Dear NMusers,
Hi, I have data of a parent drug (intravenously administered) and its
metabolite, ¿How can I code the volume of distribution of metabolite as a
fraction of the central volume of parent?
An example of the model that I want to fit is:
$PK
V1=THETA(1)*EXP(ETA(1)) ; Central Volume of parent
V2=THETA(2)*EXP(ETA(2)) ; Peripheral Volume of parent
Q=THETA(3) ; intercompartmental clearance
V3= ???????????? ; Volume of metabolite as a fraction of V1 with variability
CL1=THETA(5)*EXP(ETA(4)) ; Formation clearance of metabolite
CL2=THETA(6)*EXP(ETA(5)) ; Elimination clearance of metabolite
CL0=THETA(7)*EXP(ETA(6)) ; Parent drug excretion by routes other than formation
of metabolite
- Thank you in advance.
Orlando.
PhD student Carlos Orlando Jacobo Cabral
Departamento de Farmacología, Lab.34
Centro de Investigación y de Estudios Avanzados del I. P. N.
Email: [email protected]; [email protected]
VD as a fraction of another VD
Hi Orlando,
This is somewhat dependent on how exactly you want the fraction to be coded.
Most likely, you want to restrict the volume to be positive and not bounded
between 0 and 1 (i.e. it is ≥0). Given that, you can define V3 as:
V3=EXP(THETA(8))*V1
You would then just exponentiate THETA(8) to find the fraction.
You can separately estimate the volume using the same ETA as the parent central
volume as:
V3=THETA(8)*EXP(ETA(1))
That way, it won’t explicitly be a fraction of the parent, and that may lead to
a more stable model.
Thanks,
Bill
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Carlos Orlando Jacobo Cabral
Sent: Monday, May 21, 2012 2:19 PM
To: nonmem users
Subject: [NMusers] VD as a fraction of another VD
Dear NMusers,
Hi, I have data of a parent drug (intravenously administered) and its
metabolite, ¿How can I code the volume of distribution of metabolite as a
fraction of the central volume of parent?
An example of the model that I want to fit is:
$PK
V1=THETA(1)*EXP(ETA(1)) ; Central Volume of parent
V2=THETA(2)*EXP(ETA(2)) ; Peripheral Volume of parent
Q=THETA(3) ; intercompartmental clearance
V3= ???????????? ; Volume of metabolite as a fraction of V1 with variability
CL1=THETA(5)*EXP(ETA(4)) ; Formation clearance of metabolite
CL2=THETA(6)*EXP(ETA(5)) ; Elimination clearance of metabolite
CL0=THETA(7)*EXP(ETA(6)) ; Parent drug excretion by routes other than formation
of metabolite
- Thank you in advance.
Orlando.
PhD student Carlos Orlando Jacobo Cabral
Departamento de Farmacología, Lab.34
Centro de Investigación y de Estudios Avanzados del I. P. N.
Email: [email protected]<mailto:[email protected]>;
[email protected]<mailto:[email protected]>
Carlos,
Why? What pharmacological or physiological reason would lead you to want to fix the volume of a metabolite to be a fraction of the parent?
Nick
Quoted reply history
On 21/05/2012 8:19 p.m., Carlos Orlando Jacobo Cabral wrote:
> Dear NMusers,
>
> Hi, I have data of a parent drug (intravenously administered) and its metabolite, ¿How can I code the volume of distribution of metabolite as a fraction of the central volume of parent?
>
> An example of the model that I want to fit is:
>
> $PK
>
> V1=THETA(1)*EXP(ETA(1)) ; Central Volume of parent
> V2=THETA(2)*EXP(ETA(2)) ; Peripheral Volume of parent
> Q=THETA(3) ; intercompartmental clearance
>
> V3= ???????????? ; Volume of metabolite as a fraction of V1 with variability
>
> CL1=THETA(5)*EXP(ETA(4)) ; Formation clearance of metabolite
> CL2=THETA(6)*EXP(ETA(5)) ; Elimination clearance of metabolite
>
> CL0=THETA(7)*EXP(ETA(6)) ; Parent drug excretion by routes other than formation of metabolite
>
> - Thank you in advance.
>
> Orlando.
>
> /P//hD //student/ Carlos Orlando Jacobo Cabral
>
> Departamento de Farmacología, Lab.34
>
> Centro de Investigación y de Estudios Avanzados del I. P. N.
>
> Email: [email protected] < mailto: [email protected] >; [email protected] < mailto: [email protected] >
--
Nick Holford, Professor Clinical Pharmacology
First World Conference on Pharmacometrics, 5-7 September 2012
Seoul, Korea http://www.go-wcop.org
Dept Pharmacology& Clinical Pharmacology, Bldg 505 Room 202D
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
email: [email protected]
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Dear Nick,
I want to try a previously reported PK model (Knibbe et al. Clin Pharmacokinet
2009; 48 (6): 371-385) to fit data similar to mine of morphine and its
metabolites in which the volumes of distribution of metabolites were estimated
as a fraction of volume of parent drug what seems to show good estimates. But
also probably I´ll try to estimate the volumes of metabolites as separate
parameters THETA with its corresponding variabilities, do you have any other
suggestions?, thank you.
And thanks also to Bill and Rob.
Kind regards,
Orlando.
PhD student Carlos Orlando Jacobo Cabral
Departamento de Farmacología, Lab.34
Centro de Investigación y de Estudios Avanzados del I. P. N.
