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Biostatistics Branch [T. R. F., J. L. D., M. H. G.], Environmental Epidemiology Branch [R. T. F.], Epidemiology and Biostatistics Program [R. N. H.], and Nutritional Epidemiology Branch [R. G. Z.], National Cancer Institute, Bethesda, Maryland 20892; Womens and Childrens Hospital, Los Angeles, California 90033 [F. Z. S.]; and MA Bioservices, Rockville, Maryland 20850 [J. B. V.]
| Abstract |
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Using the logarithm of assay measurements, we estimated the components of variance and three measures of reproducibility. The usual coefficient of variation is a function of the components that are under the control of the laboratory. The intraclass correlation between measurements for a given individual is the proportion of the total variability that is associated with individuals. The minimum detectable relative difference is important to evaluate study feasibility. Results suggest that a single sample of ADIOL G, DHEA, DHEA S, and ANDRO G (with two lab replicates per sample) can be used to discriminate reliably among women in a given menstrual phase or menopausal status. The results for DHT, TESTO, ADION, and ANDRO S are more problematic and suggest that the present measurement techniques should be used with care, especially with midluteal phase women. The results for ADIOL suggest that this assay is not yet ready for use in epidemiological studies.
| Introduction |
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To help identify appropriate techniques and laboratories for measuring
endogenous hormone in blood and urine samples collected in large
epidemiological studies, the reproducibility of several capable
laboratories was determined and compared. In earlier reports, Gail
et al. (8)
estimated the sources of variability
and reproducibility of assays of estradiol, estrone, estrone sulfate,
and progesterone in plasma from pre- and postmenopausal women; and
Ziegler et al. (9)
determined the
reproducibility and validity of new measurement techniques for
2-hydroxyestrone and 16
-hydroxyestrone in urine. The present report
presents similar results for nine androgens measured in plasma samples
from women:
ADIOL,2
ADIOL G, ADION, ANDRO G, ANDRO S, DHEA, DHEA S, DHT, and TESTO. These
include the ovarian and adrenal androgens previously analyzed in
epidemiological studies of breast cancer, as well as other androgen
metabolites of potential importance in breast cancer etiology. We have
estimated assay variability over the time required to assay samples
from a large epidemiological study by using four measurements spaced
over 3 months. Because androgen relationships have been reported to
differ for premenopausal and postmenopausal breast cancer, we present
variability and reproducibility separately for follicular phase
premenopausal women, luteal phase premenopausal women, and
postmenopausal women.
| Materials and Methods |
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Each participating lab received four batches of samples, with one batch to be assayed at the beginning of each of 4 consecutive months. Each batch contained two aliquots from each of the 15 subjects. The identifying numbers for the 30 samples within each batch were randomly assigned, separately for each batch. Lab personnel were told only whether a sample was from a premenopausal or postmenopausal woman. Each aliquot was assayed in duplicate. Thus, this study provides information on assay variability among women, among days on which assays were performed, among aliquots, and among lab replicates, but it does not provide information on temporal variations in hormone levels within women.
Laboratory Methods.
Four laboratories, two academic and two commercial, recognized for
their skill and experience in measuring endogenous hormones, were
invited and willing to participate in this study. Each lab was asked to
use their standard assay procedures and to perform only those assays
with which they had experience.
Laboratory 1.
Lab 1 assayed ADIOL G, ADION, DHEA, DHEA S, TESTO, and DHT in plasma.
The assay for ADIOL G included organic extraction of the plasma to
remove unconjugated 3
ADIOL and other unconjugated steroids,
followed by incubation of the aqueous phase with ß-glucuronidase.
After enzyme hydrolysis and celite chromatography, the product of
hydrolysis, ADIOL, was measured by RIA (10
, 11)
. ADION was
measured by extracting plasma with ethyl acetate (20%) in hexane,
celite column chromatography, and RIA (12, 13, 14)
. DHEA was
also determined by extraction with hexane:ethyl acetate (80:20), celite
column chromatography, and RIA (15, 16, 17)
. DHEA S was
measured by RIA after diluting the specimens 1:2500 with assay buffer
(15
, 18
, 19)
. TESTO was measured by RIA, preceded by
extraction of plasma with ethyl acetate (20%) in hexane and celite
column chromatography (20, 21, 22)
. DHT was also measured by
RIA involving ethyl acetate:hexane extraction and celite column
chromatography (13
, 23)
. Lab 1 reported the sensitivity of
the assays to be 3 ng/dl for ADION, 25 ng/dl for ADIOL G, 15 ng/dl for
DHEA, 5 µg/dl for DHEA S, 2 ng/dl for TESTO, and 5 ng/dl for DHT.
