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Hi
Would anyone in the PK group be able to briefly (or in depth, if
appropriate) give some sort of guidelines as to what are the relative
merits of modeling PK data or using non-compartmental PK analysis for
obtaining the usual PK parameters eg F, AUC, elimination rate constant(s),
accumulation, clearance etc..
A second but related question is would the answers to above query still
hold if the analyses were extended to include PK/PD.
My thanks in advance
Faruq H Noormohamed
Department of Therapeutics
Chelsea and Westminster Hospital
369 Fulham Road
LONDON
SW10 9NH
Tel +44 (0)181 746 8141
Fax +44 (0)181 746 8887
email f.noormohamed.aaa.cxwms.ac.uk
Back to the Top
The clearest "guideline" to me is that noncompartmental analysis is used
to describe PK parameters and PK modeling is used to decribe plasma (or
some other matrix) concentrations. Nevertheless, the same parameters
obtained via noncompartmental analysis can be obtained from PK modeling.
Take these examples:
1. Noncompartmental analysis gives you apparent clearance which allows
you to compute mean steady-state concentrations. When done correctly and
with appropriate assumptions, PK modeling will allow you to compute the
concentration at any time point following a dose, or multiple doses of a
drug.
2. Noncompartmental analysis will give you the Cmax of a drug. PK
modeling will give you Cmax and allow you to compute how long it will
take for concnentrations to decline to a sub-toxic (or sub-therapeutic)
threshold
Cases where noncompartmental analysis works best are when a predefined PK
hypothesis (bioequivalence, drug IX, ...) is defined and answered in a
well designed study. PK modeling can be used in these cases too, but its
complexity is often not warranted. PK modeling is very handy when
analyzing sparse data, when complicated dosing regimens are administered,
or when extrapolations (new doses, regimens, etc...) are required.
When doing PK/PD modeling, one associates concentrations with effects.
Therefore, PK modeling is usually used, even if only as a "smoothing"
function to supply plasma concentrations to the PD model.
Hope this helps.
Regards,
Jeffrey Wald, Ph.D.
_____________________________________________________________
Quintiles, Incorporated
Post Office Box 13979
Research Triangle Park, North Carolina
27709-3979
Phone 919-941-7245
Fax 919-941-0493
>============== Reply: BEGIN Original Message ==============<
PharmPK - Discussions about Pharmacokinetics
Pharmacodynamics and related topics
Hi
Would anyone in the PK group be able to briefly (or in depth, if
appropriate) give some sort of guidelines as to what are the relative
merits of modeling PK data or using non-compartmental PK analysis for
obtaining the usual PK parameters eg F, AUC, elimination rate
constant(s),
accumulation, clearance etc..
A second but related question is would the answers to above query still
hold if the analyses were extended to include PK/PD.
My thanks in advance
Faruq H Noormohamed
Department of Therapeutics
Chelsea and Westminster Hospital
369 Fulham Road
LONDON
SW10 9NH
Tel +44 (0)181 746 8141
Fax +44 (0)181 746 8887
email f.noormohamed.at.cxwms.ac.uk
>============== Reply: END Original Message ================<
Back to the Top
> Would anyone in the PK group be able to briefly (or in depth, if
> appropriate) give some sort of guidelines as to what are the relative
> merits of modeling PK data or using non-compartmental PK analysis for
> obtaining the usual PK parameters eg F, AUC, elimination rate constant(s),
> accumulation, clearance etc..
IMHO non-compartmental estimates are convenient ways of *describing* PK
expts. They have uses for those who enjoy stamp collecting and for
satisfying regulatory requirements. However, they are of limited use for
*predictive* and *explanatory* purposes. For this, a physiological/
compartmental model approach is more useful.
>
> A second but related question is would the answers to above query still
> hold if the analyses were extended to include PK/PD.
PKPD analyses seem to me illustrate very clearly the severe limitations
of the Cmax,Tmax,AUC (elementary) school of pharmacokinetics. It is only by
using a
model capable of describing the time course of drug concentrations that
any progress can be made in understanding the time course of drug effect
in vivo. I prefer physiological / compartmental models to the black box
models which rely on convolution or splines because the parameters of
the former classes of models are often closely linked to structure and
function and thus the influence of changes in say body size or blood
flow on PK and PD can be predicted.
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford.at.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html
Back to the Top
In reply to Faruq Noormohamed and Hans Bender:
I have found it fascinating that Nick Holford and I have come to such
similar positions by such different routes. I agree so strongly with Nick's
response to this inquiry, that I considered not replying so as not to use
up bandwidth with "me too."
