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Dear members,
What criteria is used to formulate the basis in weighting of data
(none, x, I/x, log x, 1/y, etc) in a standard curve for an analytical
method? Accepted that "Weighting is not done to improve the fit of the
data".
One of my colleague is trying to validate an plasma HPLC method for
a compound using internal standard. Concentrations are linear for standard
curve over the range 10-1000 ng/ml (deviation >15%) when a weighting of 1/x
is used for peak response. If no weighting is used the lower two
concentrations have more than 20% deviation from the expected concentration.
His question is does this use of 1/x is valid?
Thanks for your cooperation.
Delwar
M. Delwar Hussain, Ph.D.
Associate Professor
School of Pharmacy
University of Wyoming
Laramie, WY 82071-3375
Tel: 307 766 6129
Fax: 307 766 2953
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[A few replies - db]
=46rom: olaf.kuhlmann.-a-.medizin.uni-halle.de
Comments: Authenticated sender is
To: PharmPK.-a-.boomer.org
Date: Wed, 3 May 2000 09:19:05 +0000
Subject: Re: PharmPK
Priority: normal
No.
The linear range of a chromatographic detector represents the range
of concentrations or mass flows of a substance in the mobile phase at
the detector over which the sensitivity of the detector is constant
within a specified variation, usually +/- 5%.
The best way to present detector linear range is the Linearity Plot
plotting detector sensitivity against amount injected, concentration
or mass flow-rate. The upper limit of linearity can be graphically
established as the amount, concentration, or mass-flow-rate at which
the deviation exceeds the specified value (+/- x% window around the
plot). The lower limit linearity is always the minimum detectable
amount determined separately for the same compound.
See: ChromBook2; 2nd edition from MERCK, page 381-382.
Hope this helps.
Kuhlmann
Dr.rer.nat. Olaf Kuhlmann (Dipl.-Biol.)
Martin-Luther-Universitaet Halle-Wittenberg
Medizinische Fakultaet
Institut fuer Pharmakologie und Toxikologie
Sektion Pharmakokinetik
Magdeburger Str. 4
06097 Halle/Germany
Tel.: 0345-5574091
=46AX : 0345-5571835
E-mail: olaf.kuhlmann.-a-.medizin.uni-halle.de
Webpage: http://www.medizin.uni-halle.de/pharmakin/Kuhlmann.htm
---
=46rom: "Leon Aarons"
To: PharmPK.at.boomer.org
Date: Wed, 3 May 2000 09:43:55 GMT
Subject: Re: PharmPK Weighting
Priority: normal
Delwar
There is a lot in the analytical literature on this topic and you
should start there rather than the pk/statistical literature. An
excellent early reference is Garden et al. 'Nonconstant variance
regression techniques for calibration-curve-based analysis',
Anal.Chem. 52: 2310-2315 (1980)
Leon Aarons
School of Pharmacy and Pharmaceutical Sciences
University of Manchester
Manchester, M13 9PL, U.K.
tel +44-161-275-2357
fax +44-161-275-2396
email l.aarons.aaa.man.ac.uk
---
Date: Wed, 03 May 2000 08:32:31 -0400
=46rom: "Ed O'Connor"
Reply-To: efoconnor.aaa.snet.net
Organization: PM PHARMA
X-Accept-Language: en
To: PharmPK.at.boomer.org
Subject: Re: PharmPK Weighting
weighting usually reduces the overall fit, that is the pearon is reduced wit=
h
increased weighting. The difference from expected (DFE) or error is=20
reduced for
the points at the lower end of the curve. Error may increase at the upper e=
nd.
Generally for most bioanalytical assays, an error of 20% is the=20
tolerance at the
lower end and 15% for the middle and upper. These are general and may be
broadened. Again, as you increase weighting you reduce the bias from the up=
per
points, reduce the r and decrease the error (at the lower end) you=20
must balance
the effects against the accepatnce criteria of your assay-- the limits on er=
ror
and the r value.
---
=46rom: "Ossig, Dr. Joachim"
To: "'PharmPK.aaa.boomer.org'"
Subject: AW: PharmPK Weighting
Date: Wed, 3 May 2000 15:00:54 +0200
Dear Delwar (and others)
what do you think about this justification for weighting:
Linear regression is calculated by minimizing the square of the absolute
deviations from the fitting line.
Let us think about an theoretical experiment with the following result: All
calibration standards perfectly fit, except the lowest, which deviates 1% in
one direction and the highest, which deviates 1% in the opposite direction.
