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Hi,
Could anybody please help me with the following question:
How many blood samples is needed in general to establish a
two-compartment model that describes the pharmacokinetics of a drug
(here: gentamicin) sufficiently? Is there a general rule, by which one
can calculate the number of demanded blood samples to establish a one-,
two, three- etc compartment model?
Any comment would be of great help.
Kirneh
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[A few replies - db]
Sender: PharmPK.aaa.boomer.org
Reply-To: "Stephen Duffull"
MIME-Version: 1.0
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From: "Stephen Duffull"
Date: Mon, 11 Dec 2000 15:03:53 +1000
To: david.-at-.boomer.org
Subject: RE: PharmPK Number of samples for two compartment model
The following message was posted to: PharmPK
Kirneh
> (here: gentamicin) sufficiently? Is there a general rule, by which one
> can calculate the number of demanded blood samples to establish a one-,
> two, three- etc compartment model?
The answer to your question depends on whether you are undertaking an
individual or population study.
For the study of an individual the most parsimonious sampling strategy would
be one where you had 1 blood sample per parameter to estimate. In theory
using an optimal design technique this should be sufficient to fully
characterise the model - although this does depend on the accuracy of the
prior estimates of the parameters. These optimal design strategies are not
usually robust to misspecification of the model.
For the study of a population then the most parsimonious sampling strategy
where estimates of the fixed and random effects parameters are required
cannot be generalised easily. Many investigators rely on simulations and
more recently theoretic techniques for computing the "best" design. (see
http://www.uq.edu.au/pharmacy/pfim.htm for information on a theoretic
technique).
For so-called "Bayesian forecasting" using the MAP objective function it may
be possible to get reasonable parameter estimates when less blood samples
are taken than there are parameters to estimate. In these circumstances
however the values of the parameter estimates are greatly influenced by the
prior - and misspecification of the prior can result in biased estimates of
the parameters.
I hope this helps.
Regards
Steve
========================
Stephen Duffull
School of Pharmacy
University of Queensland
Brisbane, QLD 4072
Australia
Ph +61 7 3365 8808
Fax +61 7 3365 1688
---
Sender: PharmPK.-at-.boomer.org
Reply-To: Nick Holford
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From: Nick Holford
Date: Tue, 12 Dec 2000 02:01:57 +1300
To: david.aaa.boomer.org
Subject: Re: PharmPK Number of samples for two compartment model
The following message was posted to: PharmPK
"Henrik Kjer Petersen (gmx) (by way of David_Bourne)" wrote:
>
> How many blood samples is needed in general to establish a
> two-compartment model that describes the pharmacokinetics of a drug
> (here: gentamicin) sufficiently? Is there a general rule, by which one
> can calculate the number of demanded blood samples to establish a one-,
> two, three- etc compartment model?
The general rule for the *minimum* number of samples is one per
parameter in your model.
eg. 1 cpt bolus input plus additive error = CL + V + SD = 3
2 cpt first order input plus additive error = Ka + CL + V1 + CLic
+ V2 + SD = 6
n cpt first order input + lag plus additive + proportional = Ka
+Lag + 2 * (CLn + Vn) + SD + CV = 4+2*n
But the more you can get the better your modelling will be!
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 tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm
---
Sender: PharmPK.at.boomer.org
Reply-To: "Robert Hunter"
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From: "Robert Hunter"
Date: Mon, 11 Dec 2000 08:16:27 -0600
To: david.-a-.boomer.org
Subject: Re: PharmPK Number of samples for two compartment model
The following message was posted to: PharmPK
Kirneh,
I have found that when using winnonlin, a minimum of 6 time points
per compartment are needed.
Rob Hunter, MS, PhD
Assistant Professor of Veterinary Pharmacology
Department of Anatomy & Physiology
1600 Denison Ave., 129 Coles Hall
College of Veterinary Medicine
Kansas State University
785-532-4524 (office)
785-532-4516 (lab)
785-532-4557 (fax)
rhunter.-at-.vet.ksu.edu
www.vet.ksu.edu/depts/ap/faculty/hunter.htm
---
Sender: PharmPK.at.boomer.org
Reply-To: Angusmdmclean.-at-.aol.com
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From: Angusmdmclean.aaa.aol.com
Date: Mon, 11 Dec 2000 09:43:14 EST
To: david.-at-.boomer.org
Subject: Re: PharmPK Number of samples for two compartment model
The following message was posted to: PharmPK
fit the experimental data you have to a 2 compartment model. Use the model
-predicted concentrations as a guide for the shape of the profile. Then
design timepoints you need to best characterize the shape of the 2
compartment model- calculated plasma concentrations. The timepoints selected
must characterize the shape you are trying to define.
same applies for all models.
