Dear NONMEM users,
I'm wondering what equation or ODE is used in NONMEM when the steady state
is set (i.e. SS = 1). Is it the case that the initial parameter for the
compartment is set to a different value? If so, how does NONMEM set this
value?
I would appreciate if anyone can provide me with a reference or point me to
where I can find this information, including the type of equation used for
extravascular, iv bolus and iv infusion models.
Thanks,
Sherwin
Steady state model
Sherwin,
I dont understand exactly how NONMEM computes the steady state value but with ODEs it seems to be done using a numerical root finding procedure i.e. solves for the amt in each of the compartments when all the DEs have a value of zero.
The amt in each compartment is set to the steady state value. There is no initial 'parameter' for the compartment. Compartment amounts are variables. Parameters are constants. Parameters (e.g. THETA values) are used in the ODEs to define the DE values.
Perhaps Alison Boechmann (who wrote the code) could give a more thorough answer?
Nick
Sherwin K Sy wrote:
> Dear NONMEM users,
>
> I'm wondering what equation or ODE is used in NONMEM when the steady state is set (i.e. SS = 1). Is it the case that the initial parameter for the compartment is set to a different value? If so, how does NONMEM set this value?
>
> I would appreciate if anyone can provide me with a reference or point me to where I can find this information, including the type of equation used for extravascular, iv bolus and iv infusion models.
>
> Thanks,
>
> Sherwin
--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
[email protected] tel:+64(9)923-6730 fax:+64(9)373-7090
mobile: +64 21 46 23 53
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Hello Sherwin,
SS=1 infers a perfect steady state situation, i.e. a particular dosing event has been occurring with a particular time interval for infinitely long - and nothing else is happening. For the "standard PK model library" in NONMEM, i.e. for those linear ODE systems with their analytical (closed form) solutions implemented in specific NONMEM Advans, the single dose (SD) solution is a sum of exponential terms e.g. for a 1st order absorption 1st order elimination 1-cmpt model the solution for conc in the central cmpt is
C(t)= (exp(-K*t)-exp(-Ka*t)) *D*F*Ka/V/(Ka-K). Because all processes in these models are linear, when you add more doses their individual contributions to C(t) are additive. So for n doses interspaced by a constant interval tau, with the example model we get
C(t)= (exp(-K*t)+exp(-K*(t+tau))+exp(-K*(t+2tau))...+exp(-K*(t+n*tau)) -exp(-Ka*t)-exp(-Ka*(t+tau))-exp(-Ka*(t+2tau))...-exp(-Ka*(t+n*tau))) *D*F*Ka/V/(Ka-K).
This is the sum of two geometric series multplied by a constant, which reduces to
C(t)= (exp(-K*t)*(1-exp(-K*n*tau))/(1-exp(-K*tau)) -exp(-Ka*t)*(1-exp(-Ka*n*tau))/(1-exp(-Ka*tau)) *D*F*Ka/V/(Ka-K).
As n tends to infinity, 1-exp(-K*n*tau) and 1-exp(-Ka*n*tau) both tend to 1 so for true steady state i.e. infinite n you get the simpler expressions referred by Samer.
I believe the Gabrielsson & Weiner PKPD book has some of the SS solutions in it.
Best,
Andreas
Quoted reply history
-----Original Message-----
From: owner-nmusers
Behalf Of Mouksassi Mohamad-Samer
Sent: 6. august 2009 08:23
To: nmusers
Cc: n.holford
Subject: RE: [NMusers] Steady state model
Hello Sherwin,
All SS routines source code are located at the C:\nmvi\pr folder.
Each Advan closed form model has specific routines (and equations for SS) that can be used with it.
For linear models the magic factor for steady state computation will be:
exp(-rate.constant.time)/(1-exp(-rate.constant.Tau).
Monolix guide: Monolix31_PKPD_library.pdf has a lot of SS equations for commonly used models.