The unweighted linear regression line would lead to deviations of the
recalculated values from about 8% at 10 ng/ml to about 1% at the upper end
of the calibration range.
weight factor: 1/y^0
meas. spiked calc. rel. Deviation
=20 10.1 10.0 9.2 -8.25
=20 15.6 15.6 14.8 -5.60
=20 31.3 31.3 30.5 -2.35
=20 62.5 62.5 62.1 -0.72
125.0 125.0 125.1 0.10
250.0 250.0 251.3 0.50
500.0 500.0 503.5 0.71
990.0 1000.0 998.0 -0.20
Parameters of curve: A (calc.) =3D(meas. - 1.00782)/0.99099
Using 1/y weighting, the relative deviations in this example would be
between -0.8% and +0.6%:
weight factor: 1/y^1
meas. spiked calc. rel. Deviation
=20 10.1 10.0 10.0 -0.47
=20 15.6 15.6 15.5 -0.73
=20 31.3 31.3 31.2 -0.07
=20 62.5 62.5 62.7 0.25
125.0 125.0 125.5 0.42
250.0 250.0 251.3 0.50
500.0 500.0 502.7 0.54
990.0 1000.0 995.6 -0.44
Parameters of curve: A (calc.) =3D(meas. - 0.20466)/0.99419
Therefore, I would agree to use 1/y weighting in bioanalytical work, since
otherwise the data of the upper calibration range imho are overweighed.
Dr. Joachim Ossig Tel.: +49-(0)241-569-2409
Gr=FCnenthal GmbH Fax.: +49-(0)241-569-2501
Department of Pharmacokinetics (FE-PK)
Zieglerstr. 6 Mailto:
Joachim.Ossig.-a-.grunenthal.de
52078 Aachen, Germany
---
Date: Wed, 03 May 2000 08:14:43 -0700
=46rom: "David Nix, Pharm D."
Organization: College of Pharmacy
To: PharmPK.-a-.boomer.org
Subject: Re: PharmPK Weighting
=46or analytical purposes, I routinely have used 1/x^2 weighting.
Weighted based on the theoretical concentration is fairly well accepted
in the analytical field, although one could argue that weigting based on
the predicted concentration (e.g. 1/y^2) is more statistically valid.
Given the typical variability patterns for most analytical techniques,
some weighted is necessary, expecially if the standard curve range is
large (i.e. more than 1 log 10 range). 1/x^2 or 1/y^2 most closely
approaches having residuals that are normally distributed with constant
CV% over the full concentration range.
The only problem with using 1/x^2 or 1/y^2 appears when the standard
curve is being carried down to low. If the lowest standard is
associated with very poor precision, then weighting 1/x^2 or 1/y^2
places too much weight on this low concentration. This is not likely to
be a major problem as long as the CV% for the lowest standard
concentration is less than 15%.
---
=46rom: "Melethil, Srikumaran K."
To: "'PharmPK.-a-.boomer.org'"
Subject: RE: PharmPK Weighting
Date: Wed, 3 May 2000 13:18:15 -0500
Dear Delwar,
Often, I have seen weighting done to improve fit. So, it is good to hear you=
r
motive.
Weighting in principle should be based on expected error (variance)=20
of the assay
at the desired concentration. An old (classic paper?) by Boxenbaum et al (J=
PB
1973 I think) discusses this issue. A statistics text by Draper and Smith al=
so
addresses this issue.
Srikumaran Melethil, Ph.D.
Professor of Pharmaceutics and Medicine
University of Missouri-KC
203 B Katz Hall, School of Pharmacy
5005 Rockhill Road
Kansas City, MO 64110
816-235-1794 (voice); 816-235-5190 (fax)
---
Date: Wed, 03 May 2000 14:39:58 -0400
=46rom: "Ed O'Connor"
Reply-To: efoconnor.aaa.snet.net
Organization: PM PHARMA
X-Accept-Language: en
To: PharmPK.-at-.boomer.org
Subject: Re: PharmPK Weighting
expanding on my earlier response. 1. the LOD should be determined=20
first. 2.
then run the curve in triplicate using uniques standards. 3 Check the aver=
age
LOD and adjust the ELOQ as needed. 4. Now examine the curve. The native er=
ror
will be biased towards the high end. The larger the intended dynamic range =
of
the curve the larger the error at the low points. Conversely, the r value g=
ets
better and better. Now examine the effect of weighting on the error and r
values. As the weight increases, the error at the low end should=20
decrease but r
will also decrease. Possibly to an unusable point. Some assays, particula=
rly
where SPE, derivatization or immunoaffinity is involved may not be linear bu=
t
may infact require a quadratic or other equation to develop a usuable
concentration response curve and may still require weighting.