Email: [email protected]; [email protected]
---------------------------------------------------------------------------------------------------------
> Date: Mon, 21 May 2012 22:12:18 +0200
> From: [email protected]
> To: [email protected]
> Subject: Re: [NMusers] VD as a fraction of another VD
>
> Carlos,
> Why? What pharmacological or physiological reason would lead you to want
> to fix the volume of a metabolite to be a fraction of the parent?
> Nick
>
Quoted reply history
> On 21/05/2012 8:19 p.m., Carlos Orlando Jacobo Cabral wrote:
> > Dear NMusers,
> >
> > Hi, I have data of a parent drug (intravenously administered) and its
> > metabolite, ¿How can I code the volume of distribution of metabolite
> > as a fraction of the central volume of parent?
> > An example of the model that I want to fit is:
> >
> > $PK
> >
> > V1=THETA(1)*EXP(ETA(1)) ; Central Volume of parent
> > V2=THETA(2)*EXP(ETA(2)) ; Peripheral Volume of parent
> > Q=THETA(3) ; intercompartmental clearance
> >
> > V3= ???????????? ; Volume of metabolite as a fraction of V1 with
> > variability
> >
> > CL1=THETA(5)*EXP(ETA(4)) ; Formation clearance of metabolite
> > CL2=THETA(6)*EXP(ETA(5)) ; Elimination clearance of metabolite
> > CL0=THETA(7)*EXP(ETA(6)) ; Parent drug excretion by routes other than
> > formation of metabolite
> >
> >
> >
> > - Thank you in advance.
> >
> > Orlando.
> >
> > /P//hD //student/ Carlos Orlando Jacobo Cabral
> >
> > Departamento de Farmacología, Lab.34
> >
> > Centro de Investigación y de Estudios Avanzados del I. P. N.
> >
> > Email: [email protected] <mailto:[email protected]>;
> > [email protected] <mailto:[email protected]>
> >
>
> --
> Nick Holford, Professor Clinical Pharmacology
>
> First World Conference on Pharmacometrics, 5-7 September 2012
> Seoul, Korea http://www.go-wcop.org
>
> Dept Pharmacology& Clinical Pharmacology, Bldg 505 Room 202D
> University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
> tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
> email: [email protected]
> http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
>
>
>
Carlos,
The Knibbe morphine/metabolite model has no pharmacological justification for fixing the metabolite volume to a fraction of the parent. It is an empirical model with other unusual assumptions such as making central and peripheral volumes equal to each other. It is also claimed that clearance of morphine by other routes than to M3G and M6G was negligible but in fact is is impossible to draw such a conclusion from this kind of data.
I would suggest you stick to models which recognize the limitations of estimating metabolite parameters when only parent drug is administered e.g. Bouwmeester et al. 2004).
Best wishes,
Nick
Bouwmeester NJ, Anderson BJ, Tibboel D, Holford NH. Developmental pharmacokinetics of morphine and its metabolites in neonates, infants and young children. Br J Anaesth 2004; 92: 208-17.
Quoted reply history
On 22/05/2012 6:41 a.m., Carlos Orlando Jacobo Cabral wrote:
> Dear Nick,
>
> I want to try a previously reported PK model (Knibbe /et al. /Clin Pharmacokinet 2009; 48 (6): 371-385) to fit data similar to mine of morphine and its metabolites in which the volumes of distribution of metabolites were estimated as a fraction of volume of parent drug what seems to show good estimates. But also probably I´ll try to estimate the volumes of metabolites as separate parameters THETA with its corresponding variabilities, do you have any other suggestions?, thank you.
>
> And thanks also to Billand Rob.
>
> Kind regards,
>
> Orlando.
>
> /P//hD //student/ Carlos Orlando Jacobo Cabral
>
> Departamento de Farmacología, Lab.34
>
> Centro de Investigación y de Estudios Avanzados del I. P. N.
>
> Email: [email protected] < mailto: [email protected] >; [email protected] < mailto: [email protected] >
>
> ---------------------------------------------------------------------------------------------------------
>
> > Date: Mon, 21 May 2012 22:12:18 +0200
> > From: [email protected]
> > To: [email protected]
> > Subject: Re: [NMusers] VD as a fraction of another VD
> >
> > Carlos,
>
> > Why? What pharmacological or physiological reason would lead you to want
>
> > to fix the volume of a metabolite to be a fraction of the parent?
> > Nick
> >
> > On 21/05/2012 8:19 p.m., Carlos Orlando Jacobo Cabral wrote:
> > > Dear NMusers,
> > >
> > > Hi, I have data of a parent drug (intravenously administered) and its
> > > metabolite, ¿How can I code the volume of distribution of metabolite
> > > as a fraction of the central volume of parent?
> > > An example of the model that I want to fit is:
> > >
> > > $PK
> > >
> > > V1=THETA(1)*EXP(ETA(1)) ; Central Volume of parent
> > > V2=THETA(2)*EXP(ETA(2)) ; Peripheral Volume of parent
> > > Q=THETA(3) ; intercompartmental clearance
> > >
> > > V3= ???????????? ; Volume of metabolite as a fraction of V1 with
> > > variability
> > >
> > > CL1=THETA(5)*EXP(ETA(4)) ; Formation clearance of metabolite
> > > CL2=THETA(6)*EXP(ETA(5)) ; Elimination clearance of metabolite
> > > CL0=THETA(7)*EXP(ETA(6)) ; Parent drug excretion by routes other than
> > > formation of metabolite
> > >
> > >
> > >
> > > - Thank you in advance.
> > >
> > > Orlando.