Laboratory 2.
Lab 2 measured ADIOL G, ADION, DHEA, DHEA S, TESTO, and DHT in plasma.
ADIOL G was assayed using a method developed at lab 2. Plasma was
extracted with a polar solvent. The dried extract was subjected to
complete enzymatic hydrolysis, followed by extraction of free ADIOL
with hexane:ethyl acetate and purification by high performance liquid
chromatography. ADIOL in the purified eluate was quantitated by RIA.
ADION was measured by extracting plasma with hexane:ethyl acetate,
followed by RIA developed at lab 2. DHEA was also determined by
extraction with hexane:ethyl acetate and RIA developed in lab 2. The
assay for DHEA S was similar to that for DHEA, except that the initial
step was the removal of sulfate by overnight hydrolysis with sulfatase.
TESTO was measured by RIA after extraction and column chromatography
according to the method of Furuyama et al.
(24)
. DHT was measured by an RIA developed at lab 2.
Plasma samples were first extracted with hexane:ethyl acetate, followed
by treatment with a strong oxidizer to destroy all unsaturated
steroids, and purification on alumina columns. Lab 2 reported the
sensitivity of the assays to be 14 ng/dl for ADION, 10 ng/dl for ADIOL
G, 20 ng/dl for DHEA, 5 µg/dl for DHEA S, 3 ng/dl for TESTO, and 2
ng/dl for DHT.
Laboratory 3.
Lab 3 assayed DHEA, DHEAS, ADION, TESTO, DHT, ADIOL, ADIOL G, ANDRO S,
and ANDRO G. DHEA S was quantified by direct RIA after a 1000-fold
dilution of the plasma sample with assay buffer (25)
.
DHEA, ADION, TESTO, DHT, and ADIOL were measured by RIA after
extraction of plasma with diethyl ether and subsequent purification by
celite column chromatography (26, 27, 28, 29)
. ADIOL G was
quantified directly in plasma using a validated commercial kit
(Diagnostic Systems Laboratories, Webster, Texas; Ref.
30
). ANDRO S and ANDRO G were measured after unconjugated
steroids were removed by extraction with diethyl ether, and the
remaining conjugated steroids were hydrolyzed using hydrochloric acid
and ß-glucuronidase to cleave the sulfate and glucuronide moieties,
respectively (31)
. In both assays, the product of
hydrolysis, androsterone, was quantified by RIA after extraction with
ethyl acetate and purification by celite column chromatography. Lab 3
reported the sensitivity of the assays to be as follows: 2 µg/dl for
DHEA S, 20 ng/dl for DHEA, 10 ng/dl for ADION, 4 ng/dl for TESTO, 2
ng/dl for DHT, 2 ng/dl for ADIOL, 5 ng/dl for ADIOL G, 3 ng/dl for
ANDRO G, and 6 ng/dl for ANDRO S.
Laboratory 4.
Lab 4 performed measurements of ADION, DHEA, DHEA S, and TESTO in
plasma. ADION was measured by carbon tetrachloride extraction of plasma
followed by an RIA kit (ICN Biochemicals, Diagnostics Division). DHEA
was measured by dichloromethane extraction and an RIA kit from
Coat-A-Count. DHEA S was assayed directly in plasma using a double
antibody RIA kit from ICN Biochemicals, Diagnostics Division. TESTO was
also measured directly in plasma using an ICN RIA kit. The sensitivity
of the assays, as reported in the kit documentation, was 0.1 ng/ml for
ADION, 0.04 ng/ml for DHEA, 0.5 ng/ml for DHEA S, and 0.1 ng/ml for
TESTO.
