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Article written by Jessica Raney, Quality Control Group Leader, Analytical Products Group
Complete Article from Edition 7 APG eNewsletter
The Big Picture
An accurate quantitative analysis begins with accurate reference standards.
Standards are defined by their use. The information you need to know about
a standard is also defined by its use. Calibration standards are the known
standards used to generate a calibration curve. Quality control standards verify
that the calibration is correct. Only two pieces of information need to
be known about a calibration standard - the identity of the material and
the true value of the standard. Quality control standards require an
additional piece of information. They must have some measure of performance
for the sample. This information is usually provided as an acceptance range.
Often, analysts believe that any known sample can be used to check their
calibration. Without the additional information of the acceptance criteria,
the analyst has no information about the quality of the calibration.
The following are essential to generating defensible data:
- proper selection of the calibration range
- accurate calibration standards
- independent quality control standards
- careful monitoring of the calibration
Importance of the Calibration Curve
A calibration establishes a relationship between instrument response
and concentration. This relationship is usually linear and can be
represented mathematically by the equation for a straight line,
y = mx + b. In this equation, y represents the instrument
response, x, the concentration, m is the slope of the line,
and b is the y-intercept.
A linear relationship between response and concentration is
straightforward. For any one response, there can be only
one corresponding concentration. It is imperative to
work within the linear range of the calibration curve as
this relationship is essential to an analytical method.
The method development will ensure that your method is
dependable and robust, but good calibration is the
key to good analyses. A calibration is only as good
as the standards used to generate it. Accurate, precise
data will not be generated if calibration standards are
poorly prepared or the range is not carefully selected
and evaluated.
Selecting Your Calibration Range: The Low End of the Curve
The two areas to be concerned with are the low end of the range and the high
end of the range. At the low end, differentiation must be made between
response and noise. Response at the low end can be highly variable if the
analysis is not within the linear range. The Horowitz Curve can help find
the low end of the linear range. The Horowitz curve is constructed
analyzing several calibration standards at least three times each. The
concentration is plotted versus the percent relative
standard deviation (%RSD) for each standard. The Horowitz Curve has a
distinctive shape, as %RSD will dramatically increase at a certain
concentration. The area where the Horowitz Curve is flat represents
the linear range of the method. The point at which the %RSD begins to
increase above a certain level is the lowest linear point of the
calibration range.
Selecting Your Calibration Range: The High End of the Curve
At the high end of the calibration curve, the point at which the
detection mechanism can no longer differentiate between two concentrations
is important. This represents a loss of sensitivity. The difference
between the slope of the two points at the top of the curve and the
overall slope should be less than five percent. If the difference is
greater than five percent, it indicates a change in sensitivity. This
loss of sensitivity can be represented as a flattening of the curve. It
is best to operate in the area of the calibration that has the most
sensitivity. Therefore, this point is very important to find during
method development.
Validating the Calibration Curve
Determining the linear calibration range is only part of the puzzle.
As an accurate calibration is the cornerstone of a reliable analytical method,
the calibration curve must be verified each time it is generated.
The calibration should be verified against an independent quality control
standard. The quality control standard must be completely independent
from the calibration standards. The most effective way to ensure
independence is to purchase a quality control standard from a third party.
The quality control standard requires different information to accompany
it because it has a different function than a calibration standard.
In addition to the identity of the material and the true value
of the standard, a quality control standard should also have some measure
of laboratory performance. This is usually represented as the
interlaboratory study data.
Example Bracketing*
- Calibration Standard #1
- Calibration Standard #2
- Calibration Standard #3
- Quality Control #1
- Unknown Sample(s)
- Quality Control #2
*Additional samples removed for clarity
The quality control standard should be treated exactly as an
unknown sample and should bracket any unknown samples being
analyzed. The curve is valid if the quality control
standard analyzed directly after the calibration meets the criteria
established by the interlaboratory data. If the quality control
standard analyzed after the unknown(s) meets that criteria, then
the calibration remains valid and any data generated between them
can be considered valid.
Measuring the Quality of the Calibration: The Correlation Coefficient and Slope
It is also very important to monitor the performance of the calibration curve
over time. This requires not only verification of the calibration curve, but
also some way of initially judging the quality of the curve. A widely
used quantity is the correlation coefficient, or r value.
The correlation coefficient measures the fit of the line through its
corresponding points. It is often referred to as the "Fitness for Use".
The correlation coefficient can be a deceptive measure of the quality
of the curve. The r value does not measure the accuracy
of the curve; it measures how well the points fit the line relative
to each other. For example, if your calibration was diluted from
an incorrectly prepared calibration stock, the fit of the curve might
be 0.999 - a good fit. However, your result will be inaccurate. In this
case, the quality control standard will establish the quality of the
curve. The slope of the curve can be used in conjunction with the
correlation coefficient to judge the quality of the curve. The steeper
the slope, the more sensitive the method. The slope should be established
during the method development and should be monitored during each
analysis. The slope of the curve should be within a 95% confidence interval
(CI) of the last slope generated.
It is important to use all three tools to verify the calibration:
- Correlation coefficient
- Slope Evaluation
- Results of the quality control standard
It is essential to the success of the method to verify the calibration. A calibration
standard cannot be used to verify the calibration curve. It lacks the measure
of laboratory performance therefore a reliable judgment of performance cannot be
achieved. It also lacks the level of independence necessary to ensure defensibility.
Defensible data can be ensured through careful selection of the calibration
range, the proper use of quality control standards, and proper monitoring of
method performance.
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