Of course general Advans have their general SS routines too and as Nick mentioned there is some root finding going on:
a comment from the SS6.FOR routine reads
C SS IS SOLUTION A OF: 0DT(A)+R
C APPROXIMATION: DADT(A)DT(0)+DA*A
C 0DT(0)+DA*A+R
C A=-DAINV*(DADT(0)+R)
...
Happy Reading !
Bests,
Samer
-----Original Message-----
From: owner-nmusers
Sent: Wed 8/5/2009 15:44
To: nmusers
Subject: Re: [NMusers] Steady state model
Sherwin,
I dont understand exactly how NONMEM computes the steady state value but with ODEs it seems to be done using a numerical root finding procedure i.e. solves for the amt in each of the compartments when all the DEs have a value of zero.
The amt in each compartment is set to the steady state value. There is no initial 'parameter' for the compartment. Compartment amounts are variables. Parameters are constants. Parameters (e.g. THETA values) are used in the ODEs to define the DE values.
Perhaps Alison Boechmann (who wrote the code) could give a more thorough answer?
Nick
Sherwin K Sy wrote:
> Dear NONMEM users,
>
> I'm wondering what equation or ODE is used in NONMEM when the steady
> state is set (i.e. SS = 1). Is it the case that the initial parameter
> for the compartment is set to a different value? If so, how does
> NONMEM set this value?
>
> I would appreciate if anyone can provide me with a reference or point
> me to where I can find this information, including the type of
> equation used for extravascular, iv bolus and iv infusion models.
>
> Thanks,
>
> Sherwin
>
>
--
Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand n.holford
90
mobile: +64 21 46 23 53
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Hello Sherwin,
All SS routines source code are located at the C:\nmvi\pr folder.
Each Advan closed form model has specific routines (and equations for SS) that
can be used with it.
For linear models the magic factor for steady state computation will be:
exp(-rate.constant.time)/(1-exp(-rate.constant.Tau).
Monolix guide: Monolix31_PKPD_library.pdf has a lot of SS equations for
commonly used models.
Of course general Advans have their general SS routines too and as Nick
mentioned there is some root finding going on:
a comment from the SS6.FOR routine reads
C SS IS SOLUTION A OF: 0=DADT(A)+R
C APPROXIMATION: DADT(A)=DADT(0)+DA*A
C 0=DADT(0)+DA*A+R
C A=-DAINV*(DADT(0)+R)
...
Happy Reading !
Bests,
Samer
Quoted reply history
-----Original Message-----
From: [email protected] on behalf of Nick Holford
Sent: Wed 8/5/2009 15:44
To: nmusers
Subject: Re: [NMusers] Steady state model
Sherwin,
I dont understand exactly how NONMEM computes the steady state value but
with ODEs it seems to be done using a numerical root finding procedure
i.e. solves for the amt in each of the compartments when all the DEs
have a value of zero.
The amt in each compartment is set to the steady state value. There is
no initial 'parameter' for the compartment. Compartment amounts are
variables. Parameters are constants. Parameters (e.g. THETA values) are
used in the ODEs to define the DE values.
Perhaps Alison Boechmann (who wrote the code) could give a more thorough
answer?
Nick
Sherwin K Sy wrote:
> Dear NONMEM users,
>
> I'm wondering what equation or ODE is used in NONMEM when the steady
> state is set (i.e. SS = 1). Is it the case that the initial parameter
> for the compartment is set to a different value? If so, how does
> NONMEM set this value?
>
> I would appreciate if anyone can provide me with a reference or point
> me to where I can find this information, including the type of
> equation used for extravascular, iv bolus and iv infusion models.
