# RE: distribution assumption of Eta in NONMEM

From: Matt Hutmacher <matt.hutmacher>
Date: Fri, 28 May 2010 14:43:04 -0400

Hi Ethan,

If the random effects (etas) enter the model in a nonlinear way, then
(considering NONMEM VI or lower) one would consider an approximation to the
overall likelihood which was based on assuming the random effects were
normally distributed (Laplace approximation). If however, the random
effects enter the model in an additive way, no approximation is necessary.
In this case, assumptions about the random effects are not as critical for
estimation. The extended least squares estimates of the fixed effects and
variance components of the model are consistent and asymptotically normal
provided the marginal variance (based on the random effects and epsilons)
are correctly specified. This property holds even if the data are not
normally distributed. If the data are normal, then extended least squares
is essentially maximum likelihood and you get an efficiency to your
estimates. (my statements are based on Chapter 9 of Linear and Nonlinear
Models for the Analysis of Repeated Measurements by Vonesh and Chinchilli)

Best,
Matt

From: owner-nmusers
Behalf Of Ethan Wu
Sent: Friday, May 28, 2010 2:27 PM
To: Serge Guzy; nmusers
Subject: Re: [NMusers] distribution assumption of Eta in NONMEM

I could not find in the NONMEM help guide that explicitly mentioned a normal
distribution is assumed, only it was clearly mentioned of assumption of mean
of zero.

_____

From: Serge Guzy <GUZY
To: Ethan Wu <ethan.wu75
Sent: Fri, May 28, 2010 1:25:24 PM
Subject: RE: [NMusers] distribution assumption of Eta in NONMEM

As far as I know, this is the assumption in most of the population programs
like NONMEM, SADAPT, PDX-MC-PEM and SAEM. Therefore when you simulate,
random values from a normal distribution are generated. However, you have
the flexibility to use any transformation to create distributions for your
model parameters that will depart from pure normality. For example,
CL=theta(1)*exp(eta(1)) will generate a log-normal distribution for the
clearance although the random deviates are all from the normal distribution.

I am not sure how you can simulate data sets if you are using the non
parametric option that is indeed available in NONMEM.

Serge Guzy; Ph.D

President, CEO, POP_PHARM

www.poppharm.com <http://www.poppharm.com/>

From: owner-nmusers
Behalf Of Ethan Wu
Sent: Friday, May 28, 2010 9:08 AM
To: nmusers
Subject: [NMusers] distribution assumption of Eta in NONMEM

Dear users,

Is it true NONMEM dose not assume Eta a normal distribution?

If it does not, I wonder what distribution it assumes? I guess this is
critical when we do simulations.

Thanks

_____

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Received on Fri May 28 2010 - 14:43:04 EDT

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