> > >
> > > /P//hD //student/ Carlos Orlando Jacobo Cabral
> > >
> > > Departamento de Farmacología, Lab.34
> > >
> > > Centro de Investigación y de Estudios Avanzados del I. P. N.
> > >
> > > Email: [email protected] <mailto:[email protected]>;
> > > [email protected] <mailto:[email protected]>
> > >
> >
> > --
> > Nick Holford, Professor Clinical Pharmacology
> >
> > First World Conference on Pharmacometrics, 5-7 September 2012
> > Seoul, Korea http://www.go-wcop.org
> >
> > Dept Pharmacology& Clinical Pharmacology, Bldg 505 Room 202D
> > University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
> > tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
> > email: [email protected]
> > http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
> >
> >
> >
--
Nick Holford, Professor Clinical Pharmacology
First World Conference on Pharmacometrics, 5-7 September 2012
Seoul, Korea http://www.go-wcop.org
Dept Pharmacology& Clinical Pharmacology, Bldg 505 Room 202D
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
email: [email protected]
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Dear Orlando,
There are multiple models available for morphine in children younger than
three years. The model by Knibbe is based on a data-driven analysis, which
causes this model to be empirical, but supported by the data. In addition to
that and very importantly the Knibbe model is the only model that was proven
to have accurate model performance in extensive internal and external
validation procedures. (Clin Pharmacokinet. 2011 Jan;50(1):51-63 & Pharm
Res. 2011 Apr;28(4):797-811)
Based on the available data, it was not possible to determine the
distribution volume of the metabolites in the model. This would require data
on the metabolites after direct intravenous infusion of the metabolites, but
this is unethical and therefore not possible in children. We were therefore
bound to include assumptions in our model. We have chosen to estimate the
distribution volumes of the metabolites as a proportion of the central
morphine compartment using the following code:
V1 = THETA(1)*EXP(ETA1) ; central volume for morphine
V2 = THETA(2)*V1 ; volume for M3G
By using only 1 eta, we made the implicit assumption that the
inter-individual variability in the volume of the metabolites is
proportional to the variability in the central volume of morphine. This
assumption cannot be proven or disproven with the available data, but to us
it does not seem to be too unrealistic to envision that if one of the
volumes increases or decreases the others will proportionally increase or
decrease as well.
Additionally, we found that when estimating the fraction for M3G and M6G
independently, their 95% confidence interval overlapped significantly and
the same was true for the distribution volume of the peripheral and central
compartment of morphine. According to the rule of parsimony these parameters
were therefore set to be equal.
V3 = V2 ; volume for M6G equal to volume M3G
V4 = V1 ; peripheral volume morphine equal to central volume
For both adults and children morphine elimination through routes other than
glucuronidation has been reported. In our model, with our assumptions, we
found that when estimating a clearance parameter for elimination through
other routes, 0 was included in 95% confidence interval of this parameter.
According to the rule of parsimony we therefore did not include this
parameter in the model. I would suggest that for your data you test
inclusion of this parameter and decide based on statistical criteria and
validation of your model whether you retain it or not.
Regards,
Elke
_____
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Carlos Orlando Jacobo Cabral
Sent: Tuesday, May 22, 2012 6:42 AM
To: nonmem users
Subject: RE: [NMusers] VD as a fraction of another VD
Dear Nick,
I want to try a previously reported PK model (Knibbe et al. Clin
Pharmacokinet 2009; 48 (6): 371-385) to fit data similar to mine of morphine
and its metabolites in which the volumes of distribution of metabolites were
estimated as a fraction of volume of parent drug what seems to show good
estimates. But also probably I´ll try to estimate the volumes of metabolites
as separate parameters THETA with its corresponding variabilities, do you
have any other suggestions?, thank you.
And thanks also to Bill and Rob.
Kind regards,
Orlando.
PhD student Carlos Orlando Jacobo Cabral
Departamento de Farmacología, Lab.34
Centro de Investigación y de Estudios Avanzados del I. P. N.
Email: [email protected]; [email protected]
----------------------------------------------------------------------------
-----------------------------
> Date: Mon, 21 May 2012 22:12:18 +0200
> From: [email protected]
> To: [email protected]
> Subject: Re: [NMusers] VD as a fraction of another VD
>
> Carlos,
> Why? What pharmacological or physiological reason would lead you to want
> to fix the volume of a metabolite to be a fraction of the parent?
> Nick
>
> On 21/05/2012 8:19 p.m., Carlos Orlando Jacobo Cabral wrote:
> > Dear NMusers,
> >
> > Hi, I have data of a parent drug (intravenously administered) and its
> > metabolite, ¿How can I code the volume of distribution of metabolite
> > as a fraction of the central volume of parent?
> > An example of the model that I want to fit is:
> >
> > $PK
> >
> > V1=THETA(1)*EXP(ETA(1)) ; Central Volume of parent
> > V2=THETA(2)*EXP(ETA(2)) ; Peripheral Volume of parent
> > Q=THETA(3) ; intercompartmental clearance
> >
> > V3= ???????????? ; Volume of metabolite as a fraction of V1 with
> > variability
> >
> > CL1=THETA(5)*EXP(ETA(4)) ; Formation clearance of metabolite
> > CL2=THETA(6)*EXP(ETA(5)) ; Elimination clearance of metabolite
> > CL0=THETA(7)*EXP(ETA(6)) ; Parent drug excretion by routes other than
> > formation of metabolite
> >
> >
> >
> > - Thank you in advance.
> >
> > Orlando.
