(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
