Understanding the concepts associated with variability of laboratory results would help laboratorians improve the quality of laboratory service as well as aid the drive towards harmonization of laboratory quality practices.

1. Variability Of Clinical
Chemistry Laboratory
Results.
Adetokunbo Ajala
Chemical Pathology OAUTHC
tokunboajala@yahoo.com

2.  “Every laboratory result is erroneous; it is the degree
that counts”.
 A true result could be therefore regarded as an abstract
ideal with an error of zero.

3.  Repeating the same test on the same specimen under
the same conditions would not give the same result for
all the repetitions even when the process is performed
under optimal conditions.
 An increase in this inherent variability of results
beyond specific limits is what signifies the occurrence
of an unacceptable error within the system of the
testing process.

4.  The concept of variation of processes was brought to
the attention of industry by the works of Walter
Shewart and Edward Deming[1].
 Chance/Common causes: due to consistent factors
causing predictable variation within a process.
 Assignable/Special causes: due to erratic factors
causing unpredictable variation within a process.
 Deming advised the complete eradication of special
causes and the continuous improvement of the process
by reducing as much as possible the common
causes[2].

5.  Variation in the laboratory could be pre-analytical,
analytical, and post-analytical.
 Analytical variation is that which is associated with the
actual analysis of analytes, preanalytical variation is
that due to factors prior to analysis, post-analytical
variation: after analysis.

6. Variability estimates may be used in the clinical
chemistry laboratory for:
 the establishment of quality goals or performance
specifications for test methods,
 comparison of successive patient’s results,
 determining the utility of established reference
intervals,
 establishing quality control protocols, and
 assessing the clinical utility of laboratory tests[3].

7. Some important concepts related to analytical variation
in the laboratory as defined in the International
Vocabulary of Metrology include[4]:
 Random error: Component of measurement error that
in replicate measurements varies in an unpredictable
manner.
 Precision: Closeness of agreement between
indications or measured quantity values obtained by
replicate measurements on the same or similar objects
under specified conditions (Measurement precision is
usually expressed numerically by measures of
imprecision, such as standard deviation, variance, or
coefficient of variation under the specified conditions
of measurement). Imprecision is an estimate of
random error.

8.  Systematic error: Error component of measurement
error that in replicate measurements remains constant
or varies in a predictable manner.
 Bias: An estimate of a systematic measurement error.
 Accuracy: Closeness of agreement between a
measured quantity value and a true quantity value of a
measurand.
 Trueness: Closeness of agreement between the average
of an infinite number of replicate measured quantity
values and a reference quantity value.

9. Broader concepts of variability
BIOLOGICAL VARIATION:
Biological variation of analytes occurs due to the natural
fluctuation of body fluid constituents around a
homeostatic set point in turn due to variation of
natural factors e.g. changes in sunlight intensity,
humidity, temperature, diet and other natural
phenomena.
There are two components of biological variation:
 within-subject biological variation: natural variation
in levels of an analyte in the same healthy individual,
 between-subject biological variation: natural variation
in the levels of an analyte in different healthy
individuals.

10.  The within- and between-subject components of
variation are expressed in coefficients of variation (CVi
and CVg), respectively.
Biological variation data is used to establish
performance goals:
 Three levels of performance are specified for analytical
variability according to the degree of their effects on
test results: ‘Optimal’, ‘Desirable’, and ‘Minimum’,
performance.
 Generally, analytical variation should be low in
addition to the biologic variation for a given test for
good performance.

11.  Total Analytic Error(TAE) of an analytical method
must be less than the Allowable Total Error(ATE) for
the analyte in question to satisfy performance goals.
 Total analytic error(TAE) is derived via method
validation.
 Allowable total error is derived from biological
variation data.

12.  TAE = Bias + imprecision
=systematic error + random error
= Bias% + k*CV

13. For example,
Desirable performance specification for a method:
Bias should not exceed 0.25(CVi2 + CVg2)1/2
and
Imprecision should not exceed 0.5 CVi.
(Cvi and CVg are intra- and inter-individual biological
variation respectively).
Hence, for a given analyte;
ATE ≤ 0.25(CVi2 + CVg2)1/2 + k*0.5CVi.
where k = 1.65 at α = 0.05(one sided test at 95%
confidence interval)
For desirable performance, TAE of a method should not
exceed the estimated ATE above.

