variables. These points can be used to fit a
response surface model, if a functional form for the
surface is suggested by the data. The optimal
set-point combination can then be calculated from
the model equation. Alternatively, the data points
can be used as a starting point for an empirical
search algorithm. Search algorithms seek out optima
in an iterative fashion: using the response data from
the preceding step, the algorithms indicate the most
informative set-point combinations to test next. The
iterations continue until the maximum system
response and its associated set-point combination is
identified. The popular search algorithms are highly
efficient and rapidly converge to the response
surface optimum. This means that the delineation of
the optimal analytical variable set-point combination
for a new method can be achieved without undue
expense. Multivariate optimization should,
therefore, be considered whenever there is uncer-
tainty about the validity of the univariate optimiza-
tion approach.
Characterization of the calibration curve
The most common form for the equation of the
calibration curve is a straight line. Sentiments of the
sort, “Linearity is a state sought by all clinical
laboratorians. It means straight and predictable,
good work, and good value” (Passey and Maluf
1992) are common despite the fact that there are
measurement systems in the clinical laboratory, such
as competitive immunoassay systems, that produce
results of high quality despite having nonlinear
calibration curves. Nevertheless, when calibration
linearity is possible, considerable efforts are made to
assure that the operating conditions for a measure-
ment system yield a linear calibration curve.
In order to evaluate the linearity of a calibration
curve, a measure or test of linearity is needed. Such
a measure has not proven easy to come by. Tholen
(1992) listed 22 different statistical techniques that
had been proposed for evaluating calibration linear-
ity up to the time he wrote his review. Since then, a
technique developed by Kroll and Emancipator
(1993, Emancipator and Kroll 1993) has achieved a
degree of acceptance in the laboratory medicine
community as a linearity measure. That technique is
based upon the quantification of nonlinearity as the
root mean square of the deviation of the calibration
curve from an ideal straight line,
nonlinearity
=
¶
x
low
x
high
(
c
(
x
) −
g
(
x
))
2
dx
x
high
−
x
low
where
c(x)
is the equation of the curve that best fits
the empirical calibration data,
g(x)
is the equation of
the ideal straight line fit of the data, and
x
high
and
x
low
are the values of the high and low calibrators,
respectively. Defining the relative nonlinearity as,
relative nonlinearity
=
nonlinearity
y
high
−
y
low
where
y
high
and
y
low
are the highest and lowest signal
magnitudes recorded during the linearity study,
Emancipator and Kroll (1993) found that calibration
curves that are acceptably linear by visual inspection
have relative nonlinearities of less than 2.5%. Using
this technique, Luque de Castro
et al.
found that
their phosphate method demonstrated acceptable
linearity over the range of measurement,
The linearity of the method was assessed by
means of Kroll and Emancipator's procedure
(18,19) recently adopted by the College of
American Pathologists (20). the . . . nonline-
arity was 0.063 mmol/L; the relative nonline-
arity, 1.29%.
A number of practical considerations are
involved in the implementation of the technique of
Kroll and Emancipator. The number and spacing of
the calibrators need to be chosen. Kroll and
Emancipator suggest using 5 equally spaced calibra-
tors. This scheme will reveal both monotonic and
sigmoidal nonlinearity. In cases in which the curva-
ture in the calibration curve appears to be limited to
one or the either end of the curve, such as when
there is concavity at the high end of a calibration
curve for a method which suffers substrate exhaus-
tion at high analyte concentrations, it may be neces-
sary to add additional calibrators within the suspect
interval. Each calibrator should be run in replicate.
The number of replicates needed depends upon the
measurement variability of the method: for highly
precise methods, duplicates are adequate; for
methods that are imprecise, quintuplicates are
warranted. Most authors report the use of
triplicates, a convenient compromise number. The
replicates should be between-run rather than within-
run (Kroll and Emancipator 1993, Emancipator and
Kroll 1993).
Laboratory Methods
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