---
Sender: PharmPK.-a-.boomer.org
Reply-To: "Dr. Sander Vinks"
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From: "Dr. Sander Vinks"
Date: Mon, 11 Dec 2000 10:31:16 -0500
To: david.at.boomer.org
Subject: Re: PharmPK Number of samples for two compartment model
The following message was posted to: PharmPK
Dear Kirneh,
An attractive approach is to employ optimal sampling strategy
to determine
information-rich sampling times for obtaining data. Given the intended
dosage regimen and assuming that structural pharmacokinetic and
observational model are known, along with reasonable estimates of the
expected pharmacokinetic parameters and observation error, D-optimal times
can be determined to maximize the precision of pharmacokinetic parameter
value estimation for an individual subject . Typically for a 2-compartment
model one would need 4 samples; one time point for every parameter in the
model. For this the sample module in the ADAPT software can be used:
See also http://www.usc.edu/dept/biomed/BMSR/Software/1999.html:
D'Argenio DZ. Optimal sampling times for pharmacokinetic experiments. J
Pharmacokinet Biopharm 1981;9:739-56.
and examples for 2-compt PK:
Drusano GL, Forrest A, Snyder MJ, Reed MD, Blumer JL. An evaluation of
optimal sampling strategy and adaptive study design. Clin Pharmacol Ther
1988;44:232-8.
Forrest A, Ballow CH, Nix DE, Birmingham MC, Schentag JJ. Development of a
population pharmacokinetic model and optimal sampling strategies for
intravenous ciprofloxacin. Antimicrob Agents Chemother 1993;37:1065-72.
Vinks AATMM, Mouton JW, Touw DJ, Heijerman HGM, Danhof M, Bakker W.
Population pharmacokinetics of ceftazidime in cystic fibrosis patients
using a nonparametric algorithm and optimal sampling strategy. Antimicrob
Agents Chemother 1996;40:1091-7.
***************************************************************************
Alexander A. Vinks, PharmD, PhD,
Research Professor of Pediatrics
Pharmacology Research Center & Clinical Trials Office
Children's Hospital Medical Center
3333 Burnet Avenue
Cincinnati, Ohio 45229-3039
Tel: (513) 636-0159; (513) 636-0160 (secretary).
Fax: (513) 636-0168.
CHMCC email: sander.vinks.aaa.chmcc.org
****************************************************************************
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Dear Kirneh,
An attractive approach is to employ optimal sampling strategy
to determine
information-rich sampling times for obtaining data. Given the intended
dosage regimen and assuming that structural pharmacokinetic and
observational model are known, along with reasonable estimates of the
expected pharmacokinetic parameters and observation error, D-optimal times
can be determined to maximize the precision of pharmacokinetic parameter
value estimation for an individual subject . Typically for a 2-compartment
model one would need 4 samples; one time point for every parameter in the
model. For this the sample module in the ADAPT software can be used:
See also http://www.usc.edu/dept/biomed/BMSR/Software/1999.html:
D'Argenio DZ. Optimal sampling times for pharmacokinetic experiments. J
Pharmacokinet Biopharm 1981;9:739-56.
and examples for 2-compt PK:
Drusano GL, Forrest A, Snyder MJ, Reed MD, Blumer JL. An evaluation of
optimal sampling strategy and adaptive study design. Clin Pharmacol Ther
1988;44:232-8.
Forrest A, Ballow CH, Nix DE, Birmingham MC, Schentag JJ. Development of a
population pharmacokinetic model and optimal sampling strategies for
intravenous ciprofloxacin. Antimicrob Agents Chemother 1993;37:1065-72.
Vinks AATMM, Mouton JW, Touw DJ, Heijerman HGM, Danhof M, Bakker W.
Population pharmacokinetics of ceftazidime in cystic fibrosis patients
using a nonparametric algorithm and optimal sampling strategy. Antimicrob
Agents Chemother 1996;40:1091-7.
