From: Gastonguay, Marc <*marcg*>

Date: Fri, 17 Jul 2009 08:52:34 -0400

Joachim, nmusers:

First of all, I need to correct a typo in the LNCL equation... Thanks

to Nicolas Simon for reminding me that I missed the LOG on (WT/70).

Here's the corrected code:

Instead of:

1). CL = THETA(1)*(WT/70)**THETA(2)*EXP(ETA(1))

Parameterize as:

2). LNCL= THETA(1)+THETA(2)*LOG(WT/70)+ETA(1)

CL=EXP(LNCL)

The problem with Model 1 above occurs when you simulate with an

additional level in the random effects hierarchy at the inter-trial or

inter-replicate level, representing the parameter uncertainty (e.g.

imprecision), AND when you obtain that parameter uncertainty from

NONMEM's variance-covariance matrix of the estimates, which is Multi-

Variate Normal. Given large enough parameter uncertainty (imprecision)

it is possible to draw negative random variates for THETA from the MVN

distribution. Model 2 avoids this problem. This is not a concern with

Model 1 when parameter uncertainty is ignored, or when the uncertainty

is derived from other sources, such as bootstrap or posterior Bayesian

parameter distributions.

I hope that this explanation gets you back on the boat :)

Marc

On Jul 17, 2009, at 4:13 AM, Grevel, Joachim wrote:

*> 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
*

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*

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*

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*> Bakewell Road
*

*> Loughborough, LE11 5RH
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*

*> joachim.grevel *

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*> -----Original Message-----
*

*>
*

*> From: owner-nmusers *

*> ]On Behalf Of Gastonguay, Marc
*

*> 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 - 08:52:34 EDT

Date: Fri, 17 Jul 2009 08:52:34 -0400

Joachim, nmusers:

First of all, I need to correct a typo in the LNCL equation... Thanks

to Nicolas Simon for reminding me that I missed the LOG on (WT/70).

Here's the corrected code:

Instead of:

1). CL = THETA(1)*(WT/70)**THETA(2)*EXP(ETA(1))

Parameterize as:

2). LNCL= THETA(1)+THETA(2)*LOG(WT/70)+ETA(1)

CL=EXP(LNCL)

The problem with Model 1 above occurs when you simulate with an

additional level in the random effects hierarchy at the inter-trial or

inter-replicate level, representing the parameter uncertainty (e.g.

imprecision), AND when you obtain that parameter uncertainty from

NONMEM's variance-covariance matrix of the estimates, which is Multi-

Variate Normal. Given large enough parameter uncertainty (imprecision)

it is possible to draw negative random variates for THETA from the MVN

distribution. Model 2 avoids this problem. This is not a concern with

Model 1 when parameter uncertainty is ignored, or when the uncertainty

is derived from other sources, such as bootstrap or posterior Bayesian

parameter distributions.

I hope that this explanation gets you back on the boat :)

Marc

On Jul 17, 2009, at 4:13 AM, Grevel, Joachim wrote:

Received on Fri Jul 17 2009 - 08:52:34 EDT