- On 14 Mar 2003 at 10:19:45, Jennifer Norman (jnorman.at.uctgsh1.uct.ac.za) sent the message

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Hi,

What would the scientific reason be for a weighted curve (1/y*y using

weighted least squares) being the best fit for certain assay

calibration curves and not others? Both assays are HPLC-based, the one

using UV detection and the other MS.

Thanks.

Jennifer Norman

Division of Pharmacology

University of Cape Town - On 14 Mar 2003 at 14:42:07, Daniel Rossi de Campos (Daniel.Campos.at.anvisa.gov.br) sent the message

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Jennifer,

Weighted least squares regression should be used when the error term

variance is not constant for all observations.

In HPLC methods, low concentration has high variance and high

concentration

has low variance.

In Chromatographic methods the calibrations curves are generally

evaluated

by ordinary linear (unweight) regression. This technique might be less

accurate in the LOWER part of calibration curve, because the regression

equation to a great extent curve is determined by values in the high

concentration range.

A consequence of this is that when the concentration of the standards

are

back calculated using the standard line parameters (y=ax+b) there may

be a

large discrepancies between the actual concentrations and the back

calculated concentrations, particularly at the LOWEST concentrations.

So, the problem may be overcome in a number of ways. One method is to

use

weighted regression (1/x;1/x2;1/Y or 1/y2)

I hope this help,

Daniel Rossi de Campos

Technical Consultant of BE - Brazil - On 17 Mar 2003 at 09:57:21, Kasiram Katneni (kasiram.katneni.-at-.vcp.monash.edu) sent the message

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Dear Daniel,

Your explanation on use of weighted calibration curves is very nice. In

the

end you said one can use weighted regression (1/x;1/x2;1/Y or 1/y2) for

not

so linear curves to have a more appropriate values. But, my doubt is

when to

use what, i.e., are there any criteria to chose the exact term.

To be more detailed, commonly the non linearity in the calibration curve

could be due to poor extraction (sometimes combined with interference)

and/or signal saturation. Generaly, the former affects the lower range

of

curve and the later affects the higher range. My question is which

weighting

term to use when.

Thanks in advance,

Kasiram Katneni.

PhD student,

Victorian College of Pharmacy

Monash University, Australia. - On 17 Mar 2003 at 09:05:06, "Hans Proost" (j.h.proost.-at-.farm.rug.nl) sent the message

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Dear Daniel and Karisam,

Two short comments on your notes on weighted calibration curves:

Daniel wrote:

> Weighted least squares regression should be used when the error

> term variance is not constant for all observations.

This is correct.

> In HPLC methods, low concentration has high variance and

> high concentration has low variance.

No, low concentrations will show low variance and high variance will

show

high variance. Perhaps you mean that the coefficient of variation at low

concentrations is generally higher than for high concentrations.

However, if

this difference is really relevant (say, more than a factor 2 or so),

the

LOQ may be chosen too low.

A weighting scheme should be chosen to correct for the differences in

variance of low and high concentrations. The conclusion that weighted

regresssion analysis should be applied is correct!

Karisam wrote:

> To be more detailed, commonly the non linearity in the calibration

> curve

> could be due to poor extraction (sometimes combined with interference)

> and/or signal saturation.

IMHO, this is a completely different topic. Nonlinearity of calibration

curves has nothing to do with differences in variance at low and high

concentration, and weighting is definitely not the solution to this

problem.

In this case the mathematical relationship between signal and

concentration

should be adapted from a linear to a more complex relationship.

In some cases, however, both problems (and even a third, see below) can

be

solved satisfactorily by a single technique. Sometimes the nonlinearity

of

the calibration curve can be treated by a logarithmic transformation.

Instead of a calibration curve

RR = a + b . X

where RR is the response ratio (signal) and X is the amount of analyte

in

the calibration sample, use the following equation:

RR = a . X^b

or after logarithmic transformation at both sides:

log RR = log a + b . log X

representing a straight line.

This transformation can be used as an alternative if the curve of log RR

versus log X is reasonably close to a straight line.

The logarithmic transformation has been described and applied in our

paper:

Kleef UW, Proost JH, Roggeveld J, Wierda JMKH. Determination of

rocuronium

and its putative metabolites in body fluids and tissue homogenates. J

Chromatogr 1993;621:65-76.

If the coefficient of variation at low and high concentrations is

broadly

the same, the logarithmic transformation results in equal variances

over the

entire concentration range, thus complying to the requirement for linear

regression and circumventing the problem of weighting.