******
Alexander A. Vinks, PharmD, PhD,
Research Professor of Pediatrics
Pharmacology Research Center & Clinical Trials Office
Children's Hospital Medical Center
3333 Burnet Avenue
Cincinnati, Ohio 45229-3039
Tel: (513) 636-0159; (513) 636-0160 (secretary).
Fax: (513) 636-0168.
CHMCC email: sander.vinks.-a-.chmcc.org
******
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Hi!
There is a lot written on this subject.
The literature notes that if one assumes one "true" mean parameter vector,
that there will be EXACTLY four optimal points to sample under a D optimality
criterion (the factor being minimized or maximized is a scalar and is related
to the determinant of the Fisher Information Matrix). This has the particular
property of replication. That is, if one asks for the 5th through 8th points,
it will say to replicate the first four points, as this will be the minimum
variance solution. David D'Argenio and JJ Di Stefano have written extensively
on this topic.
HOWEVER, this approach misses the fact that there IS NO ONE "TRUE" MEAN
PARAMETER VECTOR. Patients have true between-patient variability. To approach
this in a stochastic framework, D'Argenio has developed a new optimality
criterion that is related to the log of the D-optimal criterion and has an
expectation taken over a population to make it explicitly stochastic. This
does not have the property of replication and, when asked for the 5th point,
provides a time that is different from the first four and provides more
information about patients removed from the mean parameter values.
Tod and Rocchisani have also written a few papers on this topic.
Hope this helps,
George Drusano --part1_55.e93fef4.2768094c_boundary--
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The following message was posted to: PharmPK
Dear Sir,
I was quite puzzled by the answers to the question how
many samples are 'needed in general to establish a
two-compartment model that describes the pharmacokinetics of a drug
(here: gentamicin) sufficiently?'
In my view, the mathematical questions that arise are not
yet precise; i.e. what do we want?
1) Model selection in order to show that a two compartent
model is sufficient (best) to describe the data.
2) Parameter estimation with help of data in order to
determine a quantitative description for the dynamic
behaviour of the drug.
3) Experimental design in order to optimize data
acquisition with respect to number of samples,.....
Not for all of these problems, in my view, there is a
best answer.
In case 1, one could rely on one of the
many model selection approaches (AIC, BIC, LR-tests, ....).
Unfortunately there are still many open questions and I do
not agree with Nick Holford that 'the more you can get
the better your modelling will be!' since the complexity of
the model will certainly depend of the number of data
points.
In case 2, assuming that the two compartment model is
sufficient, there should be no problems. Just write down
the error model for the measurement error, determine which
level of accuracy is needed/desired for the estimated
parameters and calculate the number of data points needed to
establish this level (e.g. for equally spaced sampling
times).
Case 3 was already commented and many experimental design
techniques are readily available.
I hope that my comments are of any value and I would
appreciate any reply.
Sincerely yours,
Thorsten M=FCller
--
Thorsten Mueller FDM, Freiburg Centre for
muellert.aaa.fdm.uni-freiburg.de Data Analysis and Modelling
Tel. ++49 761 / 203 5764 Eckerstr.1 79104 Freiburg (Germany)
=46ax. ++49 761 / 203 7700 http://www.fdm.uni-freiburg.de
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The following message was posted to: PharmPK
Kirneh,
Although there is literature regarding the theoretical
aspects of how many levels to obtain to adeqautely determine
the parameters of a two compartment model, practical considerations
would demand at least two levels for each phase of the plasma
concentration curve. Two levels in the alpha phase, and two levels
in the elimination phase, would allow some estimation of alpha
and beta macroconstants. The goodness of fit the of the two
compartment model could be assessed by such tests as the Akaike
Information Criterion and F-test.
Mike Leibold, PharmD, RPH
ML11439.-a-.goodnet.com
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The following message was posted to: PharmPK
"Thorsten Mueller (by way of David_Bourne)" wrote:
Thorsten,
> In my view, the mathematical questions that arise are not
> yet precise; i.e. what do we want?
I quite agree that the design of an experiment intended to build a
model and estimate its parameters is dependent on the question being
asked.
> Unfortunately there are still many open questions and I do
> not agree with Nick Holford that 'the more you can get
> the better your modelling will be!' since the complexity of
> the model will certainly depend of the number of data
> points.
