- On 13 Feb 2003 at 10:26:28, "Suresh.B.L." (suresh_bl1.at.rediffmail.com) sent the message

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The following message was posted to: PharmPK

Dear all,

I am using a calibration curve of very huge range(approx. 30 fold

difference when compared to my lowest and highest conc.) for the

estimation of conc. in pk studies (in order to pick the conc. for

all the time points). I am using around 10 stds.

If i construct a calibration curve (conc. vs area), r2=0.99 and

more but the intercept will be very high, so if i use this

equation to back calculate the conc. at lower stds it is way off

(more than 15-20% deviation from the actual conc.)but at higher

conc. it is good.

My question is can i break this CC of 10 stds into 2 parts so that

i have one CC from 1st-6th std, and another from 5th-10th std. Is

it acceptable? Using these 2 CC equations, can i calculate the

conc. of the drug in plasma study samples.

OR

Converting these conc. and area into log values (since it is a

huge range) and plotting LogConc. Vs Log area, and back calculate

the conc. using this regression equn. and then take antilog of

these values. By this at lower conc. there is lot more

improvement. So same way using this regression requ. calculate the

conc. in the plasma study samples and take antilog of these

values. Is this acceptable?

I am not changing any values but only that i am converting the no.

into log values and then using simple regression equation.

Is there any literature/publication regarding this?

Thanks in advance for your inputs,

Regards,

B.L.Suresh

[Maybe a lower power polynomial would work, i.e. adding a square term -

db] - On 13 Feb 2003 at 10:09:05, "Chen, Takung" (tchen.at.neurocrine.com) sent the message

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The following message was posted to: PharmPK

You may have more than one issue here. Regarding to the calibration

curve

supporting PK and TK studies, my understanding is that one method can

have

only ONE mathematical model. This means one curve per quantitation

range.

Two different models covering different part of the same concentration

range

are not acceptable due to 2 different concentrations may resulted from

the

same response. I would suggest to validate the method using a model

fit for

the lower part of concentration ranges and dilute the high concentration

samples down to the quantitation range. Of course, the dilution process

needed to be validated.

The 30 fold range is not uncommon. In my lab, LC-MS/MS method normally

provide a quantitation range of 3 order of magnitudes and ELISA methods

can

provide a quantitation range of at least 2 order of magnitudes. High

interception normally indicates interference (high background) or lack

of

sensitivity. If problem can't be fixed by putting more weights at the

lower

end of the calibration curve, you may want to find a way to clean up

sample

more or adjust your LLOQ up.

Ta Kung Chen, Ph.D.

Associate Director, Bioanalytical Chemistry

Neurocrine Biosciences, Inc.

10555 Science Center Dr.

San Diego, CA 92121, USA

tele: 858 658-7726, fax: 858 320-7830 - On 14 Feb 2003 at 07:15:32, Nick Holford (n.holford.at.auckland.ac.nz) sent the message

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The following message was posted to: PharmPK

Suresh,

The problem you have is caused by using ordinary least squares linear

regression (OLS). OLS assumes that the residual error in your observed

area at every concentration is similar.

I am sure you are familiar with the idea that assays have a residual

error and that this is commonly described as being proportional to the

concentration e.g. assay imprecision will be said to have say a 10% CV.

If you study the SD of replicate samples at different concentrations

you can empirically determine how the residual error varies with

concentration.

This empirical residual error can then be used to correctly assign

appropriate weights to the area you measure at each concentration when

you do the linear regression. You will need linear regression software

that allows weighted least squares regression. Most PK modelling

packages e.g. WinNonLin, will let you do this.

When you now fit your calibration curve with a linear model and using

1/(SD*SD) as the weight for each observation then you should find a

much better fit without the large intercept you got with ordinary least

squares.

This is a very old problem and a helpful solution with application to

PK modelling is described here:

Peck CC, Sheiner LB, Nichols AI. The problem of choosing weights in

nonlinear regression analysis of pharmacokinetic data. Drug Metabolism

Reviews 1984;15(1 & 2):133-148.

A web search for "weighted least squares" will bring up many on line

pages with further discussion of the problem and solutions.

e.g. http://www.itl.nist.gov/div898/handbook/pmd/section4/pmd432.htm

Nick

Nick Holford, Divn 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 13 Feb 2003 at 14:27:55, RPop.-at-.pharmamedica.com sent the message
Hi Suresh B.L.,

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I assume you are using a linear equation to fit the experimental data

for your calibration curve.

From the large y-intercept mentioned by you and the lack of precision

in the lower part of the calibration curve I suspect your experimental

data are better fitted with a quadratic and not a linear equation. It

is possible that even an exponential equation will be better, even thus

your attempt to log-transform the data did not work very well.

Therefore, before partitioning the calibration range in two or three

linear sections try to use a quadratic equation to fit the experimental

data.

Let me know how it works.

radu

Radu D. Pop

Director Biopharmaceutics

Pharma Medica Research Inc.

966 Pantera Drive

Mississauga, Ontario

Canada, L4W 2S1 - On 13 Feb 2003 at 14:31:33, Mohsen Hedaya (mhedaya.aaa.e-pharmacokinetics.com) sent the message

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The following message was posted to: PharmPK

Suresh,

1- The weighted linear regression method suggested by

professor Nick Holford can solve this problem and

improves that unknown concentration prediction by the

CC.