But then I saw the post from Hans Bender regarding PK in transgenic
animals, and I thought a combined response to the two inquiries might be
useful.
I have been working with a group at the US National Heart Lung and Blood
Institute's Molecular Disease Branch on a kinetic model of lipoprotein
metabolism in human LCAT transgenic rabbits. The principal experimental
investigators are Drs. Meg Brousseau and Jeff Hoeg and the lab is guided by
Dr. Bryan Brewer. An abstract on this work will be presented at the 1997
meeting of the American Heart Association in Orlando in November.
My experience is that analysis of data from transgenic animals is
tremendously more informative in the context of a
physiological/compartmental model than it could be using noncompartmental
methods. This is because, as Nick emphasized, the parameters of a
compartmental model are explicitly associated with known or hypothesized
physiological processes. This means that a powerful constraint is available
to the modeler because he or she can point to a rate constant or a
clearance and say with conviction that *this* process should be
up-regulated in the transgenic animal because this process is mediated by
the gene product of the transgene. Such constraints make it much easier to
extract new and useful information from the available experimental data.
There may well be additional control mechanisms that lead to secondary
changes in other clearances, but it is really powerful to see if the effect
of the transgene alone is sufficient to account for the data.
Because the parameters of noncompartmental analysis are combinations of
many rate constants or clearances, they can be used efficiently to make
predictions. But they will not permit you to impose constraints such as the
one I allude to above, and they will keep you in the dark concerning the
underlying physiological mechanisms. Biologists think mechanistically, and
medicine, as Lewis Thomas has eloquently emphasized, is at its best when
based on mechanism. To build strong working relationships with these two
constituencies, mechanistic compartmental models are highly desirable. And
while Nick is entirely correct that noncompartmental parameters are all you
currently need for the FDA, there are already well-placed people in the FDA
who see the power of compartmental approaches and the prudent
pharmacokineticist should certainly consider adding this approach to his or
her professional toolbox.
Regards,
Bob
----------
Robert D. Phair, Ph.D. rphair.-a-.bioinformaticsservices.com
BioInformatics Services http://www.bioinformaticsservices.com
12114 Gatewater Drive
Rockville, MD 20854 U.S.A. Phone: 1.301.315.8114
Partnering and Outsourcing for Computational Biology
Back to the Top
I agree with Nick on the advantages and power of using physiologically
based/compartmental modeling of PK data. There is one significant reason
for the development and success of Non-Compartmental modeling of kinetic
data. As the name suggests, there is no mathematical modeling of the
data i.e. no judgements have to be made regarding the selection of the
appropriate number of physiological compartments or exponentials to fit
the data. Additionally, since the mathematical `best' fit of sum of
exponential data is based on statistical parameters such as `goodness of
fit', sum of squares, selection of optimal weighting factors, etc. this
interpretation can be subjective and kineticist dependent. I am sure
many kineticists have experienced difficulty in modeling oral data which
falls through a 3-4 log orders of magnitude--where in attempting to fit
the terminal phase, the profile around Cmax is not well fit (It is also
for this reason the FDA prefers an observed Cmax rather than a
calculated Cmax). Non-Compartmental analysis of the data allows one to
estimate most of the basic kinetic parameters for characterizing the
disposition of the drug. Granted that mechanistic interpretation of the
kinetic data is limited.
I prefer to use Non-compartmental analysis for basic kinetic
interpretations of pilot studies etc. If there is a need for further
kinetic evaluation modeling is recommended. I do not see how
Non-Compartmental estimates can be extended to PK-PD modeling since we
have not established the time-course of drug disposition. At best we can
make qualitative (non-predictive) interpretations on the kinetic and
dynamic data.
Anup Zutshi
Back to the Top
From: "Robert D. Phair, Ph.D."
To: "'PharmPK.-at-.pharm.cpb.uokhsc.edu'"
Subject: Modeling vs non-compartmental PK Analysis
Date: Tue, 16 Sep 1997 16:07:35 -0400
MIME-Version: 1.0
In reply to Anup Zutshi:
I am always surprised when people assert that no judgements have to be made
with noncompartmental approaches. It appears to me than many of the most
common noncompartmental parameters depend critically on the kineticist's
judgement as to how to extrapolate the tail of the plasma disappearance
curve to infinity. If we guess wrong or miss a slow exponential because we
didn't have data points for enough hours or days, our noncompartmental
answers are simply wrong. Moreover, they are wrong precisely because our
judgement was faulty.