> >
> > /P//hD //student/ Carlos Orlando Jacobo Cabral
> >
> > Departamento de Farmacología, Lab.34
> >
> > Centro de Investigación y de Estudios Avanzados del I. P. N.
> >
> > Email: [email protected] <mailto:[email protected]>;
> > [email protected] <mailto:[email protected]>
> >
>
> --
> Nick Holford, Professor Clinical Pharmacology
>
> First World Conference on Pharmacometrics, 5-7 September 2012
> Seoul, Korea http://www.go-wcop.org
>
> Dept Pharmacology& Clinical Pharmacology, Bldg 505 Room 202D
> University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
> tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
> email: [email protected]
> http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
>
>
>
Dear Elke
I really appreciate all your comments and suggestions which I´ll take into
account, thank you.
Kind regards,
Orlando.
PhD student Carlos Orlando Jacobo Cabral
Departamento de Farmacología, Lab.34
Centro de Investigación y de Estudios Avanzados del I. P. N.
Email: [email protected]; [email protected]
Quoted reply history
From: [email protected]
To: [email protected]; [email protected]
Subject: RE: [NMusers] VD as a fraction of another VD
Date: Wed, 23 May 2012 11:45:56 +0200
Dear Orlando,
There are multiple models available for morphine in children younger than three
years. The model by Knibbe is based on a data-driven analysis, which causes
this model to be empirical, but supported by the data. In addition to that and
very importantly the Knibbe model is the only model that was proven to have
accurate model performance in extensive internal and external validation
procedures. (Clin Pharmacokinet. 2011 Jan;50(1):51-63 & Pharm Res. 2011
Apr;28(4):797-811)
Based on the available data, it was not possible to determine the distribution
volume of the metabolites in the model. This would require data on the
metabolites after direct intravenous infusion of the metabolites, but this is
unethical and therefore not possible in children. We were therefore bound to
include assumptions in our model. We have chosen to estimate the distribution
volumes of the metabolites as a proportion of the central morphine compartment
using the following code:
V1 = THETA(1)*EXP(ETA1) ; central volume for morphine
V2 = THETA(2)*V1 ; volume for M3G
By using only 1 eta, we made the implicit assumption that the inter-individual
variability in the volume of the metabolites is proportional to the variability
in the central volume of morphine. This assumption cannot be proven or
disproven with the available data, but to us it does not seem to be too
unrealistic to envision that if one of the volumes increases or decreases the
others will proportionally increase or decrease as well.
Additionally, we found that when estimating the fraction for M3G and M6G
independently, their 95% confidence interval overlapped significantly and the
same was true for the distribution volume of the peripheral and central
compartment of morphine. According to the rule of parsimony these parameters
were therefore set to be equal.
V3 = V2 ; volume for M6G equal to volume M3G
V4 = V1 ; peripheral volume morphine equal to central volume
For both adults and children morphine elimination through routes other than
glucuronidation has been reported. In our model, with our assumptions, we found
that when estimating a clearance parameter for elimination through other
routes, 0 was included in 95% confidence interval of this parameter. According
to the rule of parsimony we therefore did not include this parameter in the
model. I would suggest that for your data you test inclusion of this parameter
and decide based on statistical criteria and validation of your model whether
you retain it or not.
Regards,
Elke
From: [email protected] [mailto:[email protected]] On
Behalf Of Carlos Orlando Jacobo Cabral
Sent: Tuesday, May 22, 2012 6:42 AM
To: nonmem users
Subject: RE: [NMusers] VD as a fraction of another VD
Dear Nick,
I want to try a previously reported PK model (Knibbe et al. Clin Pharmacokinet
2009; 48 (6): 371-385) to fit data similar to mine of morphine and its
metabolites in which the volumes of distribution of metabolites were estimated
as a fraction of volume of parent drug what seems to show good estimates. But
also probably I´ll try to estimate the volumes of metabolites as separate
parameters THETA with its corresponding variabilities, do you have any other
suggestions?, thank you.
And thanks also to Bill and Rob.
Kind regards,
Orlando.
PhD student Carlos Orlando Jacobo Cabral
Departamento de Farmacología, Lab.34
Centro de Investigación y de Estudios Avanzados del I. P. N.
Email: [email protected]; [email protected]
---------------------------------------------------------------------------------------------------------
> Date: Mon, 21 May 2012 22:12:18 +0200
> From: [email protected]
> To: [email protected]
> Subject: Re: [NMusers] VD as a fraction of another VD
>
> Carlos,
> Why? What pharmacological or physiological reason would lead you to want
> to fix the volume of a metabolite to be a fraction of the parent?
> Nick
>
> On 21/05/2012 8:19 p.m., Carlos Orlando Jacobo Cabral wrote:
> > Dear NMusers,
> >
> > Hi, I have data of a parent drug (intravenously administered) and its
> > metabolite, ¿How can I code the volume of distribution of metabolite
> > as a fraction of the central volume of parent?
> > An example of the model that I want to fit is:
> >
> > $PK
> >
> > V1=THETA(1)*EXP(ETA(1)) ; Central Volume of parent
> > V2=THETA(2)*EXP(ETA(2)) ; Peripheral Volume of parent
> > Q=THETA(3) ; intercompartmental clearance
> >
> > V3= ???????????? ; Volume of metabolite as a fraction of V1 with
> > variability
> >
> > CL1=THETA(5)*EXP(ETA(4)) ; Formation clearance of metabolite
> > CL2=THETA(6)*EXP(ETA(5)) ; Elimination clearance of metabolite
> > CL0=THETA(7)*EXP(ETA(6)) ; Parent drug excretion by routes other than
> > formation of metabolite
> >
> >
> >
> > - Thank you in advance.