>
> Thanks,
>
> Sherwin
>
>
--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
[email protected] tel:+64(9)923-6730 fax:+64(9)373-7090
mobile: +64 21 46 23 53
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Hello Sherwin,
SS=1 infers a perfect steady state situation, i.e. a particular dosing event
has been occurring with a particular time interval for infinitely long - and
nothing else is happening. For the "standard PK model library" in NONMEM, i.e.
for those linear ODE systems with their analytical (closed form) solutions
implemented in specific NONMEM Advans, the single dose (SD) solution is a sum
of exponential terms e.g. for a 1st order absorption 1st order elimination
1-cmpt model the solution for conc in the central cmpt is
C(t)= (exp(-K*t)-exp(-Ka*t)) *D*F*Ka/V/(Ka-K). Because all processes in these
models are linear, when you add more doses their individual contributions to
C(t) are additive. So for n doses interspaced by a constant interval tau, with
the example model we get
C(t)= (exp(-K*t)+exp(-K*(t+tau))+exp(-K*(t+2tau))...+exp(-K*(t+n*tau))
-exp(-Ka*t)-exp(-Ka*(t+tau))-exp(-Ka*(t+2tau))...-exp(-Ka*(t+n*tau)))
*D*F*Ka/V/(Ka-K).
This is the sum of two geometric series multplied by a constant, which reduces
to
C(t)= (exp(-K*t)*(1-exp(-K*n*tau))/(1-exp(-K*tau))
-exp(-Ka*t)*(1-exp(-Ka*n*tau))/(1-exp(-Ka*tau)) *D*F*Ka/V/(Ka-K).
As n tends to infinity, 1-exp(-K*n*tau) and 1-exp(-Ka*n*tau) both tend to 1 so
for true steady state i.e. infinite n you get the simpler expressions referred
by Samer.
I believe the Gabrielsson & Weiner PKPD book has some of the SS solutions in it.
Best,
Andreas
Quoted reply history
-----Original Message-----
From: [email protected] [mailto:[email protected]] On
Behalf Of Mouksassi Mohamad-Samer
Sent: 6. august 2009 08:23
To: nmusers
Cc: [email protected]
Subject: RE: [NMusers] Steady state model
Hello Sherwin,
All SS routines source code are located at the C:\nmvi\pr folder.
Each Advan closed form model has specific routines (and equations for SS) that
can be used with it.
For linear models the magic factor for steady state computation will be:
exp(-rate.constant.time)/(1-exp(-rate.constant.Tau).
Monolix guide: Monolix31_PKPD_library.pdf has a lot of SS equations for
commonly used models.
Of course general Advans have their general SS routines too and as Nick
mentioned there is some root finding going on:
a comment from the SS6.FOR routine reads
C SS IS SOLUTION A OF: 0=DADT(A)+R
C APPROXIMATION: DADT(A)=DADT(0)+DA*A
C 0=DADT(0)+DA*A+R
C A=-DAINV*(DADT(0)+R)
...
Happy Reading !
Bests,
Samer
-----Original Message-----
From: [email protected] on behalf of Nick Holford
Sent: Wed 8/5/2009 15:44
To: nmusers
Subject: Re: [NMusers] Steady state model
Sherwin,
I dont understand exactly how NONMEM computes the steady state value but with
ODEs it seems to be done using a numerical root finding procedure i.e. solves
for the amt in each of the compartments when all the DEs have a value of zero.
The amt in each compartment is set to the steady state value. There is no
initial 'parameter' for the compartment. Compartment amounts are variables.
Parameters are constants. Parameters (e.g. THETA values) are used in the ODEs
to define the DE values.
Perhaps Alison Boechmann (who wrote the code) could give a more thorough answer?
Nick
Sherwin K Sy wrote:
> Dear NONMEM users,
>
> I'm wondering what equation or ODE is used in NONMEM when the steady
> state is set (i.e. SS = 1). Is it the case that the initial parameter
> for the compartment is set to a different value? If so, how does
> NONMEM set this value?
>
> I would appreciate if anyone can provide me with a reference or point
> me to where I can find this information, including the type of
> equation used for extravascular, iv bolus and iv infusion models.
