Reevaluation of the Variable Component of the Systematic Error Calls for Paradigm Change in Clinical Laboratory Quality Control
The existence of the variable component of the systematic error (VCSE) is known since 1963, but seems to be a kind of taboo: neither has definition in VIM, nor is present in equations, being considered transformed in time into random error. Present study using methods of mathematical statistics, computer simulations and examples from the day-to-day practice of the author makes an attempt to reevaluate its role and significance in the QC in clinical laboratory.
“The bias” (which one?) it is a definitional uncertainty, because it is time-variable. Making clear distinction between bias measured in repeatability respective reproducibility within laboratory (RW) conditions as in case of standard deviations, and also separating constant and variable subcomponents of the systematic error, two sets of error parameters are obtained each set being consistent with the measurement conditions. The link between them is the time-variable VCSE function.
The conditions of calculations and predictions based on them must be consistent with the conditions of their determination, to avoid the redundant use. Being consequent, several differences can be discovered between the constant and the variable component of the systematic error respective random phenomena, also between variable and random error components.
The variable components of the systematic errors are cyclical, mostly predictable variations (shifts and drifts) in the daily mean. However, it is presented a direct method to determine the SD of the VCSE, its easiest calculation is possible from accurate values of sr and sRW. There are presented methods to calculate sr and sRW from long term data.
As conclusion there is necessary a new paradigm of the QC in clinical laboratory based on the proposed error model.
Motto “Everything Should Be Made as Simple as Possible, But Not Simpler” (A. Einstein) .
### Competing Interest Statement
The authors have declared no competing interest.
### Funding Statement
This study did not receive any funding
### Author Declarations
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All data produced in the present work are contained in the manuscript.
* VIM
: International Vocabulary of Metrology
QC
: Quality Control
EQA
: External Quality Assessment
MU
: measurement uncertainty
TE
: total measurement error
RE
: Random error component
SE
: Systematic error component
VCSE(t)
: Variable Component of Systematic Error in the moment t (a time-variable function)
CCSE
: Constant Component of Systematic Error
SD
: Standard Deviation (in general)
sr
: SD measured in constant, repeatability conditions
sRW
: SD measured in variable, reproducibility within laboratory conditions
sVCSE
: the SD calculable from the daily(run) mean (bias, VCSE(t)) values
smean
: the SD calculable from the monthly means
CV
: Coefficient of Variation, the SD expressed as percent of the mean of measurements
CVr
: CV measured in constant, repeatability conditions
CVRW
: CV measured in variable, reproducibility within laboratory conditions
CVVCSE
: CV of the VCSE(t), sVCSE expressed as percent of the target value
B
: bias
B%
: bias expressed as percent of the long-term mean of measurements
∆ B %
: percent expressed bias variation in a shift (percent of the long-term mean value)
Br(t)
: (short term or within day) bias measured in repeatability conditions in the moment t (a time-variable function)
BRW
: long term mean bias, measured in RW conditions, a constant
RMS
: root mean square - the root of the arithmetic mean of squares (not to be confused with the RMSE)
max□ (max index before)
: the maximum value of a parameter in given conditions
z
: coefficient of confidence
c
: concentration or activity of a measurand
n
: number of measurements
t
: time or moment, expressed as run number
Fcal
: the slope factor of the linear calibration curve
x
: (control) measurement result
xt
: (control) measurement result in the moment t
![Graphic][1]</img>
: mean of measurements
![Graphic][2]</img>
: the daily (run) mean in the moment t (repeatability conditions)
CLSI
: Clinical and Laboratory Standards Institute
ANOVA
: analysis of variance
V
: variance, the square of the SD
Vw
: Variance within run (notation in CLSI EP15-A3), the square of sr
Vb
: Variance between runs (notation in CLSI EP15-A3), the square of sVCSE
Vwl
: Variance within laboratory (notation in CLSI EP15-A3), the square of sRW
[1]: /embed/inline-graphic-19.gif
[2]: /embed/inline-graphic-20.gif
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