Statistical Methods.
Measurements were analyzed on the natural logarithmic scale. This
transformation reduces the dependence of the SD of the response on
the mean so that variance can be assumed to be unrelated to subject.
For each of the three groups of women (midfollicular, midluteal, and
postmenopausal), a nested component of variance analysis was performed.
Components were estimated for subjects
(
2
a), month
(
2
b), aliquots on the same
day (
2
c), and replicates from
the same aliquot (
2
). Letting
zijkl denote the hormone measurement for
woman i (i = 1,2,3,4,5) on analysis day
j(i) (j = 1,2,3,4), using aliquot
k(ij) (k = 1,2) and replicate
l(ijk) (l = 1,2), the statistical
model is written (1)
:
![]() | (1) |
l(ijk) are normal independent
variates with means zero and variances
2a,
2b,
2c, and
2, respectively. Restricted maximum likelihood
estimates of the variance components were obtained using the SAS
procedure PROC VARCOMP (32)
. The procedure also
provides estimates of the SE of the estimated variance components.
Restricted maximum likelihood estimates cannot be less than zero, and
they agree with the usual ANOVA estimates when all estimates are
greater than zero. Knowledge of the variance components allows a careful quantitative consideration of assay reproducibility. We use three measures of reproducibility derived from these components: the CV, the ICC coefficient, and the MDRD. The three measures are quite different, but each measure is useful depending on the application.
The common measure of reproducibility used by the labs is the CV,
namely the population SD of a measurement divided by its mean. The
components associated with day, aliquot, and replicate are the
components that are under the control of the lab. An application of the
method (33)
shows that the sum of these components is a good estimate of the square of the CV (8)
. Because the labs all used two replicates, the CV expressed as a percentage is
estimated by 100(
2b +
2c +
2/2)1/2, where hats denote
estimates of corresponding parameters. This CV incorporates the
variation associated with day and may be much larger than a CV based
only on variability due to aliquots and replicates on a single day. The
validity of this approximation depends heavily on the model and
particularly on the assumption that after logarithmic transformation
the variance is unrelated to subject.
The assay would not be useful if the differences in true values between
subjects were not large compared to total assay variability. For this
to be the case, the variability associated with subjects should be
large compared to the variability under the control of a lab. It is
appropriate then to compare
2a, the component associated
with subjects, with the sum of all components. The ratio is close to
unity when the biological component is large relative to the components
associated with the lab. In fact, the ICC between measurements on
different days from a given individual is exactly this ratio. If two
replicates are used for each sample, the estimated ICC between two
measurements on different days is ICC =
2a/(
2a
+
2b +
2c+
2/2). We
express the ICC in percent by multiplying by 100. If
2a is small, the ICC may
not be near one, even when the CV is small. The ICC is of importance to
the epidemiologist because it indicates the effect of measurement error
on study results. Specifically, regression analyses relating the log
relative risk of disease to the log hormone assay level will be
attenuated by the ICC. If the ICC is 0.90, there will be a downward
bias that is slight, only 10%, but an ICC of <0.80 results in bias
that may be important.
Assay variability can decrease the power of a study to detect a
difference in hormone levels between cases and controls. Knowing the
variance components allows one to determine the minimum difference that
is reliably detected with a given number of cases and controls.
Specifically, for a two-sided
= 0.05 level test, the minimum
difference in average log assay values (
=
µ1 - µ2) detectable
with power 0.90 is the solution to
![]() |
, one can calculate the minimum percentage difference
detectable with power 0.90 as
100{exp(µ1) -
exp(µ2)}/exp(µ2) = 100{exp(
) - 1}. We call this quantity the MDRD. Usually
an investigator has a sense of what differences exist and what sample
sizes can be used so the MDRD is useful. If
2a is small, the value of
and therefore the MDRD may be small even when the CV is large.