>
> Thanks,
>
> Sherwin
>
>
--
Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical
Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland,
New Zealand [email protected] tel:+64(9)923-6730 fax:+64(9)373-7090
mobile: +64 21 46 23 53
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Does anyone have any reference for "typical" R^2 for pk/pd relationships. I have an analysis with an R^2 of 0.13 (highly significant), and the sponsor is unimpressed - thinking that an R^2 should be > 0.9 - apparently like it was in physics class.
Mark Sale MD
Next Level Solutions, LLC
www.NextLevelSolns.com
919-846-9185
(image/png attachment: left.letterhead)
Can't you just explain that r2 is not a good measurement for goodness of fit for these types of models?
Matt.
Quoted reply history
________________________________
From: owner-nmusers
On Behalf Of Mark Sale - Next Level Solutions
Sent: Thursday, August 06, 2009 9:39 AM
Cc: nmusers
Subject: RE: [NMusers] Steady state model
[cid:866303515
Does anyone have any reference for "typical" R^2 for pk/pd relationships. I have an analysis with an R^2 of 0.13 (highly significant), and the sponsor is unimpressed - thinking that an R^2 should be > 0.9 - apparently like it was in physics class.
Mark Sale MD
Next Level Solutions, LLC
http://www.NextLevelSolns.com
919-846-9185
This e-mail (including any attachments) is confidential and may be legally privileged. If you are not an intended recipient or an authorized representative of an intended recipient, you are prohibited from using, copying or distributing the information in this e-mail or its attachments. If you have received this e-mail in error, please notify the sender immediately by return e-mail and delete all copies of this message and any attachments.
Thank you.
(image/png attachment: left.letterhead)
Can't you just explain that r2 is not a good measurement for goodness of fit
for these types of models?
Matt.
Quoted reply history
________________________________
From: [email protected] [mailto:[email protected]] On
Behalf Of Mark Sale - Next Level Solutions
Sent: Thursday, August 06, 2009 9:39 AM
Cc: nmusers
Subject: RE: [NMusers] Steady state model
[cid:866303515@06082009-2B87]
Does anyone have any reference for "typical" R^2 for pk/pd relationships. I
have an analysis with an R^2 of 0.13 (highly significant), and the sponsor is
unimpressed - thinking that an R^2 should be > 0.9 - apparently like it was in
physics class.
Mark Sale MD
Next Level Solutions, LLC
http://www.NextLevelSolns.com
919-846-9185
This e-mail (including any attachments) is confidential and may be legally
privileged. If you are not an intended recipient or an authorized
representative of an intended recipient, you are prohibited from using, copying
or distributing the information in this e-mail or its attachments. If you have
received this e-mail in error, please notify the sender immediately by return
e-mail and delete all copies of this message and any attachments.
Thank you.
<<inline: left.letterhead>>
Dear all,
I thank you very much for pointing me to the references that mention them
and also illustrating the solutions for SS equations. They are very helpful.
What's interesting also is that Monolix uses the summation of the individual
linearized solution to fit a multiple dose profile, rather than setting it
up as ODE and use something like a unit delta function to simulate an
injection multiplied by the dose. What are your experiences with this
approach?
Cheers,
Sherwin
Quoted reply history
On Thu, Aug 6, 2009 at 3:38 AM, AVG (Andreas Velsing Groth) <
[email protected]> wrote:
> Hello Sherwin,
>
> SS=1 infers a perfect steady state situation, i.e. a particular dosing
> event has been occurring with a particular time interval for infinitely long
> - and nothing else is happening. For the "standard PK model library" in
> NONMEM, i.e. for those linear ODE systems with their analytical (closed
> form) solutions implemented in specific NONMEM Advans, the single dose (SD)
> solution is a sum of exponential terms e.g. for a 1st order absorption 1st
> order elimination 1-cmpt model the solution for conc in the central cmpt is
> C(t)= (exp(-K*t)-exp(-Ka*t)) *D*F*Ka/V/(Ka-K). Because all processes in
> these models are linear, when you add more doses their individual
> contributions to C(t) are additive. So for n doses interspaced by a constant
> interval tau, with the example model we get
> C(t)= (exp(-K*t)+exp(-K*(t+tau))+exp(-K*(t+2tau))...+exp(-K*(t+n*tau))
> -exp(-Ka*t)-exp(-Ka*(t+tau))-exp(-Ka*(t+2tau))...-exp(-Ka*(t+n*tau)))
> *D*F*Ka/V/(Ka-K).