> >
> > Orlando.
> >
> > /P//hD //student/ Carlos Orlando Jacobo Cabral
> >
> > Departamento de Farmacología, Lab.34
> >
> > Centro de Investigación y de Estudios Avanzados del I. P. N.
> >
> > Email: [email protected] <mailto:[email protected]>;
> > [email protected] <mailto:[email protected]>
> >
>
> --
> Nick Holford, Professor Clinical Pharmacology
>
> First World Conference on Pharmacometrics, 5-7 September 2012
> Seoul, Korea http://www.go-wcop.org
>
> Dept Pharmacology& Clinical Pharmacology, Bldg 505 Room 202D
> University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
> tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
> email: [email protected]
> http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
>
>
>
Dear Elke, Orlando and Nick,
I have to give Nick my full hearted support in this question. Parent
drug/metabolite models are common practice in population PK and there should
be a kind of best practice for how to parameterize these instead of
inventing one new way after another. I do not doubt that the Knibbe model
gives an excellent fit to that data and is predictive with respect to
external data. That is not the point, the point is that an identical fit to
the data could have been obtained by another parameterization that makes for
a much more straight forward interpretation.
The volume of distribution for the metabolite (e.g. M3G) is unidentifiable
in the exact same way that the volume of distribution is unidentifiable for
any drug where only data following oral administration is available. The
estimate of both Volume and CL for the metabolites will be estimates over
Fmet (i.e. the fraction of the parent compound that forms the metabolite).
To estimate V2 as a fraction of V1 is a pointless parameterization that
serves no purpose. It is reasonable to believe that there will be a high
correlation between the volumes of distribution (e.g. V1 and V2) and this
can be assessed by applying an OMEGA BLOCK to estimate the covariance (e.g.
OMEGA1 and OMEGA2, see below).
V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine
V2 = THETA(2)*EXP(ETA(2)) ; central volume for M3G/Fm3g
$OMEGA BLOCK(2) 0.1 ; VAR_V1
0.08 ; COVAR_V1_V2
0.1 ; VAR_V2
The outcome of this could be that the estimated covariance corresponds to
approximately 100% correlation. In this case it is still not clearly
justified to reduce the model to assume the same OMEGA variance for both
parameters since the magnitude of variability could still differ between the
two parameters. To assume 100% correlation but different variances can be
done with this parameterization:
V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine
V2 = THETA(2)*EXP(ETA(1)*THETA(3)) ; central volume for M3G/Fm3g
Where THETA(4) relates the standard deviation of V2 to the standard
deviation of V1 random effect. This model is hierarchically related to a
parameterization that is mathematically equivalent to the parameterization
in the Kibbe model:
V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine
V2 = THETA(2)*EXP(ETA(1)) ; central volume for M3G/Fm3g
This parameterization could very well turn out to be a sufficient
characterization of the system but it is not true that it cannot be tested
if a more complex model is better (see above steps).
When it comes to the fraction of morphine that is metabolized into M3G and
M6G it can as pointed out not be estimated without access to data following
iv. administration of the metabolites or making very strong assumption such
as fixing distribution volumes etc. Instead it is better to in the model
have all morphine that is eliminated forms both M3G and M6G. This way the
estimated clearance parameters for the metabolites will be (CLm3g/Fm3g and
CLm6g/Fm6g). By the same logic that it isnt identifiable to quantify the
relative formation of M3G and M6G it is also impossible to characterize any
additional rout of elimination.
Reducing the model by setting similar volumes of distribution to the one and
same parameter is nothing that I would practice and I think that it is more
transparent to show the certainty estimates for each parameter in the model.
Let me again stress that I do not question the predictive performance of the
Knibbe model or that it has been useful for its purposes. I have no insight
to this . However I dont think that it has applied a type of
parameterization that should be put forward as a good example since it has
no advantages compared to the standard parameterization that I suggest that
does facilitate a straight forward interpretation and easy comparison to
results from other studies (with or without data following iv administration
of M3G/M6G).
Regards,
Martin Bergstrand, PhD
Pharmacometrics Research Group
Dept of Pharmaceutical Biosciences
Uppsala University
Sweden
<mailto:[email protected]> [email protected]
Visiting scientist:
Mahidol-Oxford Tropical Medicine Research Unit,
Bangkok, Thailand
Phone: +66 8 9796 7611
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of e.krekels
Sent: den 23 maj 2012 16:46
To: 'Carlos Orlando Jacobo Cabral'; 'nonmem users'
Subject: RE: [NMusers] VD as a fraction of another VD
Dear Orlando,
There are multiple models available for morphine in children younger than
three years. The model by Knibbe is based on a data-driven analysis, which
causes this model to be empirical, but supported by the data. In addition to
that and very importantly the Knibbe model is the only model that was proven
to have accurate model performance in extensive internal and external
validation procedures. (Clin Pharmacokinet. 2011 Jan;50(1):51-63 & Pharm
Res. 2011 Apr;28(4):797-811)
Based on the available data, it was not possible to determine the
distribution volume of the metabolites in the model. This would require data
on the metabolites after direct intravenous infusion of the metabolites, but
this is unethical and therefore not possible in children. We were therefore
bound to include assumptions in our model. We have chosen to estimate the
distribution volumes of the metabolites as a proportion of the central
morphine compartment using the following code:
V1 = THETA(1)*EXP(ETA1) ; central volume for morphine
V2 = THETA(2)*V1 ; volume for M3G
By using only 1 eta, we made the implicit assumption that the
inter-individual variability in the volume of the metabolites is
proportional to the variability in the central volume of morphine. This
assumption cannot be proven or disproven with the available data, but to us
it does not seem to be too unrealistic to envision that if one of the
volumes increases or decreases the others will proportionally increase or
decrease as well.