I cannot understand why you disagree with my general statement. The
more data one has then generally speaking the more one will learn
about the reality underlying the observations. In that sense the more
data points (with suitable design) then the more complex the model
may become but in practice there is some user specified perspective
of the use of the model that says the model is good enough and the
focus will turn perhaps to the precision of the estimates. In this
case the more data points (with suitable design) the better the
precision.
Can you please explain more clearly why you disagree with my assertion?
> In case 2, assuming that the two compartment model is
> sufficient, there should be no problems. Just write down
> the error model for the measurement error, determine which
> level of accuracy is needed/desired for the estimated
> parameters and calculate the number of data points needed to
> establish this level (e.g. for equally spaced sampling
> times).
You do not say how you would do the calculation of the number of
points nor do you mention how you would decide on the spacing (design
times). There is a strong interaction between number and timing of
points and there is no simple calculation that I know of that can
solve this problem. A solution can be obtained depending on what you
want to know. D-optimality methods will attempt to improve precision
of parameter estimates but pay no attention to accuracy as far as I
understand the methods. A better optimization metric may be one that
include both imprecision and bias (aka precision and accuracy) e.g.
based on the root mean square error of the parameter estimate
compared with its true value.
--
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)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm
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The following message was posted to: PharmPK
I guess it is the practicality that dictates number of samples in a clinical
study. While there are no hard and fixed rules that guides how many samples
to be drawn in a clinical study following guidelines should give you some
clue.
1. At least 2 plasma draws before the Tmax for the purpose of
calculating the early exposure (which is a recommendation in the recently
issued BA/BE guidance).
2. We need at least three plasma draws for calculating terminal phase.
3. Same criteria as item # 2 if you want to calculate distribution
half-life.
4. While items # 1 and 2 are a must my personal preference is to have
two/three blood draws before and after the Tmax.
5. Maximum blood one can draw from a subject is pretty much limited to
a pint in a study of one month duration.
6. Finally in the current scenario where majority of the studies are
conducted in CROs. Convenience of the CROs and subject of the volunteer
dictating the blood draw times and number of draws.
These are my thoughts may be I am not be totally accurate.
Prasad Tata
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The following message was posted to: PharmPK
Dear Nick Holford,
thank you for your reply, I hope I am able to clarify my
point:
> > Unfortunately [...] I do
> > not agree with Nick Holford that 'the more you can get
> > the better your modelling will be!' since the complexity of
> > the model will certainly depend of the number of data
> > points.
> I cannot understand why you disagree with my general statement. The
> more data one has then generally speaking the more one will learn
> about the reality underlying the observations. In that sense the more
> data points (with suitable design) then the more complex the model
> may become but in practice there is some user specified perspective
> of the use of the model that says the model is good enough and the
> focus will turn perhaps to the precision of the estimates. In this
> case the more data points (with suitable design) the better the
> precision.
In my view, biological and medical dynamical systems
possess an infinite number of degrees of freedom.
Although, for the researcher, more data points
may mean more insight into the experiment and the
underlying dynamics, current model selection procedures will
select the most complex model which is not always the one
desired. Instead the researcher will use "some user
specified perspective of the use of the model that says
the model is good enough" which, in my view, is a rather
subjective method.
Although I am no expert in model selection procedures, in
my view the current alternatives are rather unsatisfactory,
especially in bio/med dynamical systems.
I would be happy to receive any comment on this topic.
> You do not say how you would do the calculation of the number of
> points nor do you mention how you would decide on the spacing (design
> times). There is a strong interaction between number and
> timing of
> points and there is no simple calculation
> that I know of that can
> solve this problem.
This is a question for an expert for experimental
design, but I would use D-optimality methods to compute the
time points and then do a Monte Carlo simulation to
approximate the confidence intervals of the estimates. For a
specified desired level of precision the number of time
points can then be calculated.
Merry Christmas and a happy new year 2001!
Best wishes,
Thorsten M=FCller
--
Thorsten Mueller FDM, Freiburg Centre for
muellert.at.fdm.uni-freiburg.de Data Analysis and Modelling
Tel. ++49 761 / 203 5764 Eckerstr.1 79104 Freiburg (Germany)
=46ax. ++49 761 / 203 7700 http://www.fdm.uni-freiburg.de
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