RE: AW: Simulations with/without residual error
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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Tel: +44 1509 644035
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Quoted reply history
-----Original Message-----
From: [email protected] [mailto:[email protected]]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. < [email protected] >
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