The logarithmic transformation may also solve another problem. Linear

regression analysis is valid only if the X-values are (broadly) equally

spaced on the X-axis. A calibration curve of equally spaced

concentrations

is not the most efficient way in HPLC analysis (unless the concentration

range is rather narrow). If the distance between concentrations is

gradually

increasing with concentration (much more efficient), the logarithmic

transformation results in broadly equally spaced log X values, thus

complying to the requirement of linear regression.

Any comment to my view is welcomed.

Hans Proost

Johannes H. Proost

Dept. of Pharmacokinetics and Drug Delivery

University Centre for Pharmacy

Antonius Deusinglaan 1

9713 AV Groningen, The Netherlands

tel. 31-50 363 3292

fax 31-50 363 3247

Email: j.h.proost.-at-.farm.rug.nl - On 17 Mar 2003 at 10:41:07, "Ossig, Dr. Joachim" (Joachim.Ossig.-at-.grunenthal.de) sent the message

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Hi Jennifer,

Look for the article "Linear regression for calibration lines revisited:

weighting schemes for bioanalytical methods" of A.M. Almeida, M.M.

Castel-Branco, A.C. Falcao in J. Chromatogr. B, 774 (2002) 215.

They made it easy to justify the weighting and the decision between

weigting

factors 1, x^0.5, y^0.5, x, y, x^2 and y^2.

Joachim

Joachim Ossig, PhD

Grünenthal GmbH

Department of Pharmacokinetics (FO-PK)

52099 Aachen, Germany

Office: Zieglerstr. 6, 52078 Aachen, Germany

Tel.: +49-(0)241-569-2409

Fax.: +49-(0)241-569-2501

Mailto:Joachim.Ossig.aaa.grunenthal.de

http://www.grunenthal.com - On 17 Mar 2003 at 08:19:39, Daniel Rossi de Campos (Daniel.Campos.-a-.anvisa.gov.br) sent the message

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Kasiram,

Generally, we use the weighted LINEAR regression (1/x2). This is the

"true"

weighted regression because x2 is the variance. 1/x is an alternative

but it

do not improve your results more than ordinary regression.

Regards

Daniel - On 17 Mar 2003 at 11:06:48, eoconnor.-a-.Therimmune.com sent the message

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Generally if the curve range is large, if there is large error at the

low end, try 1/y then 1/y2, these are the most appropriate, since they

weight the response. You will alos have to exxamine the coefficeint of

determination since that will get weaker as you weight the data. If

the proble is at the high end you may need to weight using the log. - On 17 Mar 2003 at 17:33:39, "J.M.Lanao" (jmlanao.at.usal.es) sent the message

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Dear Karisam

The appropriate election of the weighting term depends on the variance

model of your analytical technique. A simplified linear variance model

as var = a.C determines a weighting term of 1/C. However a potential

variance model var = a.Cb determines a weighting term of 1/Cb. When

the analytical technique as a constant variation coefficient this

implies that b=2 and then a weighting term of 1/C2 may be used.

Dr. J.M. Lanao

Dpt. Pharmacy and Pharmaceutical Technology

University of Salamanca

Spain - On 20 Mar 2003 at 09:26:57, Nick Holford (n.holford.at.auckland.ac.nz) sent the message

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May I suggest that the following classical paper be consulted as an

alternative to the range of ad hoc weighting suggestions that have been

made. It proposes a method for a more general model for the residual

error variance and allows model selection based on the use of the

extended least squares objective function.

Peck CC, Beal SL, Sheiner LB, Nichols AI. Extended least squares

nonlinear regression: A possible solution to the "choice of weights"

problem in analysis of individual pharmacokinetic parameters. Journal

of Pharmacokinetics and Biopharmaceutics 1984;12(5):545-57.

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New

Zealand

email:n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556

http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ - On 20 Jun 2003 at 10:35:44, "Jennifer Norman" (jnorman.aaa.uctgsh1.uct.ac.za) sent the message

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Dear All,

I need a step by step procedure for performing weighted least squares

regression using WinNonlin ver 3.3, using the preselected weighting

scheme 1/Y*Y

Thanks very much.

Jennifer Norman

Quality Assurance

Division of Pharmacology

University of Cape Town

Tel. +27 (0)21 406 6498

Fax. +27 (0)21 448 1989

[Another 10-12 messages in the queue to send out but I might let this

group go out first - db]

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