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Re: AW: Simulations with/without residual error

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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> -----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

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