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Hello all,
Im just wondering how others handle the situation where the
concentration range within a PK profile is very large, for example
10000-fold (0.05-500 ng/ml), due to a very sensitive assay. From the
rich data that I have it is clear that there is at least 2
compartments, 1 rapid decline and one much longer decline. The former
is more relevant for dosing the multiple dosing, while the latter is
much more "interesting" to me as a phenomenon in this case. The problem
I experience is that I have a choice:
1. "weight" the data heavily (1/y^2) which results in a poor capture of
the peak concentrations
or
2. dont "weight" the data at all and seriously under/over estimate the
terminal phase concentrations
I dont really understand the problem, as the terminal phase is very
well characterised (5+ samples) as is the initial decline. Im
performing POP-PK analysis, but have others experienced this problem
more generally, and how did you deal with it? Hope this sparks a bit
of discussion...
David Foster, PhD
Department of Clinical and Experimental Pharmacology
Faculty of Health Sciences
Adelaide University
Adelaide, South Australia 5005
Email: david.foster.-at-.adelaide.edu.au
http://www.adelaide.edu.au/Pharm/index.htm
[Do you have an estimate of the variance in the high concentration
data and the low concentration data (and in between)? This should
guide you with the choice of weight. A 'simple' 1/val^2 for all data
may not be satisfactory. You might be able to develop a variance -
concentration (v-c) relationship and use this to estimate appropriate
weights. With a good idea of the form of the v-c relationship,
extended least squares could be used - db]
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[Two replies - db]
From: Iñaki Fernández de Trocóniz
Date: Tue, 16 Apr 2002 17:21:40 +0200
To: david.aaa.boomer.org
Subject: Re: PharmPK Large concentration ranges in PK analysis
Dear David,
What about using Log transformation of your concentration data,
Best,
Iñaki
Iñki F. Trocóniz Ph. D
Farmacia y Tecnología Farmacéutica
Facultad de Farmacia
Universidad de Navarra
Pamplona 31080
Spain
e-mail: itroconiz.aaa.unav.es
---
From: "Bachman, William"
Date: Tue, 16 Apr 2002 12:19:05 -0400
To: david.-at-.boomer.org
Subject: RE: PharmPK Large concentration ranges in PK analysis
In situations where the data covers a large concentration range such as
yours, the possibility exists that different error structures may be
exhibited over the range. Often, near the limit of quantitation, the error
may be homoscedastic whereas at higher concentrations, the error may be
heteroscedastic. Some population software, such as NONMEM, allows you to
model the error structure of your data instead of apriori choosing a
weighting scheme. For example, you might code an additive plus proportional
random error model to cope with the differing error structure across the
concentration range. The data will then determine if this error model is
appropriate. (If either the additive or proportional component of the error
model predominates, the model parameter representing the non-dominant
component will go to zero and can be dropped from your model.)
William J. Bachman, Ph.D.
GloboMax LLC
7250 Parkway Dr., Suite 430
Hanover, MD 21076
bachmanw.at.globomax.com
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[Three more replies - db]
From: Joel Owen
Date: Tue, 16 Apr 2002 13:42:31 -0400
To: david.-a-.boomer.org
Subject: Re: PharmPK Large concentration ranges in PK analysis
David,
You might consider a model which treats the second phase as drug 'binding
with high affinity and to a significant extent' to a target site which has
some limited total amount. The approach is outlined in a recent article
by Mager and Jusko entitled "General Pharmacokinetic Model for Drugs
Exhibiting Target-Mediated Drug Disposition", in J. Pharmacokinetics and
Pharmacodynamics, vol 28, No. 6, December 2001. An example of this
phenomenon is the receptor binding of ACE inhibitors.
Joel S. Owen, Ph.D.
PK/PD Scientist
Cognigen Corporation
395 Youngs Road
Buffalo, NY 14221
(v) (716) 633-3463 ext. 247
(f) (716) 633-7404
(e) joel.owen.aaa.cognigencorp.com
http://www.cognigencorp.com/
---
From: Stephen Day
Date: Tue, 16 Apr 2002 14:54:05 -0400 (EDT)
To: david.-at-.boomer.org
Subject: Re: PharmPK Large concentration ranges in PK analysis
David,
I'm not sure this is relevant to your question, but
isn't is possible your data is is good (has little
error) but the model is bad?
