NONMEM Users Network Archive

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RE: AW: Simulations with/without residual error

From: Grevel, Joachim <Joachim.Grevel>
Date: Fri, 17 Jul 2009 09:13:30 +0100

Dear Marc,
 
I am sorry, but I am missing your boat. You wrote:
 
For example:


Instead of:
CL = THETA(1)*(WT/70)**THETA(2)*EXP(ETA(1))


Parameterize as:
LNCL = THETA(1)+THETA(2)*(WT/70)+ETA(1)
  CL = EXP(LNCL)


This sort of transformation is a useful thing to do for NONMEM =
simulation and estimation in general, because it creates a parameter =
uncertainty distribution that is consistent (for THETA) with the MVN =
assumption implicit in Maximum Likelihood methods for continuous data. =
This means that confidence intervals (for THETA) from NONMEM's =
asymptotic standard errors ($COV) should be more realistic. You may also =
find improved stability in estimation runs.


Best regards,
Marc
How can your first line of your code ever result in negative CL. I have =
adopted the log-transformation of data before estimation (thanks to =
Matts for promoting this!), but I cannot see the reason why to =
log-transform parameters before simulation when I use proportional error =
terms.
 
Thanks,
 
Joachim
_________________________________
AstraZeneca R&D Charnwood
Clin. Pharmacology and DMPK
Bakewell Road
Loughborough, LE11 5RH
Tel: +44 1509 644035
joachim.grevel


 
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-----Original Message-----
From: owner-nmusers
[mailto:owner-nmusers
Sent: 16 July 2009 18:59
To: nmusers
Subject: Re: AW: [NMusers] Simulations with/without residual error



(Apologies for the delayed posting.. this apparently didn't make it to =
nmusers on the initial attempt).

Dear Nick, Andreas, Andreas and nmusers,

Here are a couple of additional methods for including uncertainty in =
parameters at the inter-trial (or inter-replicate) level, when =
simulating with NONMEM:

1. You can take advantage the PRIOR subroutine in NONMEM VI (and VII - =
although I haven't tried it yet) simulations, to generate random =
variates from a Multi-Variate Normal distribution for THETA and an =
Inverse Wishart distribution for OMEGA. This works fine if your prior =
uncertainty distributions are adequately described by these =
distributions. Of course the MVN assumption is consistent with the =
var-covar matrix of the estimates in NONMEM, but you'll have to =
translate the uncertainty in OMEGA into the required parameters of an =
Inv. Wishart (e.g. mode and degrees of freedom). This method does not =
directly allow for prior uncertainty on SIGMA.

2. If you'd like to simulate from other distributions, or pull-in =
uncertainty in parameter estimates from other sources, such as the =
resulting parameter estimates from bootstrap replicates or MCMC Bayesian =
posterior distributions, you'll need to use an external tool with =
NONMEM. As Andreas points out, R is a useful choice. Leonid Gibiasnky =
and I had developed a toolkit of R functions called NMSUDS to facilitate =
these types of simulations in NONMEM. These functions have been extended =
and are now part of the broader MIfuns package ( =
http://cran.r-project.org/).

There's another important issue to consider... Be careful that the =
specification of the prior uncertainty distribution is consistent with =
reality for the parameters in your model. This point has been discussed =
by Pascal Girard and others in past nmusers threads. For example, a MVN =
uncertainty distribution for THETA is not realistic for PK parameters =
and is never realistic for OMEGA and SIGMA, in that MVN allows for =
simulation of negative values. To work-around this problem for THETA, =
you could choose to log-transform typical values of PK parameters to =
constrain resulting replicates within a physiologically realistic range. =


For example:

Instead of:
CL = THETA(1)*(WT/70)**THETA(2)*EXP(ETA(1))

Parameterize as:
LNCL = THETA(1)+THETA(2)*(WT/70)+ETA(1)
  CL = EXP(LNCL)

This sort of transformation is a useful thing to do for NONMEM =
simulation and estimation in general, because it creates a parameter =
uncertainty distribution that is consistent (for THETA) with the MVN =
assumption implicit in Maximum Likelihood methods for continuous data. =
This means that confidence intervals (for THETA) from NONMEM's =
asymptotic standard errors ($COV) should be more realistic. You may also =
find improved stability in estimation runs.

Best regards,
Marc



Marc R. Gastonguay, Ph.D. < marcg
President & CEO, Metrum Research Group LLC < metrumrg.com >
Scientific Director, Metrum Institute < metruminstitute.org >
2 Tunxis Rd, Suite 112, Tariffville, CT 06081 Direct: +1.860.670.0744 =
Main: +1.860.735.7043 Fax: +1.860.760.6014




Received on Fri Jul 17 2009 - 04:13:30 EDT

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