For each hormone and laboratory, we examined graphs of grand means,
daily means, and aliquot means and examined these quantities for
stability over time. We also examined differences in variability and
agreement of results among the lab assays. These graphs are presented
for ADIOL G and for DHT. Graphs for other androgens are available upon
request. Spearman rank correlations are used to measure concordance of
grand means among lab assays. The estimated components of variance and
SEs of the estimates are tabulated in the "Appendix." The
components of variance are used to obtain estimates of the CVs, ICCs,
and MDRDs, which are compared among the labs. To calculate ICCs and CVs
in Tables 1
2
, we assume that the measurement used is the mean of
the two logarithmic-transformed replicates. To calculate MDRD, we
assume, in addition, that n1 = 300
cases and n2 = 600 controls are used;
these numbers approximate the sample sizes available in an ongoing
study of Asian-American women that motivated these assay reliability
studies.
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| Results |
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The geometric means of all ADIOL G measurements were 151 ng/dl at lab 3, 74.4 at lab 1, and 64.1 ng/dl at lab 2. These differences are not surprising because the labs do not correct for molecular weight differences, hydrolysis, and procedural losses in the same way. The correlations of the ranks of the subjects mean responses were 0.94 between labs 1 and 2, but only 0.88 between labs 1 and 3 and 0.80 between labs 2 and 3.
For midfollicular and midluteal women, the CVs ranged from 13 to 17%
at labs 1 and 3 but were somewhat higher, about 30%, at lab 2 (Table 1)
. The CV was 16% for measurements from postmenopausal women at lab 1
and much higher at labs 2 and 3 (2535%). The ICCs were all >80%
and >90% for labs 1 and 3. The estimated MDRDs were 1418% using
measurements from lab 1 and somewhat larger for labs 2 and 3 (Table 1)
.
Estimates of individual variance components and their SEs are provided
in
of the "Appendix."
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The CVs were the smallest from lab 1, ranging from 8 to 9%, and
somewhat larger from the other labs, ranging from 13 to 28% (Table 1)
.
The CV was small for midluteal phase measurements from each lab. The
ICCs were largest for measurements at lab 1, 9799%, and somewhat
smaller for other labs (8794%). The MDRDs were smallest for
midluteal phase measurements, 913%, and larger for other phases,
1421%.
DHEA S.
No time trends were evident in measurements from any lab in any phase
(figure not shown). There was some overlap in assay measurements from
each lab for women in each phase. The ranks of the subjects mean
responses were highly correlated (0.981.00) across labs. The mean
levels of DHEA S, 85.3, 61.1, 95.1, and 76.6 µg/dl at labs 1, 2, 3
and 4, were statistically significantly different for all pairs of
labs.
The CVs were lowest from lab 4 (710%), slightly higher from lab 1
(1012%), and still higher at the other labs (1119%; Table 1
). The
ICCs were >96% at labs 1 and 4 and slightly lower but still very high
at labs 2 and 3 (9295%). The MDRD ranged from 12 to 19%.
DHT.
There were no consistent time trends (Fig. 2, a-c
). There was some overlap of aliquot means of
midfollicular women, but there was substantial overlap of aliquot means
of midluteal and postmenopausal women. In particular, there were large
differences between aliquot means of midluteal women at labs 2 and 3.
For all laboratories, the ranks of the subjects mean responses were
highly correlated (0.970.99). The geometric mean levels of DHT were
similar for labs 1 and 3 (8.53 and 8.22 ng/dl) and somewhat lower for
lab 2 (6.56 ng/ml).
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TESTO.
There were no clear time trends in the measurements for TESTO (figure
not shown). The aliquot means from lab 3 were clearly separated for
postmenopausal women; there was some overlap in the aliquot means from
other labs. There was extensive overlap of aliquot means from all labs
for midfollicular and midluteal women. The ranks of the subjects mean
responses were highly correlated (0.901.00) for labs 1, 2, and 3.
Correlations with lab 4 were smaller, -0.10 to 0.20 for midluteal and
postmenopausal women and 0.800.90 for midfollicular women. Geometric
mean levels of TESTO, 18.5, 16.0, 19.1, and 18.8 ng/dl, were
significantly different at labs 1, 2, and 3.