For example, is it possible that your drug is rapidly
eliminated as parent (or unstable conjugate) in bile
or urine and is then slowly re-absorbed until the
feces (or urine) is excreted? This could give rise to
the long "terminal elimination" phase you see, and
would not fit a two compartmental model.
Steve
Stephen Day
Merck-Frosst Centre for Therapeutic Research
Kirkland, QC CANADA
---
From: Nick Holford
Date: Wed, 17 Apr 2002 07:08:56 +1200
To: david.-a-.boomer.org
Subject: Re: PharmPK Large concentration ranges in PK analysis
David,
Weighting is not a binary choice (1/y^2 or 1). If you use an extended
least squares objective function (ELS) then you can be more flexible
in modelling the residual error. Programs such as MKMODEL, ADAPT and
NONMEM offer this choice. The use of a mixed additive and
proportional error model is often helpful.
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
--
Nick Holford, Divn Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford.aaa.auckland.ac.nz
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm
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Using cste cv from untransformed data or homoscedastic assumption
using logarithmic transformation leads to similar results. Usually
logarithmic transformation is more stable but I do not think that the
fitting curves are really different.
Serge Guzy
Head of Pharmacometrics
Xoma
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Dear David:
You might consider weighting first by what you really know
about your data - the assay error pattern, especially when the
concentrations vary over such a wide range. We feel that weighting
is best done according to the relative credibility of the data
itself, for example, the Fisher information, the reciprocal of the
variance with which each data point is known.
You can start by determining the assay error pattern first by
determining a blank, low, middle, high, and very high sample covering
the working range of the assay, each in at least quadruplicate, for
example. The more samples and the more determinations per sample the
better. Then you can fit a polynomial to this relationship such that,
for example, the assay SD - A0 + A1C1+ A2C2+A3C3, where C1 is the
mean of the concentrations for each sample, C2 is C1 squared, and C3
is C1 cubed, and the A's are the coefficients. Usually only the
squared term is needed to get a pretty good relationship, but this is
much better than simply an intercept and a slope. This has been trrue
for almost all assays we have seen. This has been discussed in
Jelliffe R, Schumitzky A, Van Guilder M, Liu M, Hu L, Maire P, Gomis
P, Barbaut X, and Tahani B: Therapeutic Drug Monitoring 15: 380-393,
1993.
After this, the remaining intraindividual variability, which
we call gamma, can be estimated using a parametric population
modeling program such as the IT2B iterative Bayesian program in the
USC*PACK collection. This lets you see the relative contribution of
the assay error against the other environmental factors such as the
errors in the preparation, administration, and recording of the
doses, the errors on recording when the samples were obtained, the
model misspecification, and any unsuspected changes in the PK/PD
parameter values during the period on the data analysis.
In this way, weighting is not an art form, but is done in a
way that respects the relative contributions of the assay error and
the other sources of noise in the system. If gamma is low (2 for
example) then you can say you have a pretty clean study. If it is 10,
then there is considerably more noise in the environment. With proper
skepticism, gamma might even be a way to compare the relative
therapeutic precision in which a certain form of drug therapy is
given to a group of patients.
Very best regards,
Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine,
Laboratory of Applied Pharmacokinetics,
USC Keck School of Medicine
2250 Alcazar St, Los Angeles CA 90033, USA
email= jelliffe.aaa.hsc.usc.edu
Our web site= http://www.lapk.org
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Then by definition wouldn't the data be heteroscedastic??? How finely can
one dissect the data? It might be more appropriate to transfrom the data as
suggested rather than assemble a montage of differing fits. And if we are
basing conclusions on the assumption that drug effects are greater than
inon-drug effects would not a non-parametric regression be more
appropriate???
