- On 2 Jul 2003 at 09:43:23, Daniel Rossi de Campos (Daniel.Campos.-at-.anvisa.gov.br) sent the message

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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 - On 2 Jul 2003 at 10:41:29, Boy China (boychina00.aaa.yahoo.com) sent the message

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Daniel,

We are using gel permeation chromatography for the

determination of molecular weight of polysaccharides.

The Millennium software can do the polynomial

regression. - On 2 Jul 2003 at 13:36:03, Roger Jelliffe (jelliffe.-at-.usc.edu) sent the message

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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 - On 3 Jul 2003 at 07:16:14, jose-antonio.allue.-a-.ipsen.com sent the message

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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 - On 3 Jul 2003 at 10:50:52, Bob Leary (leary.-at-.sdsc.edu) sent the message

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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 - On 4 Jul 2003 at 09:50:14, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message

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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/ - On 5 Jul 2003 at 10:40:03, "Sima Sadray" (sadrai.at.sina.tums.ac.ir) sent the message

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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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