± 1.8 meqil.
DISCUSSION
The mean for this series, 146 meqil, is somewhat higher than that commonly ac-cepted as normal. It is difficult, however, to find an exact source for the latter. As
al-ready mentioned and shown in Table I,
“normal averages” as reported range from
139 to 145 meqil. The mean temperature
during the period of this study was 73.8#{176}F
(23.2#{176}C). Adolph12 pointed out that a sig-nificant degree of dehydration is seen ill active subjects in hot environments even with free access to water. This phenome-non, termed “voluntary dehydration” by Adolph, may well result in increased con-centrations of sodium in serum of normal
persons studied during periods of hot weather.
The present data, when subjected to analysis of variance, indicate that all
oh-served differences in concentration of so-dium in serum are due to variations in
individuals with time, since no difference between individual means could be
demon-strated. In other words, the variability in a number of normals is the same as that to be
expected from an equal number of succes-sive observations in a single subject. With this information, it is possible to find the maximum difference to be expected between
any two successive values in a member of the normal population. This can be done
in two ways. The first and simplest is to
construct a range limit by multiplying the standard deviation (4 meq/l) by 2.77, the
‘2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 21 22 23 24 26 30 143 147 146 148 147 14 141 143 145 150 144 146 149 152 146 142 142 141 149 145 142 143 147 147 147 141 152 159 148 147 146 146 145 141 142 147 142 144 145 145 148 143 146 150 145 143 144 141 148 144 144 143 143 142 144 151 150 150 143 143 145 146 147 143 154 152 143 142 147 145 146 141 148 147 148 146 152 150 145 142 146 153 142 148 143 138 142 145 146 147 149 154 156 159 148 147 146 147 149 142 145 142 150 142 142 141 147 142 150 146 143 147 145 144 143 143 145 144 142 141 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 141 142 147 141 146 143 148 148 160 151 147 143 l52 142 147 143 146 150 151 143 140 135 142 138 143 144 144 148 146 Mean 141 146 147 142 152 141 146 151 161 146 146 143 146 149 143 144 149 151 142 144 144 140 145 144 145 150 141 147 145 139 143 145 145 141 147 143 139 143 145 143 138 145 143 147 149 144 150 143 142 15’2 152 148 148 144 143 150 1.53 153 157 150 149 146 144 149 148 146 148 146 146 144 147 148 146 150 151 152 148 144 147 148 148 142 150 145 149 143 140 146
ABCD . (MEAN (46±5.6. RANGE IIMEQ/L(
EFG . (R2 . 47.36 - 4(M- (46(2)
7
(2 (0 9 RANGE. 6 MEQ/L 40(3_ (50 DI
Ftc. 1. Mean and range of concentration of sodium in serum of normal children. The critical regions defined by the rectangle and parabola include 90%
of the normal population.
Ea 42
(46 MEAN. MEQ/L
TABLE II
DATA FROM PRESENT STUDY
Occasion Occasion
Subject Subject
First Second First Second
the normal range for means of samples of size two (146 ± 5.6). The restriction is due to the selection of clinically normal
chil-dren as sources of data for the calculation
of the mean and variance. The rectangle
ABCD in Figure 1 shows the area of the
normal population of concentrations of
sodium in serum according to the joint en-tenia: mean 146 ± 5.6 and range = 11 meqil. The critical region so defined in-eludes 90% of the combinations of mean and range to be expected in a normal popu-lation, leaving 10% outside its bonders.
The curve EFG in Figure 1, constructed from the same data, defines a second
cniti-R2
-TABLE III
ANALYSIS OF VARIANCE FOR THE VARIATION OF CONCENTRATION OF SODIUM IN SERUM
BETWEEN AND WITHIN HEALTHY CHILDREN
Source d. f.
Sums of Squared Deviations
Mean Squared Deviations
F Probability
Between individuals
Between occasions (within-individuals)
Residual variatioll
58
59
118
1439
1561
758
24 .80
26 .45
6.419
.94 4.12
-NS 1
0
-600
146)2 =: 73.68#{176},
R
being the range of thetwo values for each norma! individual and
ni their mean. The resulting area is an
ellipse, only half of which is shown since
all the differences between values are given a positive sign. Again, 90% of normals are within the Figure. By inspection, the fun-then the mean of any two samples departs from 146, the smaller the difference
com-patible with normality. This relationship, not considered in the rectangular Figure, produces a minimum area for a given level of probability, and hence, in a sense,
greater precision.
Use of the rectangular description of normality has the virtue of simplicity. Only three numbers (146, 5.6 and 11) need to
be memorized to evaluate any pain of
re-ported concentrations of sodium in serum
without the use of Chants or Graphs. If more than two values for an individual are to be considered, appropriate rectangles can be constructed easily by using different range limit factors. Use of the ellipse, on
the hand, requires a graph on table and construction of a figure for samples of
greater than size two would be difficult.
0 This equation is derived from the expression for
chi-square:
(X-) (X-) (_,)2
x2= = +
a2 .2
with n degrees of freedom. When n = 2,
X2 - (X1 X2) +2 M)2
R2
_______
- 2o2 y2 j2
The values for x’ with 2 degrees of freedom, 0.9
probability, I and a’ are respectively: 4.605, 146,
and 16.