Additionally, we found that when estimating the fraction for M3G and M6G
independently, their 95% confidence interval overlapped significantly and
the same was true for the distribution volume of the peripheral and central
compartment of morphine. According to the rule of parsimony these parameters
were therefore set to be equal.
V3 = V2 ; volume for M6G equal to volume M3G
V4 = V1 ; peripheral volume morphine equal to central volume
For both adults and children morphine elimination through routes other than
glucuronidation has been reported. In our model, with our assumptions, we
found that when estimating a clearance parameter for elimination through
other routes, 0 was included in 95% confidence interval of this parameter.
According to the rule of parsimony we therefore did not include this
parameter in the model. I would suggest that for your data you test
inclusion of this parameter and decide based on statistical criteria and
validation of your model whether you retain it or not.
Regards,
Elke
_____
From: [email protected] [mailto:[email protected]] On
Behalf Of Carlos Orlando Jacobo Cabral
Sent: Tuesday, May 22, 2012 6:42 AM
To: nonmem users
Subject: RE: [NMusers] VD as a fraction of another VD
Dear Nick,
I want to try a previously reported PK model (Knibbe et al. Clin
Pharmacokinet 2009; 48 (6): 371-385) to fit data similar to mine of morphine
and its metabolites in which the volumes of distribution of metabolites were
estimated as a fraction of volume of parent drug what seems to show good
estimates. But also probably I´ll try to estimate the volumes of metabolites
as separate parameters THETA with its corresponding variabilities, do you
have any other suggestions?, thank you.
And thanks also to Bill and Rob.
Kind regards,
Orlando.
PhD student Carlos Orlando Jacobo Cabral
Departamento de Farmacología, Lab.34
Centro de Investigación y de Estudios Avanzados del I. P. N.
Email: [email protected]; [email protected]
----------------------------------------------------------------------------
Dear Orlando,
I think Martin has put the matter to bed in terms of how you ought to
parameterise your model. One more thing to consider is that depending how rich
are your data, your model might start getting over parametrised. In this case
fixing volumes to known physiological values is a good idea. I don't agree
with Elke that infusion of metabolites is unethical, and luckily for you
neither did Lotsch et al CPT 1998 63;629-39. Morphine is a common drug with
well characterised active metabolites, so you should find enough information in
the literature to fix volume parameters if needed.
Best wishes,
Joe
PS All models are wrong, some are useless
Quoted reply history
________________________________
From: [email protected] [[email protected]] On Behalf Of
Martin Bergstrand [[email protected]]
Sent: 23 May 2012 18:56
To: 'Nick Holford'; 'e.krekels'; 'Carlos Orlando Jacobo Cabral'; 'nonmem users'
Subject: RE: [NMusers] VD as a fraction of another VD
Dear Elke, Orlando and Nick,
I have to give Nick my full hearted support in this question. Parent
drug/metabolite models are common practice in population PK and there should be
a kind of best practice for how to parameterize these instead of inventing one
new way after another. I do not doubt that the Knibbe model gives an excellent
fit to that data and is predictive with respect to external data. That is not
the point, the point is that an identical fit to the data could have been
obtained by another parameterization that makes for a much more straight
forward interpretation.
The volume of distribution for the metabolite (e.g. M3G) is unidentifiable in
the exact same way that the volume of distribution is unidentifiable for any
drug where only data following oral administration is available. The estimate
of both Volume and CL for the metabolites will be estimates over Fmet (i.e. the
fraction of the parent compound that forms the metabolite).
To estimate V2 as a fraction of V1 is a pointless parameterization that serves
no purpose. It is reasonable to believe that there will be a high correlation
between the volumes of distribution (e.g. V1 and V2) and this can be assessed
by applying an OMEGA BLOCK to estimate the covariance (e.g. OMEGA1 and OMEGA2,
see below).
V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine
V2 = THETA(2)*EXP(ETA(2)) ; central volume for M3G/Fm3g
$OMEGA BLOCK(2) 0.1 ; VAR_V1
0.08 ; COVAR_V1_V2
0.1 ; VAR_V2
The outcome of this could be that the estimated covariance corresponds to
approximately 100% correlation. In this case it is still not clearly justified
to reduce the model to assume the same OMEGA variance for both parameters since
the magnitude of variability could still differ between the two parameters. To
assume 100% correlation but different variances can be done with this
parameterization:
V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine
V2 = THETA(2)*EXP(ETA(1)*THETA(3)) ; central volume for M3G/Fm3g
Where THETA(4) relates the standard deviation of V2 to the standard deviation
of V1 random effect. This model is hierarchically related to a
parameterization that is mathematically equivalent to the parameterization in
the Kibbe model:
V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine
V2 = THETA(2)*EXP(ETA(1)) ; central volume for M3G/Fm3g
This parameterization could very well turn out to be a sufficient
characterization of the system but it is not true that it cannot be tested if a
more complex model is better (see above steps).
When it comes to the fraction of morphine that is metabolized into M3G and M6G
it can as pointed out not be estimated without access to data following iv.
administration of the metabolites or making very strong assumption such as
fixing distribution volumes etc. Instead it is better to in the model have all
morphine that is eliminated forms both M3G and M6G. This way the estimated
clearance parameters for the metabolites will be (CLm3g/Fm3g and CLm6g/Fm6g).
