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(5)
Coefficient of Variation
Indexation
International Collaboration
Repeated Measures
Standard Deviation
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Use of Coefficient of Variation in Assessing Variability of Quantitative Assays
Use of Coefficient of Variation in Assessing Variability of Quantitative Assays,10.1128/CDLI.9.6.12351239.2002,Clinical and Vaccine Immunology,George
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Use of Coefficient of Variation in Assessing Variability of Quantitative Assays
(
Citations: 25
)
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George F. Reed
,
Freyja Lynn
,
Bruce D. Meade
We have derived the mathematical relationship between the
coefficient of variation
associated with repeated measurements from quantitative assays and the expected fraction of pairs of those measurements that differ by at least some given factor, i.e., the expected frequency of disparate results that are due to assay variability rather than true differences. Knowledge of this frequency helps determine what magnitudes of differences can be expected by chance alone when the particular
coefficient of variation
is in effect. This frequency is an operational index of variability in the sense that it indicates the probability of observing a particular disparity between two measurements under the assumption that they measure the same quantity. Thus the frequency or probability becomes the basis for assessing if an assay is sufficiently precise. This assessment also provides a standard for determining if two assay results for the same subject, separated by an intervention such as vaccination or infection, differ by more than expected from the variation of the assay, thus indicating an intervention effect. Data from an international collaborative study are used to illustrate the application of this proposed interpretation of the coefficient of variation, and they also provide support for the assumptions used in the mathematical derivation. Although assay variability is well recognized as pertinent to the interpretation of quantitative bioassays such as the en zymelinked immunosorbent assay (ELISA), few tools that link assay precision with interpretation of results are readily avail able. In our investigations, we have expanded on previous studies that evaluated the relationship between assay precision and the capabilities and limitations of a given assay system. In this article we develop a simple procedure to determine the probability that an assay will accurately discern whether two samples have the same analyte concentration or not based on a knowledge of the assay variability as measured by the coef ficient of variation (CV). In many laboratories, the variability of the ELISA and other methods of chemical assay that produce continuoustype val ues is summarized not by the
standard deviation
(SD) but by the CV, which is defined as the SD divided by the mean, with the result often reported as a percentage. The main appeal of the CV is that the SDs of such assays generally increase or decrease proportionally as the mean increases or decreases, so that division by the mean removes it as a factor in the variabil ity. The CV is therefore a standardization of the SD that allows comparison of variability estimates regardless of the magni tude of analyte concentration, at least throughout most of the working range of the assay. In serological assays a twofold difference in measurements of the same sample has been widely regarded as the upper limit on acceptable variability, and the frequency of such differences among pairs of repeated measurements has been proposed as an apt index for assay variability (5). Wood (4) showed the mathematical relationship between that frequency and the size of the SD of repeated assay measurements, under the assump tion that the logarithm of measurements is normally distrib uted. The tables he provided indicate how small an SD of the log measurements must be in order to ensure that only some predetermined fraction of pairs of measurements differ by a factor of two or more. Wood's formulation was a valuable link between the precision of titration assays and an operational assessment of assay performance. As expressed above, in the context of serum assays and other applications the CV may be preferred over SD as a measure of precision, but there is no published formulation that links the CV to assay performance in a manner analogous to Wood's treatment of the SD in the log scale. Such a formulation would be even more useful if it were to generalize from twofold to kfold disparities in replicate measurements (where k can be any number greater than one and arbitrarily close to one). This generalization would take advantage of the fact that ELISAs and other assays with continuous scales are capable of mea suring a continuous range of differences in samples, unlike classic titration assays utilizing stepwise, usually twofold, serial dilutions. The intent of this article is to introduce the mathe matical relationship between the CV and the frequency of kfold or moredisparate assay values when the same sample is subjected to repeated measurements. We also demonstrate how this relationship can be used to address practical problems in a clinical laboratory.
Journal:
Clinical and Vaccine Immunology  CLIN VACCINE IMMUNOL
, vol. 9, no. 6, pp. 12351239, 2002
DOI:
10.1128/CDLI.9.6.12351239.2002
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Citation Context
(9)
...In chemistry, the CV is used to compare the precision of two laboratories in measuring quantities of interest (see Reed et al,
2002
)...
Richard A. Groeneveld
.
Influence Functions for the Coefficient of Variation, Its Inverse, and...
...The results of repeated trials of such assays tend to be reported in terms of the CV because the standard deviations of assays generally increase (or decrease) in proportion to the increase (or decrease) in the mean [
77
]...
Bente C. D. Anda
,
et al.
Variability and Reproducibility in Software Engineering: A Study of Fo...
...where n is the number of replicates (n = 5), Ii is the normalized mean spot intensity value and I is the spot’s overall mean, calculated from the means of the corresponding spots in the n replicates; 2) coefficient of variation (CV) [
30
]...
Emmanouil I. Athanasiadis
,
et al.
Segmentation of Complementary DNA Microarray Images by WaveletBased M...
...Standardized serologic assays might be sensitive and specific enough to be utilized in diagnostic test evaluations, given that the variability inherent in these quantitative assays does not exceed the minimal levels for acceptance criteria (
40
)...
Andrew L. Baughman
,
et al.
Utility of Composite Reference Standards and Latent Class Analysis in ...
...A simple procedure was used in this study to measure the quality of the PET and CT images, using the coefficient of variance [
7
]...
Sora Nam
,
et al.
Quantitative imaging with lowdose CT in the PET/CT system
References
(2)
Collaborative Study for the Evaluation of EnzymeLinked Immunosorbent Assays Used To Measure Human Antibodies toBordetella pertussisAntigens
(
Citations: 19
)
FREYJA LYNN
,
GEORGE F. REED
,
ANDBRUCE D. MEADE
Published in 1996.
Statistical considerations in the quantitation of serum immunoglobulin levels using the EnzymeLinked Immunosorbent Assay (ELISA)
(
Citations: 35
)
K KARPINSKI
,
S HAYWARD
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H TRYPHONAS
Journal:
Journal of Immunological Methods  J IMMUNOL METHOD
, vol. 103, no. 2, pp. 189194, 1987
Sort by:
Citations
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Peak and average rectified EMG measures: Which method of data reduction should be used for assessing core training exercises?
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Citations: 1
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A. E. Hibbs
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K. G. Thompson
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Journal:
Journal of Electromyography and Kinesiology  J ELECTROMYOGRAPH KINESIOL
, vol. 21, no. 1, pp. 102111, 2011
Influence Functions for the Coefficient of Variation, Its Inverse, and CV Comparisons
Richard A. Groeneveld
Journal:
Communications in Statisticstheory and Methods  COMMUN STATISTTHEOR METHOD
, vol. 40, no. 23, pp. 41394150, 2011
Reproducibility and reliability of repeated semen analyses in male partners of subfertile couples
(
Citations: 1
)
Esther Leushuis
,
Jan Willem van der Steeg
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Pieternel Steures
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Sjoerd Repping
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Marinus A. Blankenstein
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Botulinum neurotoxin in the treatment of headache disorders
Alexander Mauskop
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Handbook of Clinical Neurology
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Cocaine and metabolites in waste and surface water across Belgium
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Citations: 19
)
Alexander L. N. van Nuijs
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Nathalie Dubois
,
Corinne Charlier
,
Philippe G. Jorens
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Lieven Bervoets
,
Ronny Blust
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Hugo Neels
,
Adrian Covaci
Journal:
Environmental Pollution  ENVIRON POLLUT
, vol. 157, no. 1, pp. 123129, 2009