> This is the sum of two geometric series multplied by a constant, which
> reduces to
> C(t)= (exp(-K*t)*(1-exp(-K*n*tau))/(1-exp(-K*tau))
> -exp(-Ka*t)*(1-exp(-Ka*n*tau))/(1-exp(-Ka*tau)) *D*F*Ka/V/(Ka-K).
> As n tends to infinity, 1-exp(-K*n*tau) and 1-exp(-Ka*n*tau) both tend to 1
> so for true steady state i.e. infinite n you get the simpler expressions
> referred by Samer.
>
> I believe the Gabrielsson & Weiner PKPD book has some of the SS solutions
> in it.
>
> Best,
> Andreas
>
> -----Original Message-----
> From: [email protected] [mailto:[email protected]]
> On Behalf Of Mouksassi Mohamad-Samer
> Sent: 6. august 2009 08:23
> To: nmusers
> Cc: [email protected]
> Subject: RE: [NMusers] Steady state model
>
>
> Hello Sherwin,
>
> All SS routines source code are located at the C:\nmvi\pr folder.
>
> Each Advan closed form model has specific routines (and equations for SS)
> that can be used with it.
> For linear models the magic factor for steady state computation will be:
> exp(-rate.constant.time)/(1-exp(-rate.constant.Tau).
> Monolix guide: Monolix31_PKPD_library.pdf has a lot of SS equations for
> commonly used models.
>
> Of course general Advans have their general SS routines too and as Nick
> mentioned there is some root finding going on:
>
> a comment from the SS6.FOR routine reads
>
> C SS IS SOLUTION A OF: 0=DADT(A)+R
> C APPROXIMATION: DADT(A)=DADT(0)+DA*A
> C 0=DADT(0)+DA*A+R
> C A=-DAINV*(DADT(0)+R)
> ...
> Happy Reading !
>
> Bests,
>
> Samer
>
> -----Original Message-----
> From: [email protected] on behalf of Nick Holford
> Sent: Wed 8/5/2009 15:44
> To: nmusers
> Subject: Re: [NMusers] Steady state model
>
> Sherwin,
>
> I dont understand exactly how NONMEM computes the steady state value but
> with ODEs it seems to be done using a numerical root finding procedure i.e.
> solves for the amt in each of the compartments when all the DEs have a
> value of zero.
>
> The amt in each compartment is set to the steady state value. There is no
> initial 'parameter' for the compartment. Compartment amounts are variables.
> Parameters are constants. Parameters (e.g. THETA values) are used in the
> ODEs to define the DE values.
>
> Perhaps Alison Boechmann (who wrote the code) could give a more thorough
> answer?
>
> Nick
>
> Sherwin K Sy wrote:
> > Dear NONMEM users,
> >
> > I'm wondering what equation or ODE is used in NONMEM when the steady
> > state is set (i.e. SS = 1). Is it the case that the initial parameter
> > for the compartment is set to a different value? If so, how does
> > NONMEM set this value?
> >
> > I would appreciate if anyone can provide me with a reference or point
> > me to where I can find this information, including the type of
> > equation used for extravascular, iv bolus and iv infusion models.
