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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]
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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
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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/
Hi Suresh B.L.,Back to the Top
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
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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
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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
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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
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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.
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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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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)