We all make errors if we think that there are no assumptions and no calls
for judgement in the application of noncompartmental analysis. If PK did
not require judgement, but only required plugging into published formulas,
then the discipline of pharmacokinetics could be reduced to an algorithm.
Noncompartmental analysis has made tremendous contributions to the rational
design of therapy, but it is not magic.
The bottom line is that it's impossible to hide from insufficient data.
Noncompartmental advocates do the field of PK a disservice by pretending
that one method of analysis requires no assumptions or judgement while the
other requires both.
Regards,
Bob
----------
Robert D. Phair, Ph.D. rphair.at.bioinformaticsservices.com
BioInformatics Services http://www.bioinformaticsservices.com
12114 Gatewater Drive
Rockville, MD 20854 U.S.A. Phone: 1.301.315.8114
Partnering and Outsourcing for Computational Biology
*
X-Sender: jelliffe.-at-.hsc.usc.edu
Date: Tue, 16 Sep 1997 13:10:43 -0700
To: PharmPK.aaa.pharm.cpb.uokhsc.edu
From: Roger Jelliffe
Subject: Modeling vs non-compartmental PK Analysis
Mime-Version: 1.0
I would like to second Dr. Holford's desctiption of the strengths and
weaknesses on noncompartmental vs physiological / compartmental models. The
latter give structure to the analysis, and result in a controllable system
for which one can plan dosage regimens not just to achieve a desired goal
in a steady state situation, but which can grab a patient (if you will) in
an unsteady state and achieve a desired goal then and thereafter, until the
steady state is reached. As far as I kow, noncompartmental models are good
for writing papers, but not so good for taking care of real people in
unstable and changing clinical situations. Models having structure are
better suited for developing individualized regimens to achieve, and then
to maintain, chosen target goals.
Roger Jelliffe
************************************************
Roger W. Jelliffe, M.D.
USC Lab of Applied Pharmacokinetics
CSC 134-B, 2250 Alcazar St, Los Angeles CA 90033
Phone (213)342-1300, Fax (213)342-1302
email=jelliffe.at.hsc.usc.edu
************************************************
Take a look at our Web page for announcements of
new software and upcoming workshops and events!!
It is http://www.usc.edu/hsc/lab_apk/
************************************************
*
Mime-Version: 1.0
Date: Tue, 16 Sep 1997 17:16:30 -0700
From: Jun_Shi.-a-.berlex.com (Jun Shi)
Subject: Modeling vs non-compartmental PK Analysis
To: PharmPK.at.pharm.cpb.uokhsc.edu
PharmPK - Discussions about Pharmacokinetics
Pharmacodynamics and related topics
I agree with Nick on the advantages and power of using physiologically
based/compartmental modeling of PK data. There is one significant reason
for the development and success of Non-Compartmental modeling of kinetic
data. As the name suggests, there is no mathematical modeling of the
data i.e. no judgements have to be made regarding the selection of the
appropriate number of physiological compartments or exponentials to fit
the data. Additionally, since the mathematical `best' fit of sum of
exponential data is based on statistical parameters such as `goodness of
fit', sum of squares, selection of optimal weighting factors, etc. this
interpretation can be subjective and kineticist dependent. I am sure
many kineticists have experienced difficulty in modeling oral data which
falls through a 3-4 log orders of magnitude--where in attempting to fit
the terminal phase, the profile around Cmax is not well fit (It is also
for this reason the FDA prefers an observed Cmax rather than a
calculated Cmax). Non-Compartmental analysis of the data allows one to
estimate most of the basic kinetic parameters for characterizing the
disposition of the drug. Granted that mechanistic interpretation of the
kinetic data is limited.
I prefer to use Non-compartmental analysis for basic kinetic
interpretations of pilot studies etc. If there is a need for further
kinetic evaluation modeling is recommended. I do not see how
Non-Compartmental estimates can be extended to PK-PD modeling since we
have not established the time-course of drug disposition. At best we can
make qualitative (non-predictive) interpretations on the kinetic and
dynamic data.
Anup Zutshi
*
X-Sender: dfarrier.aaa.mail.bright.net (Unverified)
Date: Wed, 17 Sep 1997 01:28:21 -0400
To: PharmPK.-at-.pharm.cpb.uokhsc.edu
From: "David S. Farrier"
Subject: Modeling vs non-compartmental PK Analysis
Mime-Version: 1.0
Regarding Faruq Noormohamed's query and the flourish of excellent comments
that followed:
In the course of planning our pharmacokinetics analysis software, "PK
Solutions", we took a look at what parameters researchers are publishing
and what methods they favor. A survey of all the articles dealing with
pharmacokinetics appearing during the last 5 years in the Drug Metabolism
and Dispoistion and in the Journal of Pharmaceutical Sciences revealed a
>96% use of noncompartmental methods. Most papers included results derived
from both graphic (AUC, etc.) and summed exponential calculations.
