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The following message was posted to: PharmPK
Hello list members,
My question relates to the use of the linear portion of the
calibration curve for LC/MS quantification of samples. My calibration
curve fits to a sigmoidal curve (r2 = 1.00). Why not just use the
sigmoidal curve for the calculations? Why use only the linear portion
of the curve? I can quantify my samples with good accuracy and
precision using the sigmoidal curve. In fact, I can quantify a larger
range of concentrations with much better accuracy and precision than
if I try to use only the linear range. Has anyone else had this
experience? Does anyone use a sigmoidal or other type of curve to fit
the calibration data for quantification?
Any references would be highly appreciated.
Thanks!
Alene McCoy, Ph.D.
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The following message was posted to: PharmPK
Hi Arlene
I dont think there is any problem using a sigmoidal calibration curve provided all the calibrators are within 15% of their nominal values and the LOQ is 20% of its nominal value regardless of the r2 value. Admittedly the r2 should be no less than 0.990. I have to stress that 15-20% rule is more important as this corresponds to the FDA, guidelines. I have used a sigmoidal curve in several circumstances for bioanalytical investigations, placing a greater emphasis on the 15-20% rule provided you achieve good reproducibility on all the calibrators. I would conduct at least 3-4 determinations for each calibrator to achieve reproducible 15-20% and linearity prior to conducting quantification investigations in your choice of matrix. I usually use 1/x or 1/x2 weighting schemes to achieve the best curve fit IF a no weighting scheme does not achieve good linearity.
If it is imperative to use a linear curve fit then I suggest adjusting your calibration curve range otherwise make sure you conduct precision and reproducibility experiments using quality controls covering the range of the calibration curve (linear or sigmoidal with different weighting schemes) to be absolutely sure on 3-4 different occasions (usually over 3-4 days).
Dr. J. Odontiadis (MRACI CChem., Ph.D., M.Phil., Dip. App. Chem).
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Alene,
Instrumentation, and equipment in general, tends to have a sigmoidal response: the response flattens out at the bottom because of the additional contribution of noise as one goes lower, and at the top because there is a finite limit to the output. We have all experienced both of these effects with audio equipment. So output at the two ends of the sigmoid depend upon conditions other than the sample. For the instrument in your lab right now, those other conditions may not vary much, but they certainly will over time and from instrument to instrument.
Frank Bales, Ph.D.
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Alene,
We have encountered this situation several times. Eventhough, i believe there is nothing in FDA guidlines that explicitly ban the use of sigmoidal or hyperbolic curves, we always break the curve into 2 or more linear curves in such situations.
People from the industry may have other opinions.
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The following message was posted to: PharmPK
Dear John,
You wrote:
> I dont think there is any problem using a sigmoidal calibration
>curve provided all the calibrators are within 15% of their nominal
>values and the LOQ is 20% of its nominal value regardless of the r2
>value. Admittedly the r2 should be no less than 0.990.
What is the rationale behind the requirement that r2 should be no less
than 0.990? I know what r2 means and I know that r2 is often used as a
criterion for goodness-of-fit, but I have never seen a convincing
evidence that r2 is a suitable measure of goodness-of-fit. In
contrast, there is good evidence that it is not (Sheiner LB and Beal
SL. Some suggestions for measuring predictive performance. J
Pharmacokin Biopharm. 9:503-512 (1981)).
>I usually use 1/x or 1/x2 weighting schemes to achieve the
>best curve fit IF a no weighting scheme does not achieve good
>linearity.
How do you define 'the best cuve fit'?
best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics, Toxicology and Targeting
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
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The guidance suggests using the simplest curve that fits the data. If a linear regression does not fit the data, even with weighting, you can move to the next most complicated, with or without weighting. You should not use fitting as a way to overcome the limitations of an instrument- that is use of mass spec beyond manufacturers limit for response counts, since this will get you in a tangle with the regulatory agencies.
You should also keep evidence of your trials of other curve fit algorithyms, showing their failure. Acceptance of the curve should be based on the returned accuracy of your calibrators. R2 is relatively meaningless for 4 or 5 parameter fits. Sigmoidal fits are routinely used in ligand binding and cell based assays, but if you validate with these in LC-MS, you should be good to go!
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Arlene: Your reasoning is fine regarding using a sigmoidal curve. Validate across the range following the FDA Guideline criteria. I have done this at an earlier date. It is advisable to use 4 QC concentrations. .....one at the lower end of the curve and one at the higher end of the curve plus two within the linear portion (middle) of the curve. Angus McLean Ph.D.
8125 Langport Terrace
Gaithersburg,
MD 20877
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The following message was posted to: PharmPK
Thanks Dr. O'Connor. Which guidance are you referring to?
Alene McCoy, Ph.D.
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The following message was posted to: PharmPK
Thanks for all of the responses to my query so far. Has anyone had a
chance to publish on a method using a sigmoidal or other non-linear
curve fit for the calibration? I am writing a manuscript and I would
like to reference others who have done the same.
Thanks!
Alene McCoy, Ph.D.
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The following message was posted to: PharmPK
Hi Hans
I agree that r2 is not good predictor of curve fit, however, I place more emphasis on the accuracy and reproducibility of the calibrators achieved from the calibration curve, that is within 15% of their nominal values and 20% for the LOQ as stated in the FDA guidelines. If the calibration curve fit (whether weighted or not weighted at all) achieves good accuracy and reproducibility for each calibrator from their nominal values together with the quality controls then, I would place more emphasis on this than the r2 value.
Regards
John.
Dr. J. Odontiadis (MRACI CChem., Ph.D., M.Phil., Dip. App. Chem).
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FDA 2001 Guidance on Bioanalytical Method Validation, EMEA is essentially the same, perhaps more detail.
[This
http://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/UCM070107.pdf
- db]
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