> >
> > Thanks,
> >
> > Sherwin
> >
> >
>
> --
> Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical
> Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019,
> Auckland, New Zealand [email protected] tel:+64(9)923-6730
> fax:+64(9)373-7090
> mobile: +64 21 46 23 53
> http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
>
>
>
>
Dear Mark,
Vonesh and Chinchilli discuss an R^2 adapted for generalized nonlinear
mixed-effects models. The derivation they describe needs a reference model
in order to compute the relative amount of explained variation and they
discuss the undervalue or R^2 computed for the population see
Vonesh, E.F., Chinchilli, V.M. (1997). Linear and Nonlinear Models for the
Analysis of Repeated Measurements. New York, NY: Marcel Dekker. p. 420-423
In general, however I agree with Matts response below, and would look into
the following manuscripts for demonstrating the adequacy of your model:
http://www.ncbi.nlm.nih.gov/pubmed/16906454?ordinalpos=4&itool=EntrezSystem
2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DefaultReportPanel.Pubmed_RVDocS
um Metrics for external model evaluation with an application to the
population pharmacokinetics of gliclazide.
Brendel K, Comets E, Laffont C, Laveille C, Mentré F.
Pharm Res. 2006 Sep;23(9):2036-49. Epub 2006 Aug 12.
http://www.ncbi.nlm.nih.gov/pubmed/16284919?ordinalpos=69&itool=EntrezSyste
m2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DefaultReportPanel.Pubmed_RVDoc
Sum Prediction discrepancies for the evaluation of nonlinear mixed-effects
models.
Mentré F, Escolano S.
J Pharmacokinet Pharmacodyn. 2006 Jun;33(3):345-67. Epub 2005 Nov 13.
Hope this helps.
Kind regards,
Matt
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Fidler,Matt,FORT WORTH,R&D
Sent: Thursday, August 06, 2009 11:36 AM
To: Mark Sale - Next Level Solutions
Cc: nmusers
Subject: RE: [NMusers] Steady state model
Can't you just explain that r2 is not a good measurement for goodness of fit
for these types of models?
Matt.
_____
From: [email protected] [mailto:[email protected]] On
Behalf Of Mark Sale - Next Level Solutions
Sent: Thursday, August 06, 2009 9:39 AM
Cc: nmusers
Subject: RE: [NMusers] Steady state model
Does anyone have any reference for "typical" R^2 for pk/pd relationships. I
have an analysis with an R^2 of 0.13 (highly significant), and the sponsor
is unimpressed - thinking that an R^2 should be > 0.9 - apparently like it
was in physics class.
Mark Sale MD
Next Level Solutions, LLC
www.NextLevelSolns.com
919-846-9185
This e-mail (including any attachments) is confidential and may be legally
privileged. If you are not an intended recipient or an authorized
representative of an intended recipient, you are prohibited from using,
copying or distributing the information in this e-mail or its attachments.
If you have received this e-mail in error, please notify the sender
immediately by return e-mail and delete all copies of this message and any
attachments.
Thank you.
<<image001.png>>
Hi Sherwin,
As Nick said, Alison would be the best source fro details, but I can give you the basic idea of what's done. For the constant rate input case, the solution is obtained as Nick described. In the case of multiple dosing with equal doses and dosing intervals, it is a root- finding problem that iteratively seeks a vector of values for the initial amounts in the compartments. The solution is the set of values such that the initial and final (end of dosing interval) values are equal for all compartments.
Bill
Quoted reply history
On Aug 5, 2009, at 2:44 PM, Sherwin K Sy wrote:
> Dear NONMEM users,
>
> I'm wondering what equation or ODE is used in NONMEM when the steady state is set (i.e. SS = 1). Is it the case that the initial parameter for the compartment is set to a different value? If so, how does NONMEM set this value?
>
> I would appreciate if anyone can provide me with a reference or point me to where I can find this information, including the type of equation used for extravascular, iv bolus and iv infusion models.
>
> Thanks,
>
> Sherwin