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The following message was posted to: PharmPK
Dear All,
Could anyone provide me some technical explanation about use of
polynomial
regression (ax2+bx+c)in calibration curves for chromatographic methods
(specially HPLC).
Regards,
Mr Rossi
Brazil
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The following message was posted to: PharmPK
Daniel,
We are using gel permeation chromatography for the
determination of molecular weight of polysaccharides.
The Millennium software can do the polynomial
regression.
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Dear Mr. Rossi:
You might look at the general issue of assay error calibration
and application in
Jelliffe RW, Schumitzky A, Van Guilder M, Liu M, Hu L, Maire P,
Gomis P, Barbaut X, and Tahani B: Individualizing Drug Dosage Regimens:
Roles of Population Pharmacokinetic and Dynamic Models, Bayesian
Fitting, and Adaptive Control. Therapeutic Drug Monitoring, 15:
380-393, 1993.
The real issue is not just in making an assay become acceptably
precise, but in using the specific SD for each observation to fit each
data point by a good index of its credibility - its Fisher information.
You will see also that for PK work, there is im fact no lower limit of
quantification.
Very best regards,
Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine,
Division of Geriatric Medicine,
Laboratory of Applied Pharmacokinetics,
USC Keck School of Medicine
2250 Alcazar St, Los Angeles CA 90033, USA
Phone (323)442-1300, fax (323)442-1302, email= jelliffe.at.usc.edu
Our web site= http://www.lapk.org
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The following message was posted to: PharmPK
Dear Daniel,
The use of a quadratic fit is quite usual in bioanalysis. There can be
several reasons for its use, i.e. non-constant recovery of your analyte,
non-linearity of the detector response, use of stable isotope labeled
internal standard with less than 3 mass units difference with respect
to
the analyte of interest (in LC-MS or LC-MS/MS) which can lead to
significant isotopic contribution, etc....
From my point of view, there is no problem in using polynomial
equations,
they can be solved easily using linear regression. We must use the
simplest
model that describes better the experimental data, and many times you
may
need a more "complicated" model than a straight line.
Hope this helps
José Antonio Allué
Mass Spectrometry Laboratory
Metabolism & Pharmacokinetics Service
Research & Development Department
IPSEN-PHARMA S.A. Laboratories
Ctra. Laureà Miró 395
Sant Feliu de Llobregat, Barcelona, Spain
Telf.: 936858100
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The following message was posted to: PharmPK
There's one caveat - it is important not to extrapolate the
assay error polynomial,
particularly if it contains quadratic or higher order terms, into
regions well outside of the data that were used to fit the polynomial.
Otherwise, for example, in regression models fitting PK parameters to
data, values of the PK parameters that result in absurd predictions can
be
offset by even more absurd CVs computed from the assay error polynomial,
giving the absurd predictions an unreasonably high likelihood.
(from someone who has fallen into this trap).
Bob Leary
Senior Staff Scientist
San Diego Supercomputer Center
858-534-5123
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The following message was posted to: PharmPK
Bob,
Bob Leary wrote:
> There's one caveat - it is important not to extrapolate the
> assay error polynomial,
> particularly if it contains quadratic or higher order terms, into
> regions well outside of the data that were used to fit the polynomial.
> Otherwise, for example, in regression models fitting PK parameters to
> data, values of the PK parameters that result in absurd predictions can
> be
> offset by even more absurd CVs computed from the assay error
> polynomial,
> giving the absurd predictions an unreasonably high likelihood.
> (from someone who has fallen into this trap).
>
Thank you for this interesting reminder of the hazards of extrapolation
when using empirical models. The example you quote (assay error
polynomials for the error associated with concentration measurements)
is probably a bit subtle in the context of the original thread which
was discussing empirical models for assay calibration curves for
prediction of the signal not the noise.
Calibration curves frequently have a theoretical basis and this should
not be discarded lightly e.g. spectrophotometer absorbance should be
linearly related to concentration, immunoassays should obey the law of
mass action and be hyperbolic. All calibration curves should predict
zero concentration when the known concentration is zero and
extrapolation to negative concentrations should never be acceptable.
If an assay system is well behaved then the parameters of the
calibration curve model should be stable and indeed this is a marker of
quality assurance which I think is more important than assertions such
as "the CV is less than 10%" (referring to replicate concentration
measurements).
If real data for a calibration curve deviates importantly from the
theoretical expectation one should be cautious about blindly accepting
an empirical model such as a polynomial. If you really feel the need
for a polynomial then you should only feel comfortable if the
polynomial parameters (aka coefficients) are stable. A CV of less than
10% for the day to day precision of the polynomial parameters might be
a more robust quality assurance target.
Does anyone know of any recommendations for assay quality based on the
stability of calibration curve parameters? [I am afraid the PharmPK
search engine seems to be broken at the moment for this topic so I
cannot see if this was mentioned earlier in this thread - fixed db].
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
email:n.holford.at.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
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The following message was posted to: PharmPK
Dear All,
Linear line regression is sometimes misleading. We proved this in this
article for methotrexate in detail.
Non-linear heteroscedastic regression model for determination of
methotrexate in human plasma by high-performance liquid chromatography,
Sadray et al.Journal of chromatography B,787(2003)293-302.
Sadray, PhD
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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)