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Dear PharmPK guys:
When the assay SD or variance varies in some way with the
measured data, then it is said to be heteroschedastic. This is also
true after transforming to log concentration data, as it assumes a
constant assay coefficient of variation (CV). Many people have felt
that a constant percent error is OK. Transformations usually are not
as useful in our hands, as one must also transform the error models
for the data, to be correct, and this is not usually done. Usually,
that does not lead to optimal weighting by the Fisher information of
the data points, the reciprocal of the variance of each data point.
For example, consider an assay with a 10% CV. At a concentration of
10 units, the assay SD is 1 unit, the variance is also 1, and the
weight is again 1. Now, at a concentration of 20 units, the SD is 2,
the variance is 4, and the weight is 1/4. That is the problem with
assuming a constant CV rather than the Fisher information. While a
constant percent error may "look OK" intuitively on a graph of the
data, it does not correctly adjust for the concentration unless, and
only unless, that is the true situation. Only then is it really
correct. Usually there is also at least some intercept value, and
usually also there is a gentle bend upward in the relationship
between the concentration on the horizontal axis, and the assay SD on
the vertical axis.
We think one should dissect the data as finely as one can,
according to what is knowable. If there are multiple responses such
as concentrations and effects, then each response should ideally be
weighted by the reciprocal of its respective variance.
In addition, there are the other sources of uncertainty such
as the errors in preparation and administration of the doses,
recording when they were given, errors recording the times at which
the responses are obtained, the model misspecification, and any
changing parameter values during the period of the data analysis.
This remaining error can then be estimated separately from the assay
error, so you can know how much is due to the assay and how much to
the other noise in the therapeutic environment.
Very best regards,
Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine,
Laboratory of Applied Pharmacokinetics,
USC Keck School of Medicine
2250 Alcazar St, Los Angeles CA 90033, USA
email= jelliffe.at.hsc.usc.edu
Our web site= http://www.lapk.org
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Dear All
Regarding Davids data: Since the data in terminal phase and data
on validation are not available it is not easy to comment on it.
One of the most neglected aspect of bioanalytical technique is as
follows
The guidelines give in detail descrption of LOD, LOQ etc. However
there is is no test defined to judge the "power of resolution" of
method at LOQ levels.
What I mean is as follows. A method having say 50 ng/ml as LOQ is
used for analysing samples of BA study. the terminal phase samples
may show results like 60 ng/ml, 55 ng/ml and 51 ng/ml(or 90ng/ml,
75ng/ml, 60 ng/ml). This may mean that the drug has a very long
terminal half life.
On the contrary if we take into consideration the variability of
analytical techniques especially at levels near LOQ, carry over in
instruments, etc. etc. how good can we hold these results?
Should there be a criteria for deciding "power of resolution near
LOQ" of bioanalytical method?
any thoughts?
One way of confirming results can be anlyse double or triple
quantity of sample keeping reconstituion volume same. Thus amount
of drug injected into HPLC will be more than LOQ. However this
will induce another validation parameter - proving
non-interference due to 2 or 3 ml matrix.
May be mass balance studies would indicate a cut off point in such
case. But such studies can not be carried out easily and by
everyone.
Dr. Prashant Bodhe
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Prashant, I'm an analytical chemist by training and quite new to
bioanalysis. I agree with your point about the power of differentiation.
While many different parameters are well defined and understood in this
area, I feel that the graduation of response of the analytical system is not
well considered. By graduated response, I mean, can the analytical system
differentiate between eg. 1ng/ml steps. If it can only differentiate
between 10ng/ml steps, then little can be inferred from terminal values such
as 60 ng/ml, 55 ng/ml and 51 ng/ml.
There are inherent difficulties in the compound specific extraction and
analysis from complex matricies and relatively large errors are tolerated.
This weakens any inference made as to a relationship between dose and
response. Yet these relationships are inferred and used, without reference
to the large levels in uncertainty.
James Hillis
jhillis.aaa.hfl.co.uk
PharmPK Discussion List Archive Index page
Copyright 1995-2010 David W. A. Bourne (david@boomer.org)