The CVs differed by lab (Table 1)
. CVs for measurements from labs 1 and
3 were 914%, whereas those from labs 2 and 4 were 2126%. ICCs
ranged from 0.84 to 0.88 for midfollicular women, 0.550.75 for
midluteal women, and 0.880.96 for postmenopausal women. The ICCs
reflected the large variability of measurements between postmenopausal
women and small variability of the measurements between midluteal
women. The MDRDs were smaller for the midluteal measurements, 611%,
and somewhat larger for midfollicular or postmenopausal measurements,
815%.
ADION.
No time trends were evident in the data for lab 1 (figure not shown).
Although there was some overlap of aliquot means of the midfollicular
and postmenopausal women, measurements at the high levels were clearly
separated from those at lower levels. The grand means of the midluteal
women had a narrow range, and there was greater overlap with poor
separation. There was an increasing trend with time in means for all
menstrual phases in the data from lab 2. There was also overlap and
poor separation for all phases. The daily means from lab 3 showed
substantial variability because measurements on day 3 were consistently
lower than comparable measurements on other days. Measurements from lab
4 showed no time trends. There was no overlap of aliquot means and
clear separation for midfollicular phase women. However, there was
substantial overlap for midluteal women and some overlap for
postmenopausal women with only the highest and lowest measurements
clearly separated.
The ranks of the subjects mean responses for midluteal and
postmenopausal women were highly correlated (0.901.00), but not the
ranks for midfollicular women (0.300.90). The geometric means of
ADION were 60.0, 62.9, 55.7, and 65.6 ng/dl and were significantly
lower from labs 1 and 3 than from labs 2 and 4. Labs 2 and 3 had lower
ICCs and higher CVs than labs 1 and 4 (Table 1)
. Estimated MDRDs were
slightly larger at lab 2 than at other labs. At all labs, ICCs and
MDRDs were much smaller for women in the midluteal menstrual phase than
for women in the midfollicular and postmenopausal phases.
ANDRO G.
One lab provided measurements for ANDRO G levels. There were no
definite time trends (figure not shown). Although there was some
overlap of aliquot means for midfollicular phase women, the separation
was clear. There was some overlap among the aliquot means for midluteal
women, and only those with highest and lowest measurements were clearly
separated. For postmenopausal women, there was considerable overlap,
and only the woman with the lowest measurements were separated.
The estimated CVs were around 20% for midfollicular and midluteal
women and somewhat higher, 33%, for postmenopausal women (Table 2)
. The ICCs were high, >85% (Table 2)
. The MDRD was about 14% for
midluteal samples, but >20% for postmenopausal and midfollicular
samples. Estimates of individual variance components and their SEs are
provided in
of the "Appendix."
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a2, was relatively small for
these midfollicular women, resulting in small total variation and
therefore a small MDRD.
ADIOL.
Only one lab carried out assays for ADIOL. No definite time trends were
evident for any phase (figure not shown). There was great overlap of
aliquot means for all groups. The range of aliquot means for a
particular woman on 1 day can be large. The ICCs were only 12.1, 2.0,
and 11.3 for midfolicular, midluteal, and postmenopausal women,
respectively (Table 2)
. The CVs for the ADIOL assay were large,
4379% (Table 2)
. Nevertheless, because the total variability in the
data were small, the MDRDs were 1021% (Table 2)
.
| Discussion |
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ADIOL G, DHEA, DHEA S, DHT, TESTO, and ADION were assayed in several laboratories. There was variation in the mean assay levels among the participating labs, but the correlations of rankings of subjects mean results among the labs were high. The CVs were fairly high and did not vary widely by menstrual or menopausal states. The CVs for measurements from lab 1 were usually <15% but ranged to 20%, whereas those from lab 2 were usually <20% but ranged as high as 40%.
The ICC was 100 times the ratio of the biological variability among women to the total variability, including sources of variation associated with lab procedures. Values of ICC near 100 indicated that lab variability was small compared to biological variability. ICC values for ADIOL G, DHEA, and DHEAS exceeded 90% for lab 1 and lab 3 and usually exceeded 85% for labs 2 and 4. At all labs, the ICCs usually exceeded 80% for DHT, TESTO, and ADION in postmenopausal and midfollicular phase women. For midluteal phase women, the biological variability among women was small, and there were lower values of the ICC; specifically, they were <70% for TESTO and <22% for DHT and ADION.