2- Another approach that we used to construct

calibration curves that cover wide range of

concentrations (>50 fold), was to use two different

internal standards (IS). One IS was added in small

quantities and the other IS was added in larger

quantities. The two IS were used to construct two

different calibration curves.

For example the first internal standard (small

quantity) was used with the lower five standards to

construct a CC and this curve was used to predict the

unknown samples in the lower concentration range. The

second IS and the higher five standards were used to

construct a second CC that was used to predict the

unknown samples in the higher concentration range.

regards

Mohsen Hedaya, Pharm.D., Ph.D.

College of Pharmacy

Tanta University

Tanta - Egypt

Phone: +20 10 176 8641 +20 40 333 1779

Fax: +20 40 334 8643 e.mail: mhedaya.at.e-pharmacokinetics.com

Web site: www.e-pharmacokinetics.com - On 14 Feb 2003 at 09:20:14, "Bruce Charles" (Bruce.aaa.pharmacy.uq.edu.au) sent the message

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The following message was posted to: PharmPK

The common least squares algorithm minimizes the sums of squares of the

deviations between observed and predicted pts and since this is a

variance-like term bigger C values therefore have more "influence"

during fitting of the line and thus the parameters (especially the

Y-intercept in a linear model) reflect this resulting in the lowest QCs

often being wildly "inaccurate".

Try a weighting scheme (e.g. 1/(C**2) to give more "influence" at the

lower end of the calibration pts.

Cheers,

BC

Bruce CHARLES, PhD

Associate Professor and Director

Australian Centre for Paediatric Pharmacokinetics

School of Pharmacy, The University of Queensland

QLD 4072 Australia

[University Provider Number: 00025B]

TEL: +61 7 336 53194

FAX: +61 7 336 51688

MOB: 0403 0222 5 2

http://www.uq.edu.au/pharmacy/charles.html

http://www.mater.org.au/pharm/acpp/index.htm

B.Charles.aaa.pharmacy.uq.edu.au - On 14 Feb 2003 at 09:30:53, James Hillis (JHillis.-at-.hfl.co.uk) sent the message

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The following message was posted to: PharmPK

Suresh, The previous answers posted to the group give you good advice

regarding your problem. A concentration range of 30fold is not a great

one.

Are you using an internal standard. If not, can I recommend that you

do.

For MS an isotopically labelled analogue of the analyte works the best.

You

should not use two split calibration lines as you will have two

different

equations for the line and therefore are implying two different

relationships. A non linear model may be more appropriate. However,

You

need to be careful if the bottom end of your line is out due to the line

flattening out at the top end, there may be a problem.

1. You need to know that the detector that you are using is not

saturated at

the highest concentration you are using.

2. Curving in MS analysis can be caused by the formation of dimers and

trimers. In this case you need to look at 2M+1 and 3M+1.

3. The signal to noise ratio at for the bottom point on your curve has

to

be better than 3 and should ideally be better than 10.

4. If you do decide to do a transformation of the data, use a non linear

regression or weight the data, you should try several methods on one

dataset

and choose the simplest transformation/regression/weighting that

minimises

your %REs about the line.

You should also note that from the Shah guidelines for bioanalytical

method

validation ('Bioanalytical Method Validation - A Revisit with a Decade

of

Progress' reported by V P Shah et al (2000), Pharm. Res., Vol. 17,

No.12,

1551-1557.) that a %RE at the LLOQ of 20% is acceptable.

I hope that this helps. Please contact me if you want further

information or

references

James Hillis BSc. AMRSC

jhillis.aaa.hfl.co.uk - On 14 Feb 2003 at 10:07:50, eoconnor.at.Therimmune.com sent the message

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Suresh: Are you using ligand binding or instrumental? If the first,

use 4 parameter curve fit-r values have little value, if instrumental

latter use the simplest that will fit the data. Try 1/y or 1/y2. In

linear regression the r will fall off as you increase weighting. You

cannot really rely on the r value over such a range but rather should

use the actual back fit values. Quadratics are ok but you must

recognize that at some concentration, an absorbance be fitted to two

concentrations. - On 18 Feb 2003 at 11:14:35, =?ISO-8859-9?Q?"=DDlbeyi_A=F0abeyo=F0lu"?= (ilbeyi.aaa.tr.net) sent the message

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The following message was posted to: PharmPK

Dear Suresh,

I further support Prof. Holford's suggestions:

In our work, we have similar problems. In addition to linear regression

CC, we also try the following equations:

A = aC^2 + bC + d

and

ln A = a'(ln C)^2 + b'(ln C) + d'

th C's being the conc., and A's being the absorbances or peak heights or

peak height ratios. These are calculated with the algorithm of least

squares parabola. Further improvements might be made with nonlinear

regression. 1/y^2 weghting is probably the best choice.

Furthermore we also try the inverse of these equations, i.e. Exchange

A's and C's. Then we look for the best fit. r or r2's are not very

appropriate.

Sum of squared and weighted deviations are better. Akaie Information

Criteria might also be used.

FDA accepts such curve fitting, provided solid reasons are given.

Best wishes,

lbeyi Aabeyolu, ilbeyi.-a-.tr.net

Dept.Pharmaceutical Technology,

Faculty of Pharmacy,

Gazi University,

Ankara,Turkey.

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