Either Figure can be constructed at any desired level of probability.
Discussion thus far has been limited to decisions regarding normality. Given two
successive concentrations of sodium in serum, it is possible to decide whether the subject could have been a member of the normal population on both occasions. If so, no change in his status can be inferred from the sodium values. If not, three alter-natives exist. The first is that he was non-mal at one time and not at the other; i.e., he recovered or became ill. The second is
that he was in one abnormal population on the first occasion and a different abnormal population on the second, i.e., the nature of his illness changed. Finally, he may have been on both occasions a member of a single abnormal population characterized
by a mean and variance different from that of the normal population. An example of
the first case would be that of a child treated for hypernatremia, who had an initial sodium level of 180 meq/1 and a
subsequent level of 146 meq/l. The second case might involve a change from 180 to 135 in the same patient treated differently.
The third alternative is illustrated by chil-dren with renal disease, whose concentra-lion of sodium in the serum may fluctuate widely outside the normal range, e.g., 115 to 135. The first case presents little difficulty in practice, since decision as to the signifi-cance of an observed change is usually
aided by ancillary laboratory and clinical
data. Also, the two values can be judged independently, 180 being abnormal and
ARTICLES
defining abnormal populations. If we are
willing to assume that all abnormal
popu-lations have the same variance as that found in normals, we can apply the range limit
of 11 meq/l to any two values seen.
Other-wise we can only exclude the subject from
normality without judgment as to whether
his status has changed on not. It is
clearly impracticable to calculate variances for the large number of abnormal
popula-tions encountered clinically, each repre-sented by relatively few individuals. It is quite unsatisfactory to lump all abnormal
individuals into a single population, which is equivalent to assuming that all diseases
have an equal effect on sodium
homeo-stasis. Without additional information, therefore, no conclusions can be drawn re-garding change in the status of a subject
who presents two abnormal concentrations of sodium in serum.
All analyses in this study were performed
by a single individual working in a leisurely fashion without distraction. These
cincum-stances tend to minimize laboratory error
and hence variance. Both would probably be larger in the usual clinical laboratory
setting. The standard deviation for
mdi-viduals includes both laboratory error and individual variation with time, as has
al-ready been noted. Given an individual
variation of 3.2 meq/l apart from
labona-tony error, the effect upon the
within-individual standard deviation of increas-ing or decreasing laboratory error can be calculated. If error were reduced to zero,
the standard deviation would change from 4.1 to 3.2 meq/l. If error were doubled (to
5.0 meq/l), standard deviation would
in-crease from 4.1 to 5.9. With a laboratory error of 2.5 meq/l sample differences of less
than 7 meq/l cannot be regarded as
tech-nically significant, since this is the range limit defined by 2.5 X 2.7 = 6.9.
SUMMARY AND CONCLUSIONS
The mean concentration of sodium in
serum of a group of normal children in
Syracuse, N.Y., in midsummer was 146
meq/l.
The total standard deviation for within-individual variation was 4 meq/l,
compris-ing a laboratory error of ±2.5 meq/l and a
“true” within-individual variability of ±3.2
meq/l.
No significant difference between
mdi-viduals was demonstrated.
Within 90% confidence limits, the maxi-mum chance difference between two
sue-cessive concentrations of sodium in the
serum, whose mean falls within the normal
range for means of two samples was found
to be 11 meq/l.
Within 95% confidence limits, the maxi-mum chance difference between any t\V()
values, duplicate or successive, due to
laboratory error was 6.9 meq/l.
The implications of these findings for the interpretation of sodium levels in serum of
patients are discussed.
Acknowledgment
The authors are much indebted to Dr. Albert
J.
Schneider for assistance with the statistical analysis of the data, and to Mr. C. L. Joiner, Dr. George Bladen, and the children of Elm-crest for their enthusiastic co-operation.REFERENCES
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12. Adolph, E. F. : Physiology of Man in the Desert. New York, Interscience, 1947. 13. Pearson, E. S., and Hartley, H. 0. : The
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PATHOLOGY OF INFANCY AND CHILDHOOD,
Agnes R. MacGregor, M.D. Edinburgh,
E. & S. Livingstone, Ltd., 1960, 631 pp., $14.50.
Dr. MacGregor, one of the greatest and most respected pioneers of pediatric pathology, has
written a much expected book. It is not
pri-manly designed as a specialized monograph, but as an aid to the general pathologist un-familiar with pediatric problems. Much of the material to be found in the three other text-books on pediatric pathology is now available in a compact and well-illustrated manual. The material is enthusiastically presented; the au-thor uses the first person, a refreshing change in an era of impersonal-if clear-stylistic ap-proach.
The chapters dealing with neonatal pa-thology, infections and most malformations,
as well as an appendix on the technique of
necropsy for newborn infants are superb. The
chapters on malformations of the heart, met-abolic diseases and neoplasms appear to be somewhat sketchy. The bibliographic refer-ences are generally well chosen; more recent ones might be desired in some places. Statistical data, particularly those pertaining to the chang-ing, or constant, incidence of some conditions would give more perspective to the book.
A more complete treatise by this author would be desirable.