By the same logic that it isn’t identifiable to quantify the relative formation
of M3G and M6G it is also impossible to characterize any additional rout of
elimination.
Reducing the model by setting similar volumes of distribution to the one and
same parameter is nothing that I would practice and I think that it is more
transparent to show the certainty estimates for each parameter in the model.
Let me again stress that I do not question the predictive performance of the
Knibbe model or that it has been useful for it’s purposes. I have no insight to
this . However I don’t think that it has applied a type of parameterization
that should be put forward as a good example since it has no advantages
compared to the standard parameterization that I suggest that does facilitate a
straight forward interpretation and easy comparison to results from other
studies (with or without data following iv administration of M3G/M6G).
Regards,
Martin Bergstrand, PhD
Pharmacometrics Research Group
Dept of Pharmaceutical Biosciences
Uppsala University
Sweden
[email protected]<mailto:[email protected]>
Visiting scientist:
Mahidol-Oxford Tropical Medicine Research Unit,
Bangkok, Thailand
Phone: +66 8 9796 7611
From: [email protected] [mailto:[email protected]] On
Behalf Of e.krekels
Sent: den 23 maj 2012 16:46
To: 'Carlos Orlando Jacobo Cabral'; 'nonmem users'
Subject: RE: [NMusers] VD as a fraction of another VD
Dear Orlando,
There are multiple models available for morphine in children younger than three
years. The model by Knibbe is based on a data-driven analysis, which causes
this model to be empirical, but supported by the data. In addition to that and
very importantly the Knibbe model is the only model that was proven to have
accurate model performance in extensive internal and external validation
procedures. (Clin Pharmacokinet. 2011 Jan;50(1):51-63 & Pharm Res. 2011
Apr;28(4):797-811)
Based on the available data, it was not possible to determine the distribution
volume of the metabolites in the model. This would require data on the
metabolites after direct intravenous infusion of the metabolites, but this is
unethical and therefore not possible in children. We were therefore bound to
include assumptions in our model. We have chosen to estimate the distribution
volumes of the metabolites as a proportion of the central morphine compartment
using the following code:
V1 = THETA(1)*EXP(ETA1) ; central volume for morphine
V2 = THETA(2)*V1 ; volume for M3G
By using only 1 eta, we made the implicit assumption that the inter-individual
variability in the volume of the metabolites is proportional to the variability
in the central volume of morphine. This assumption cannot be proven or
disproven with the available data, but to us it does not seem to be too
unrealistic to envision that if one of the volumes increases or decreases the
others will proportionally increase or decrease as well.
Additionally, we found that when estimating the fraction for M3G and M6G
independently, their 95% confidence interval overlapped significantly and the
same was true for the distribution volume of the peripheral and central
compartment of morphine. According to the rule of parsimony these parameters
were therefore set to be equal.
V3 = V2 ; volume for M6G equal to volume M3G
V4 = V1 ; peripheral volume morphine equal to central volume
For both adults and children morphine elimination through routes other than
glucuronidation has been reported. In our model, with our assumptions, we found
that when estimating a clearance parameter for elimination through other
routes, 0 was included in 95% confidence interval of this parameter. According
to the rule of parsimony we therefore did not include this parameter in the
model. I would suggest that for your data you test inclusion of this parameter
and decide based on statistical criteria and validation of your model whether
you retain it or not.
Regards,
Elke
________________________________
From: [email protected]<mailto:[email protected]>
[mailto:[email protected]] On Behalf Of Carlos Orlando Jacobo Cabral
Sent: Tuesday, May 22, 2012 6:42 AM
To: nonmem users
Subject: RE: [NMusers] VD as a fraction of another VD
Dear Nick,
I want to try a previously reported PK model (Knibbe et al. Clin Pharmacokinet
2009; 48 (6): 371-385) to fit data similar to mine of morphine and its
metabolites in which the volumes of distribution of metabolites were estimated
as a fraction of volume of parent drug what seems to show good estimates. But
also probably I´ll try to estimate the volumes of metabolites as separate
parameters THETA with its corresponding variabilities, do you have any other
suggestions?, thank you.
And thanks also to Bill and Rob.
Kind regards,
Orlando.
PhD student Carlos Orlando Jacobo Cabral
Departamento de Farmacología, Lab.34
Centro de Investigación y de Estudios Avanzados del I. P. N.
Email: [email protected]<mailto:[email protected]>;
[email protected]<mailto:[email protected]>
---------------------------------------------------------------------------------------------------------
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Dear all,
>From this thread, I wanted tangentially to broach some issues/thoughts with
covariate analysis, and to a lesser extent, initial OMEGA matrix formulation
when dealing with parent-metabolite models. For simplicity, assume only one
metabolite, IV injection of parent with clearance and clearance to
metabolite of CLo and CLm, respectively, (total parent clearance is
CLt=Clo+Clm) and one compartment disposition models. Then let k = CLt/Vp
and Vp (Vm) is the volume of the parent (metabolite).
The model is well known:
Cm = Dose*k12/Vm*(exp(-k*t)-exp(k20)*t)/(k20-k) [k20 is metabolite
elimination rate constant], but to focus the discussion use
Cm = Dose*k12/Vm*A(t) to simplify, since we will not need A(t) .