14. Figure i. Performance goals for analytical variation based on biological variation.

15. TOTAL ANALYTIC ERROR (TAE):
 A concept introduced into analytical chemistry by
James O. Westgard in 1974[5].
 It is a comprehensive analytical metric that may be
used to describe the performance of a method.
 It incorporates measurements of a method’s
systematic and random error, (or bias and imprecision
respectively) into a single metric.

16.  Bias of a method could be estimated via a recovery
experiment or a comparison of methods experiment
amongst others.
 Imprecision is measured with the precision
experiment.

17. TAE% = Bias% ± 2CV (TAE = Bias ± 2SD)
or
TAE = Bias + 1.65 SD (for a one-sided estimate).

18. . Graphical representation of the TAE: Total Analytic
error. SE: Systematic Error, RE: Random Error, SD:
Standard Deviation

19.  TAE in its attempt to capture all inherent variation in
the analytic process is similar to the concept of
measurement uncertainty
 TAE has also been used for the calculation of a quality
index known as the Sigma Metric.

20. SIGMA METRIC
 The sigma metric is a quality index adapted from the
six sigma(6σ) methods that have revolutionalized the
manufacturing and service industries[8–10]
 A 6σ production method has specified tolerance limits
that can accommodate variation of up to six standard
deviations from the mean; corresponding to maximal
error rates of four defects per million units produced.

21.  Sigma metric based quality control was developed for
the clinical laboratory by James O. Westgard[11]
aiming to have laboratory methods perform at
standards similar to those of the manufacturing
industry.
 The sigma metric(SM) of an analytical method is
calculated from the TEA as follows:
SM = (TAE% – Bias%) / CV.

22.  The Sigma metric has been adapted for use in quality
control measures that are available as computer
software for laboratories that want to optimize their
quality control practices.

23. MEASUREMENT
UNCERTAINTY(MU)
 A recent measure of test method performance in
clinical chemistry.
 “The laboratory shall determine measurement
uncertainty for each measurement procedure in the
examination phase used to report measured quantity
values on patients’ samples. The laboratory shall
define the performance requirements for the
measurement uncertainty of each measurement
procedure and regularly review estimates of
measurement uncertainty”[27]: ISO 15189

24.  “Parameter, associated with the result of a
measurement, that characterizes the dispersion of the
values that could reasonably be attributed to the
measurand”[28]: GUM 2008.
 “A non-negative parameter characterizing the
dispersion of the quantity values being attributed to a
measurand, based on the information used”: VIM 2012.

25.  Measurement Uncertainty can be expressed with
individual results issued by the laboratory.
 E.g. RBG: (5.8 ± 0.2) mmol/l, where 0.2 is the
measurement uncertainty.
 The measurement uncertainty model is more inclusive
of the whole testing process but setback by the relative
complexity of its estimation[33-35].
 Schema for estimating measurement uncertainty:

27. REFERENCE CHANGE VALUE (RCV)
 utilizes knowledge of analytical and biological
variation to estimate acceptable difference between
two successive results of the same patient.
 A ‘normal’ change between two successive results
should not exceed the combined total
variation(analytical and biological) for each result.

28.  Variability of first result - Z*(CVa2+ CVi2)1/2
 Variability of second result - Z*(CVa2+ CVi2)1/2
 Total variation [root sum of squares] = [Z 2*(CVa2+
CVi2) + Z 2*(CVa2+ CVi2)]1/2
 Therefore, RCV = 2½*Z*(CVa2+ CVi2)½
 where Z = 1.96 at 95% level of significance (two sided
test), and CVa: analytical variation [of the method]
and Cvi: within subject biological variation [of the
analyte].

29.  RCV can be referred to as a means of post-analytical
quality control.

30. INDEX OF INDIVIDUALITY
 a measure of the degree of ‘within subject variation’
against ‘between subject variation’ expressed as
CVi/CVg.
 An analyte with a high index of individuality has
greater dispersion within the individual; hence
established reference intervals are likely to include all
normal test results for a given individual.
 Analytes with a low index of individuality vary less
within the individual and reference intervals may not
cover extreme but normal test results returned for an
individual.

31.  The RCV may be required to appropriately interprete
the result in such a situation.

32. Conclusion
 Understanding the concepts associated with variability
of laboratory results would help laboratorians improve
the quality of laboratory service as well as aid the drive
towards harmonization of laboratory quality practices.

33. Bibliography