Observation: you are in good company with noncompartmental methods.
A free survey of 75 noncompartmental PK equations can be downloaded from my
web site or viewed at:
http://www.bright.net/~dfarrier/equations/equations.htm
David
Dr. David S. Farrier
Summit Research Services
1374 Hillcrest Drive
Ashland, OH 44805 USA
Telephone: (419)-289-9207
E-mail: dfarrier.at.bright.net
Internet: http://www.bright.net/~dfarrier
*
Date: Wed, 17 Sep 1997 08:59:37 +0200 (MET DST)
From: Maria Durisova
To: PharmPK.-a-.pharm.cpb.uokhsc.edu
Subject: RE: modeling vs non-compartmental PK Analysis
Dear colleagues,
Our article:
Durisova, M., Dedik, L., Balan, M.:
Building a structured model of a complex pharmacokinetic
system with time delays, Bull. Math. Biol., 57, 1995,
787-808,
devoted to non-compartmental modeling, describes in
a tutorial manner a procedure for building a structured model
of a complex pharmacokinetic system on using its transfer
function. The example employed is that of the pharmacokinetic
system based on gentamicin plasma concentrations after
intravenous and intratracheal administration to guinea pigs,
describing the pathway of the drug into the systemic
circulation after the extravascular injection mentioned. The
structured model selected consisted of a submodel of
a proportional linear subsystem, two submodels of simple
linear dynamic subsystems with time constants of 0.135+-0.065
hr (95 % I.C.) and 0.052+-0.049 hr, and two submodels of
parallel subsystems with time delays of 0.254+-0.046 hr and
1.135+-0.288 hr, connected in serial. The serio-parallel
structure of the model selected allowed to estimate mean
residence times for four fractions of gentamicin. From the
methodological point of view, our paper demonstrates the
efficiency of combination of modeling in the frequency and
in the time domain, designed to facilitate studies of complex
pharmacokinetic systems.
Regards,
Maria
*************************************************************
Diploma Engineer Maria Durisova CSc.,
Scientific Secretary
Institute of Experimental Pharmacology
Slovak Academy of Sciences
Dubravska cesta 9
842 16 Bratislava
Slovak Republic
Europe
Phone/Fax: 004217375928
Note:
Diploma Engineer is comparable to M.S. from a technical university
CSc., is comparable to Ph.D.
*
From: Nick Holford
Subject: Modeling vs non-compartmental PK Analysis
To: PharmPK.at.pharm.cpb.uokhsc.edu
Date: Wed, 17 Sep 1997 22:33:45 +1200 (NZT)
reply-to: n.holford.-at-.auckland.ac.nz
MIME-Version: 1.0
Anup,
Thanks for your comments and I think we basically agree but in case
there are still some die hard anti-modelling types left out there...
> There is one significant reason
> for the development and success of Non-Compartmental modeling of kinetic
> data. As the name suggests, there is no mathematical modeling of the
> data i.e. no judgements have to be made regarding the selection of the
> appropriate number of physiological compartments or exponentials to fit
> the data. Additionally, since the mathematical `best' fit of sum of
> exponential data is based on statistical parameters such as `goodness of
> fit', sum of squares, selection of optimal weighting factors, etc. this
> interpretation can be subjective and kineticist dependent.
The very fact that there is some subjectivity and kineticist dependency is
one of the reasons why modelling is valuable. Having to THINK about what
you are doing instead of blindly cranking out Tmax,Cmax, AUC is the way
to understand what the data is trying to say. When the model does not
fit an opportunity presents itself to ask why. Indeed models that fit
the data are less interesting in the spirit of scientific enquiry than
those that don't.
> I am sure many kineticists have experienced difficulty in modeling oral
>data which
> falls through a 3-4 log orders of magnitude--where in attempting to fit
> the terminal phase, the profile around Cmax is not well fit
Sure. I recognise the problem. And it has made me more aware of the need
to think more carefully about the processes that govern drug input. The
difference between the necessarily simple prediction of the model and
the observed reality is the only way to learn more about the PK of
absorption. Tmax and Cmax are even more naive than the elementary one
compartment first-order input, first-order elimination model and will
teach you next to nothing about a drug's absorption rate.