Since metabolite is not dosed, as discussed, we have an identifiability
issue. The model can be rewritten as discussed,
Cm = Dose*Fm/Vm*k*A(t) where Fm = k12/k = Clm/(Clo+Clm) because k12 =
Clm/Vp. An estimable form of this model is
Cm = Dose/Vm0*k*A(t) where Vm0 = Vm/Fm, ie, the fraction metabolized is
absorbed into the volume
It would seem to me that covariates assumed to have the relationship
(Clm+Clo)*f(x) [f(x) is the covariate function for x] are not necessarily
required to be tested on Vm0 (the parameter we can estimate) because it
would cancel. For example, if f(x) = (WT/70)^x, then it is not a component
of Vm0 because of Clm/(Clo+Clm) and its cancelation. However, if a
covariate affects only one of Clm or Clo, or effects these in a different
way (or to a different extent), then one should evaluate this covariate on
either Vm0, or using a relative version of Fm, eg, Fm = 1 * f(x), (ideally
based on the interpretation the analyst wants to imply), because the
relationship will be implicit and not cancel. Carrying this to random
effects, if one is to fit a model to the parent with CLt*exp(etaCLt) then
this would not induce an implicit correlation with Vm0 (as above). If there
is variability in the fraction metabolized between subjects, then even if
CLt*exp(etaCLt) is used for modeling the parent, the eta in Vm0*exp(etaVm0)
should be evaluated for correlation with etaCLt, because of the underlying
variablity in Clo and Clm. Additionally, it would seem that becuase Vp
factors out of Fm, covariates influencing Vp would not necessarily need to
be tested (from an implicit viewpoint) on Vm0, and a priori correlation
between Vm0 and Vp need not be applied as there is not underlying implicit
relationship induced by the inclusion of Fm into Vm0, but that correlation
could still be evaluated.
Best regards,
Matt
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Martin Bergstrand
Sent: Wednesday, May 23, 2012 1:56 PM
To: 'Nick Holford'; 'e.krekels'; 'Carlos Orlando Jacobo Cabral'; 'nonmem
users'
Subject: RE: [NMusers] VD as a fraction of another VD
Dear Elke, Orlando and Nick,
I have to give Nick my full hearted support in this question. Parent
drug/metabolite models are common practice in population PK and there should
be a kind of best practice for how to parameterize these instead of
inventing one new way after another. I do not doubt that the Knibbe model
gives an excellent fit to that data and is predictive with respect to
external data. That is not the point, the point is that an identical fit to
the data could have been obtained by another parameterization that makes for
a much more straight forward interpretation.
The volume of distribution for the metabolite (e.g. M3G) is unidentifiable
in the exact same way that the volume of distribution is unidentifiable for
any drug where only data following oral administration is available. The
estimate of both Volume and CL for the metabolites will be estimates over
Fmet (i.e. the fraction of the parent compound that forms the metabolite).
To estimate V2 as a fraction of V1 is a pointless parameterization that
serves no purpose. It is reasonable to believe that there will be a high
correlation between the volumes of distribution (e.g. V1 and V2) and this
can be assessed by applying an OMEGA BLOCK to estimate the covariance (e.g.
OMEGA1 and OMEGA2, see below).
V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine
V2 = THETA(2)*EXP(ETA(2)) ; central volume for M3G/Fm3g
$OMEGA BLOCK(2) 0.1 ; VAR_V1
0.08 ; COVAR_V1_V2
0.1 ; VAR_V2
The outcome of this could be that the estimated covariance corresponds to
approximately 100% correlation. In this case it is still not clearly
justified to reduce the model to assume the same OMEGA variance for both
parameters since the magnitude of variability could still differ between the
two parameters. To assume 100% correlation but different variances can be
done with this parameterization:
V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine
V2 = THETA(2)*EXP(ETA(1)*THETA(3)) ; central volume for M3G/Fm3g
Where THETA(4) relates the standard deviation of V2 to the standard
deviation of V1 random effect. This model is hierarchically related to a
parameterization that is mathematically equivalent to the parameterization
in the Kibbe model:
V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine
V2 = THETA(2)*EXP(ETA(1)) ; central volume for M3G/Fm3g
This parameterization could very well turn out to be a sufficient
characterization of the system but it is not true that it cannot be tested
if a more complex model is better (see above steps).
When it comes to the fraction of morphine that is metabolized into M3G and
M6G it can as pointed out not be estimated without access to data following
iv. administration of the metabolites or making very strong assumption such
as fixing distribution volumes etc. Instead it is better to in the model
have all morphine that is eliminated forms both M3G and M6G. This way the
estimated clearance parameters for the metabolites will be (CLm3g/Fm3g and
CLm6g/Fm6g). By the same logic that it isn't identifiable to quantify the
relative formation of M3G and M6G it is also impossible to characterize any
additional rout of elimination.
Reducing the model by setting similar volumes of distribution to the one and
same parameter is nothing that I would practice and I think that it is more
transparent to show the certainty estimates for each parameter in the model.
Let me again stress that I do not question the predictive performance of the
Knibbe model or that it has been useful for it's purposes. I have no insight
to this . However I don't think that it has applied a type of
parameterization that should be put forward as a good example since it has
no advantages compared to the standard parameterization that I suggest that
does facilitate a straight forward interpretation and easy comparison to
results from other studies (with or without data following iv administration
of M3G/M6G).
Regards,
Martin Bergstrand, PhD
Pharmacometrics Research Group
Dept of Pharmaceutical Biosciences
Uppsala University
Sweden
[email protected]
Visiting scientist:
Mahidol-Oxford Tropical Medicine Research Unit,
Bangkok, Thailand
Phone: +66 8 9796 7611