substance are most often expressed in terms of
percent change in measured analyte concentration.
The substance is evaluated over the range of
substance concentrations that spans the anticipated
clinical range for the substance so that the effects
can be related to the concentration of the substance,
usually by use of a linear model. This one-at-a-time
approach that was taken by Luque de Castro
et al.
,
The effects of bilirubin and hemoglobin as
potential optical interferences and of uric acid,
ascorbic acid, xanthine, hypoxanthine, and
glucose as possible chemical interferences
were studied. Each compound was added to a
pool of serum (phosphate concentration 1.25
mmol/L) and its influence established. No
interferences were detected from bilirubin for
concentrations <600 mg/L, hemoglobin <20
g/L, uric acid <150 mg/L, ascorbic acid
<75 mg/L, and glucose <200 mmol/L . . .
The presence of allopurinol < 200 mg/L in
serum did not cause interference; it did cause
an error of ~ -4% at 400 mg/L.
Xanthine and hypoxanthine, which are substrates of
the second enzymatic reaction, produced a positive
interference, which presumably was proportional to
the concentration of the added substance. The
authors comment that interference from these
substances in the clinical setting should be "no
special problem" because they are "present in serum
very infrequently."
The one-at-a-time approach will not reveal
complex chemical interactions such as those occur
between an interferent or cross-reactant and the
analyte and those that occur between different inter-
ferents and cross-reactants. Quantitative evaluation
of complex interferences and cross-reactions requires
a response surface modeling approach similar to that
discussed in the section on optimization of analytical
variables (Kroll and Chesler 1992). In this
approach, the potential interferents and cross-
reactants are added in varying concentrations to each
aliquot of the clinical sample. For a complete facto-
rial design, all possible combinations of the various
concentrations for each of the interferents and cross-
reactants are studied (Box and Draper 1987). The
measured analyte concentrations are fit to an
response surface model by multiple regression analy-
sis. A model limited to first-order and interaction
terms is usually used, such as the following ,
analyte concentration =
b0 + b1x1 + b2x2 + b12x1x2
for two interferents where
x1
and
x2
are the concen-
trations of the respective interferents and
b0
repre-
sents the concentration of analyte in a sample free of
interferents.
The presence of complex chemical interactions is
indicated by statistically significance of the coeffi-
cients of the interaction terms. The clinical signifi-
cance of an interaction depends upon the magnitude
of the interaction effects.
Precision.
Figure 2.8 illustrates the steps in the
characterization of the precision of a method. Repli-
cate measurements are made using samples with
analyte concentrations that span the measurement
(top graph). If within-run imprecision is being
studied, all of the measurements on a sample must
be made during the same run. In a study of within-
laboratory imprecision, the measurements on a
sample need to be performed during different runs
and, preferably, on different days. An absolute
minimum of 10 replicate measurements need to be
made to obtain a moderately precise estimate of the
standard deviation; 20 replicates is better and 50
replicates is better still (Sadler and Smith 1990).
The standard deviation of each set of replicate
measurements is calculated using the formula
(Bookbinder and Panosian 1986),
standard deviation =
(
x
i
−
mean
)
2
n
−
1
where
x
i
is the
i
th replicate result,
mean
is the mean
of the replicates, and
n
is the number of replicates.
The standard deviations are plotted versus analyte
concentration. If the imprecision is constant over
the measurement range, the empirical standard
deviations will be roughly equal and will form a
fairly flat line. If the imprecision is proportional to
analyte concentration, the empirical standard devia-
tions will increase in magnitude with increasing
analyte concentration. The imprecision model that is
usually fit to the empirical data is the 3-parameter
model proposed by Sadler
et al.
(1988),
SD = (b0 + b1 concentration)
b2
This model is quite flexible. If
b2
is one, the model
defines a line. Otherwise, the model defines a curve
that can be either convex (
b2
greater than one) or
concave (
b2
less than one). Because the model is
nonlinear, it must be fit by nonlinear regression.
Laboratory Methods
2-20
