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-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com
]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. < ma...@metrumrg.com >
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
