# Re: distribution assumption of Eta in NONMEM

From: Ethan Wu <ethan.wu75>
Date: Fri, 28 May 2010 13:26:20 -0700 (PDT)

Hi Mat and all,    if I understand correctly with my limted stat k=
nowledge,  I guess it is fair to say NONMEM dose not explicitly assume no=
rmal distribution for Eta, but it is approximate (or assymptotical) to a =
normal distribution during the actual estimating.      This is wh=
y when we simulate, it is OK to use the Eta estimate and assume it is n=
ormal distributed to draw the random subjects.   ________=
________________________ From: Matt Hutmacher <matt.hutmacher

s] distribution assumption of Eta in NONMEM Hi Ethan,   If th=
e random effects (etas) enter the model in a nonlinear way, then (consideri=
ng NONMEM VI or lower) one would consider an approximation to the overall l=
ikelihood which was based on assuming the random effects were normally dist=
ributed (Laplace approximation).  If however, the random effects enter th=
e 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 t=
he marginal variance (based on the random effects and epsilons) are correct=
ly specified.  This property holds even if the data are not normally dist=
ributed.   If the data are normal, then extended least squares is essen=
tially 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)   Be=
st, Matt   From:owner-nmusers
globomaxnm.com] On Behalf Of Ethan Wu Sent: Friday, May 28, 2010 2:27 PM=

tion assumption of Eta in NONMEM   I could not find in the NONMEM hel=
p guide that explicitly mentioned a normal distribution is assumed, only it=
was clearly mentioned of assumption of mean of zero.   __________=
______________________ From:Serge Guzy <GUZY
<ethan.wu75
25:24 PM Subject: RE: [NMusers] distribution assumption of Eta in NONMEM=

ion programs like NONMEM, SADAPT, PDX-MC-PEM and SAEM. Therefore when you s=
imulate, random values from a normal distribution are generated. However, y=
ou have the flexibility to use any transformation to create distributions f=
or your model parameters that will depart from pure normality. For example,=
CL=theta(1)*exp(eta(1)) will  generate a log-normal distribution for t=
he clearance although the random deviates are all from the normal distribut=
ion. I am not sure how you can simulate data sets if you are using the n=
on parametric option that is indeed available in NONMEM. Serge Guzy; Ph.D=

rom:owner-nmusers
ehalf Of Ethan Wu Sent: Friday, May 28, 2010 9:08 AM To: nmusers
axnm.com Subject: [NMusers] distribution assumption of Eta in NONMEM =
Dear users,   Is it true NONMEM dose not assume Eta a normal di=
stribution?   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 - 16:26:20 EDT

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