# RE: distribution assumption of Eta in NONMEM

From: Mats Karlsson <mats.karlsson>
Date: Sat, 29 May 2010 10:43:56 +0200

Dear Ethan,

If you want to try a nonparametric method, you can do that already in
NONMEM, using \$NONPARAMETRIC. If you worry about distributional assumptions
this is often a good procedure. Results that agree between \$NONPARAMETRIC
and your parametric methods should give you some comfort. Check in terms of
typical value (an expected nonparametric ETA-value not importantly different
from zero), variance covariance matrix similar for parametric and
non-parametric, and cumulative nonparametric distribution not too
dissimilar to a cumulative normal are things to look out for.

Best regards,

Mats

Mats Karlsson, PhD

Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences

Uppsala University

Box 591

751 24 Uppsala Sweden

phone: +46 18 4714105

fax: +46 18 471 4003

From: owner-nmusers
Behalf Of Jurgen Bulitta
Sent: Friday, May 28, 2010 11:50 PM
To: 'nmusers
Subject: RE: [NMusers] distribution assumption of Eta in NONMEM

Dear Ethan,

There may be two aspects to your question, one is on the

assumptions of the algorithm and software implementation

and one on the use of the models as described by Nick.

To my knowledge, the EM algorithm (e.g. MC-PEM) assumes that the

etas are multivariate normally distributed. As described in Bob's paper [1]

and the underlying theoretical algorithm development work from

Alan Schumitzky [2] and others, the EM algorithm obtains the

maximum likelihood estimates for the population means and the

variance-covariance matrix by calculating the average of the conditional

means and the conditional var-cov matrices of the individual subjects

(see equations 21 and 22 in [1]). These equations assume that the

parameter population density h(theta | mu, Omega) is multivariate

normal. The residual error does not need to follow a normal distribution

(see page E64 in Bob's paper [1]).

Most of the applications of a model are based on simulations

which usually explicitly assume a multivariate normal distribution

(or some transformation thereof). Therefore, it seems fair to say

that for parametric population PK models, most of the inferences

are based on the assumption of a multivariate normal distribution

of the "etas" at one or more stages. We rarely have enough subjects

to assess the appropriateness of this assumption.

You would have to go to a full nonparametric algorithm such as

NPML, NPAG or Bob Leary's new method in Phoenix to not assume

a normal distribution of the "etas".

Best wishes

Juergen

[1] Bauer RJ, Guzy S, Ng C. AAPS J. 2007;9:E60-83.

[2] Schumitzky A . EM algorithms and two stage methods in

pharmacokinetics population analysis. In: D'Argenio DZ , ed. Advanced

Methods of Pharmacokinetic and Pharmacodynamic Systems Analysis.

vol. 2. Boston, MA : Kluwer Academic Publishers ; 1995 :145- 160.

From: owner-nmusers
Behalf Of Nick Holford
Sent: Friday, May 28, 2010 3:51 PM
To: nmusers
Subject: Re: [NMusers] distribution assumption of Eta in NONMEM

For estimation NONMEM estimates one parameter to describe the distribution
of random effects -- this is the variance (OMEGA) of the distribution. Thus
it makes no explicit assumption that the distribution is normal. AFAIK any
distribution has a variance.

For simulation NONMEM assumes all etas are normally distributed. If you use
OMEGA BLOCK(*) then the distribution is multivariate with covariances but
still normal.

Nick

Ethan Wu wrote:

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 <mailto:GUZY
To: Ethan Wu <mailto:ethan.wu75
nmusers
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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--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
email: n.holford
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford

Received on Sat May 29 2010 - 04:43:56 EDT

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