Hi,
I tried to see with brute force how well NONMEM can produce an empirical
Bayes estimate when the ETA used for simulation is uniform. I attempted
to stress NONMEM with a non-linear problem (the average DV is 0.62). The
mean estimate of OMEGA(1) was 0.0827 compared with the theoretical value
Nick,
It has been showed over and over again that empirical Bayes estimates, when
individual data is rich, will resemble the true individual parameter regardless
of the underlying distribution. Therefore I don’t understand what you think
this exercise contributes.
Best regards,
Mats
Nick, Mats
I would guess that nonmem should inflate variance (for this example)
trying to fit the observed uniform (-0.5, 0.5) into some normal N(0, ?).
This example (if I read it correctly) shows that Nonmem somehow
estimates variance without making distribution assumption.
Nick, you mention
Mats,
I agree that trying to learn anything from the EBE distribution is a
largely uninformative activity. If the shrinkage is too small then the
EBEs are driven primarily by the data distribution (which is probably
happening in the example I reported) while if they are too big they
shrink t
Leonid,
I meant by OMEGA(1) the OMEGA value estimated by NONMEM. I suppose I
should have written OMEGA(1,1) to be more precise -- sorry!
Nick
Leonid Gibiansky wrote:
Nick, Mats
I would guess that nonmem should inflate variance (for this example)
trying to fit the observed uniform (-0.5, 0.
Sorry - I misread my results. The ETA shrinkage was -0.4% not -40%. I
had forgotten that NONMEM reports the shrinkage as a % not as a fraction.
Nick Holford wrote:
Mats,
I agree that trying to learn anything from the EBE distribution is a
largely uninformative activity. If the shrinkage is t
Leonid,
The result is what I expected. NONMEM just estimates the variance of the
random effects. It doesn't promise to tell you anything about the
distribution.
It is indeed bad news for simulation if your simulation relies heavily
on the assumption of a normal distribution and the true dist
Nick,
I think, transformation idea is the following:
Assume that your (true) model is
CL=POPCL*exp(ETAunif)
where ETAunif is the random variable with uniform distribution.
Assume that you have transformation TRANS that converts normal to
uniform. Then ETAunif can be presented (exactly) as
ETA
Interesting topic. Can anyone provide specific transformations of ETAs that
they have found useful?
Mike Fossler
GSK
-Original Message-
From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On
Behalf Of Leonid Gibiansky
Sent: Monday, May 31, 2010 5:31 PM
To: Nick Ho
Leonid and Mike,
Leonid - you understood the idea.
Mike below are 3 tested transformations from Petersson et al. Pharm Res. 2009
Sep;26(9):2174-85
Box-Cox transformation
TVCL=THETA(1)
BXPAR=THETA(2)
PHI = EXP(ETA(1))
ETATR = (PHI**BXPAR-1)/BXPAR
CL=TVCL*EXP(ETATR)
Heavy tailed transformation
Mike,
For some proprietary analyses I have applied the logit transformation
with succes to normalize the posthocs. It also made the model more
stable, and made it possible to get a covariance step.
This was an example with clearly censored randomization, therefore the
logit shape made a lot of se
Nick,
In your example you simulate and estimate only one random effect. As we are
talking about situations where we have several levels of random effects, I
redid you example with a full model which simulates and estimates with 1 THETA,
1 OMEGA and 1 SIGMA. The data were still made highly
Leonid, Nick,
Plotting the uniform distribution w/o exponentation was useful to me (R
code):
hist(runif(100))
hist(runif(1000))
hist(exp(runif(100)))
hist(exp(runif(1000)))
hist(exp(runif(1)))
- Also after exponentation, the uniform distribution has very sharp
edges. I have never encountered s
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