> (It is also for this reason the FDA prefers an observed Cmax rather than a
> calculated Cmax).
The FDA prefers observed Cmax rather then 'calculated' Cmax because the
guidelines are written for commercial (i.e. generic drug) not scientific
reasons. FDA reviewers in this situation don't want to spend time
thinking about yet another me too generic (and I agree with them in this
context). There is also a certain element of ignorance among the FDA
Biometric staff who offer advice on these issues.
Almost none of them have any practical experience of PK
modelling so of course they can only see the problems and not the
advantages. If any FDA Biometrician reads this I challenge them to tell
the world what fraction of the biometrics staff have attempted any PK
or PKPD modelling in the last 12 months (Bob O'Neill are you out there :-)).
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html
Back to the Top
Further comments on compartmental vs noncompartmenta PK
I have used noncompartmental approach in PK analysis for considerable time and
feel compelled to express my opinion. I certainly agree with the merits of
compartmental PK/PD analysis in understanding mechanism of drug kinetics and
dynamics. However, let's not discard and ridicule noncomparmental approach
entirely. One can do very sophisticated PK analysis (with effects of
covariance included) using noncomparmental approach. One can even do
simulation of concentration time curves using superposition method.
The greatest advantage of noncomparmental approach is in drug development
where one needs an accurate measure of drug exposure across different species.
One of the most powerful noncompartmental PK parameter is AUC(tau) at steady
state which allows us to determine CLss/F as well as drug exposure. This
approach requires minimum assumptions .
In my opinion inaccuracies in the error and structural model in the
compartmental PK approach especially with sparse sampling is grossly
underestimated and there are times where I get the feeling that compartmental
PK is being reduced to number crunching.
Both compartmental and noncompartmental analysis have their place in
pharmacokinetics and serve as useful tools in understanding drug kinetics.
Aziz Karim, PhD
Back to the Top
As far as I have seen, the replies on this topic did not deal with
the parameters Mean Residence Time (MRT) and Vss in non-compartmental
PK analysis. Therefore I would like to add two notes:
1. Calculation of MRT and Vss in non-compartmental PK analysis
(using AUC and AUMC) implies the assumption that the rate of
elimination from the body is proportional to the (plasma)
concentration (equivalent to: elimination from the central
compartment in compartmental analysis). If this is not the case (for
many drugs, e.g. atracurium which breaks down spontaneously in any
body fluid), the values obtained for MRT and Vss are meaningless.
Of course, the same is true in compartmental analysis, but in that
case one is 'forced' to choose a model, including the route of
elimination (do we all realize this every time we use an open two- or
three-compartment model ....?).
2. Calculation of MRT and Vss in non-compartmental PK analysi implies
calculation of AUMC (area under the first moment curve). Calculation
of AUMC without a curve-fitting procedure is prone to large
extrapolation errors (much more than AUC!).
In conclusion, be very careful in calculating MRT and Vss by non-
compartmental PK analysis!
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.-at-.farm.rug.nl
Back to the Top
Dear Faruq hi!
only some observations for your first question:
1) it's important remember that non-compartmental methods (NCM) ASSUME
LINEAR PHARMACOKINETICS for observed drug.
2) NCM are useful to estimate some PK parameters, useful for clinical
practice (bioavailability, clearance, apparent volume of distribution,
fraction of a dose converted to a metabolite, rates of absorption), but
they do not describe the time course of drug in the blood (different
half-lives, k-rates, etc)
NCM do not require the assumption of a specific compartmental model for
drug and are
based essentially on the theory of statistical methods, and
concentration-time course after single administration can be considered a
statistical distribution curve. The results are also independent enough on
changes of metabolism/distribution/elimination during the time.
Compartmental methods required for PK of a drug, depends in part on the
experimental design and you can have problems of accuracy when the
frequency and timing of samples are not correct (too sparse, interrupted
too early, etc).
In addition calculation of PK parameters and of distribution rates are
dependent on the model selected, but "many" models sometimes are
structurally identifiable and give you "acceptable" solution. You should
therefore perform a robust error-analysis on your data.
Elena Strocchi
------------
Laboratorio di Farmacocinetica ANT
------------
Dipartimento di Chimica Organica | Tel +39 51 6443645
Universita' di Bologna | FAX +39 51 6443654
Viale Risorgimento, 4 |
40136 Bologna - Italy | EMAIL strocchi.-a-.antlab.cineca.it
------------
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