Simulation for future populations and diagnostics
Dear NMusers,
I had to recently run an exercise with simulations across uncertainty in not
just THETA, but also OMEGA and SIGMA. I simply parameterized the omegas and
sigmas as thetas (many thanks to Dr. Gibiansky's posting on NMusers on how to
implement this with omegas and sigmas fixed to one). With this trick all
parameters were reported out as thetas and then I simply used rmvnorm and the
covariance matrix from NONMEM to then accomplish the task. The results looked
reasonable and I was wondering if anybody has any experience with this trick to
answer the uncertainty question.
Hoping to get feedback...Mahesh
PS. The long-drawn-out way to do this could also be to use results from
bootstrap replicates (e.g. nmbs with WFN) to simulate across variability and
uncertainty. This is sometimes not very practical if the bootstrap run takes
days (or weeks) to run. See PAGE poster for implementation:
http://www.page-meeting.org/?abstract=1220
Quoted reply history
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of Smith, Mike K
Sent: Monday, November 26, 2007 9:56 AM
To: [email protected]
Subject: [NMusers] Simulation for future populations and diagnostics
If we're simulating data for a future population (= new trial or new as yet
unstudied population) then am I right in thinking that in order to "do the
correct thing" we should really be simulating across uncertainty in not just
THETA, but also OMEGA and SIGMA? This would be my understanding of what
happens in fully Bayesian prediction, integrating out over the current
posterior of *all* model parameters. My understanding is that this isn't
always done when simulating new data. We often simulate taking into
consideration uncertainty in THETA (sampling from Multivariate Normal) but
ignore uncertainty in OMEGA. I suppose that one could argue that if we have
data for a large number of subjects who are "exchangeable" with the subjects we
are simulating for then this doesn't matter much. But in other cases this may
be important. One difficulty (as mentioned previously on the this list) is the
problem of specifying the appropriate inverse-Wishart distribution for the
OMEGA matrix and then simulating from it.
In simulating data for the current population (= model diagnostics) I don't
think you need to acknowledge uncertainty in OMEGA, unless you're doing full
PPCs. Does this sound right? In that case the population you are describing
is the data you have... Again, it would be useful to know what people
currently *do* as well as what is "the correct thing".
If anybody has useful references on this topic I would really appreciate it. I
have spotted and downloaded Leonid Gibiansky and Marc Gastonguay's poster on
the R/NONMEM Toolbox from PAGE, but haven't found much else.
Cheers,
Mike
Mike K. Smith
Pharmacometrics
PGRD, Sandwich
Location: 509/1.117 (IPC 096)
Tel: +44 (0)1304 643561
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