Another way to assess the utility of these assays is to determine the minimal detectable relative difference in percent, MDRD, that can be detected in a case-control study. The comparison in this report was based on 300 cases and 600 controls, approximately the size of the study we are contemplating. For ADIOL G, DHEA, DHEA S, DHT, TESTO, and ADION, the MDRDs for this design were <20% at labs 1 and 4, and <30% at labs 2 and 3. The MDRDs were smallest for DHT, TESTO, and ADION, the assays for which the biological variability among women was particularly small.
Lab 3 was the only lab that volunteered to assay ANDRO G, ANDRO S, and ADIOL. For ANDRO G and ANDRO S, the CVs ranged from 18% to 33%, whereas the CVs for ADIOL were very high (4379%). Levels of the latter hormone were very low (usually <100 pg/ml) in both premenopausal and postmenopausal women. The ICCs ranged from 8697% for ANDRO G and 6492% for ANDRO S, but were <15% for ADIOL. For each of these assays, the MDRDs ranged from 10 to 25% for a study with 300 cases and 600 controls.
The CV is useful for lab quality control, whereas the ICC and MDRD are more important in determining the feasibility of an epidemiological study. If the variation among subjects is large, the ICC may be large even if the CV is large. If the ICC is large, estimates of the slope of the log relative risk on log (hormone) will suffer little attenuation from lab measurement error, and required sample sizes will be minimally inflated from lab measurement error. On the other hand, the MDRD depends on all sources of variability. If variation among subjects is small, the MDRD may be small enough to justify an epidemiological study even if the CV is large, provided the ICC is not too small. Conversely, a study can be impeded by small values of ICC and large values of MDRD, even when the CV is small.
Estimates of the components of variance allow one to identify the aspects of lab procedures that lead to increased variability and to learn how to efficiently allocate resources to improve assay reproducibility. For example, if there were more variation among aliquots than among replicates, one might increase the number of aliquots and decrease the number of replicates. The total effort would not change, but the CV would decrease, the ICC would increase, and the MDRD would decrease. For those interested in design issues, the estimated components of variance and their SEs for each of the androgen assays are given in the "Appendix."
Our study used aliquots from a woman whose blood was drawn on a single day, so our estimates of subject variation for a premenopausal or postmenopausal woman include both the between subject variation and the secular variation for a given woman in the middle of that phase. This reliability study design is entirely appropriate for the typical case-control study, which uses only one sample per subject. These data do not allow us to estimate the component of variation that corresponds to repeated blood samples taken over time from the same woman.
Lab 1 usually exhibited smaller CVs, higher ICCs, and smaller MDRDs than the other labs. Lab 3 also exhibited relatively small CVs, high ICCs, and small MDRDs while also providing results on more hormones than the other labs.
The present study used only five women in each men opausal or menstrual phase. Larger numbers of women would be desirable to estimate ICCs and other parameters with greater precision. This study provided valuable guidance, nonetheless, for designing epidemiological studies. These data suggest that a single sample (with two lab replicates per sample) of ADIOL G, DHEA, DHEA S, and ANDRO G can be used to discriminate reliably among women in a given menstrual phase or menopausal status. The results for DHT, TESTO, ADION, and ANDRO S are more problematic and suggest that the present measurement techniques should be used with care, especially with midluteal women. The results for ADIOL suggest that this assay is not yet ready for use in epidemiological studies.
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| Footnotes |
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1 To whom requests for reprints should be
addressed, at National Cancer Institute, Executive Plaza South, Room
8040, MSC 7368, 6120 Executive Boulevard, Bethesda, MD 20892. ![]()
2 The abbreviations used are: ADIOL,
androstanediol; ADIOL G, ADIOL glucuronide; ADION, androstenedione;
ANDRO G, androsterone glucuronide; ANDRO S, androsterone sulfate;
DHEA, dehydroepiandrosterone; DHEA S, DHEA sulfate; DHT,
dihydrotestosterone; TESTO, testosterone; CV, coefficient of variation;
ICC, intraclass correlation; MDRD, minimum detectable relative
difference. ![]()
Received 6/11/99; revised 1/12/00; accepted 2/10/00.
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