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[Two replies - db]
From: "Stephen Duffull"
To:
Subject: RE: PharmPK Re: Weighting
Date: Thu, 4 May 2000 15:14:03 +1000
X-Priority: 3 (Normal)
Importance: Normal
Why would you want to compute the limit of quantitation?
Regards
Steve
=================
Stephen Duffull
School of Pharmacy
University of Queensland
Brisbane, QLD 4072
Australia
Ph +61 7 3365 8808
Fax +61 7 3365 1688
---
X-Sender: jelliffe.-at-.hsc.usc.edu
Date: Thu, 04 May 2000 15:20:15 -0700
To: PharmPK.at.boomer.org
From: Roger Jelliffe
Subject: Re: PharmPK Weighting
Dear Dr. Hussein:
Why not determine the assay standard deviation (SD) at
several points over
its working range? Why not weight each data point by its easily known
credibility (its Fisher Information, the reciprocal of the variance of each
data point), and then distribute the other errors as intraindividual
variability? Then you know what fraction of the overall intraindividual
variability is due to the assay, for example. Many people simply assume
that assay error is a small fraction of the overall error. In our
experience, doing it our way, assay error may range from something less
than 1/4 to more than 1/2 the total error, and then you KNOW this. We
really suggest is it very useful, and more optimal, to start with the known
assay error, to use a parametric method such as the iterative Bayesian 2
stage (IT2B) population modeling program in the USC*PACK collection, find
gamma, the rest of the error, and then go to a nonparametric program such
as NPEM to get the full parameter joint density. Below is an earlier
version of this discussion as well. The basic point is - why bother to make
assumptions about the assay error? Why not simply determine it and be done
with it? Then find the remaining noise in the intraindividual variability.
It really boosts comfidence in a study if you find a low gamma, for
instance, showing that the remaining error beyond the assay is relatively
small. The converse is also useful to know.
Best regards,
Roger Jelliffe
Dear Colleagues:
I don't understand all this discussion of how to weight the data,
whether
it is better to weight by 1/y^2 or by doing the log transformation, for
example. Why not skip all thiese assumptions and simply calibrate the assay
over its working range, and then fit the relationship between the
concentration and the SD with a polynomial so one can have a good estimate
of the SD with which each single level is measured, so one can then fit
according to the Fisher information of each concentration, namely the
reciprocal of the variance of each data point? The problem is that the
coefficient of variation is hardly ever constant, and the SD needs to be
known over its entire working range.
If one uses the log transformation, for example, a concentation of 10
units has only 1/100 the weight (Fisher info) of a concentration of 1 unit,
and only 1/10,000 the weight of a concentration of 0.1 units. Is this
realistic? I don't think so. I really don't understand all this discussion
about a point that can be easily answered simply by calibrating each assay,
by determining its error pattern over its working range. This point is
discussed more fully in Therapeutic Drug Monitoring 15: 380-393, 1993.
Of course there are other errors than just the assay. There are those
associated with errors in preparing and giving each dose, and in recording
the times when the doses were given, and with recording the times when the
serum samples were drawn. What sense does it make to assume that all of
these these are also part of the measurement noise, and then to use the log
transformation or 1/y^2 as the description of them? Most of them are
actually part of the process noise, not the measurement noise. But whatever
is done, why not start by knowing what the assay errors actually are?
Sincerely,
Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine, USC
USC Laboratory of Applied Pharmacokinetics
2250 Alcazar St, Los Angeles CA 90033, USA
Phone (323)442-1300, fax (323)442-1302, email= jelliffe.at.hsc.usc.edu
Our web site= http://www.usc.edu/hsc/lab_apk
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Dear Steve:
I don't understand your question. When you are doing PK work, and have
information about the times at which doses were given and serum
concentrations (or other responses)were obtained, then you know the drug is
present, and your only concern is how much drug is present. If you
determine the assay error over its working range, down to and including the
blank (which is needed to determine the lower limit of detection for
toxicological work) then you can give correct weight to each measurement,
even down to and including the blank. Am I missing something? Can you
expand on your question?
Best regards,
Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine, USC
USC Laboratory of Applied Pharmacokinetics
2250 Alcazar St, Los Angeles CA 90033, USA
Phone (323)442-1300, fax (323)442-1302, email= jelliffe.-at-.hsc.usc.edu
Our web site= http://www.usc.edu/hsc/lab_apk
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