# Re: distribution assumption of Eta in NONMEM

From: Nick Holford <n.holford>
Date: Sat, 29 May 2010 08:40:29 +0100

Bob,

Thanks for pointing out that one cannot use NONMEM to describe the
Cauchy distribution. Presumably this explains why we dont seem to have
many physicists on nmusers :-). The normal assumption for NONMEM
simulation seems to be well accepted so no simulated spectral lines I'm
afraid.

However, can you (or anyone) else point out precisely if NONMEM makes
an assumption of normality in its estimation procedure (the answer will
presumably depend on which estimation method is chosen) ?

Juergen suggested the MCPEM flavour of EM requires a normal assumption
for the estimation. But what about SAEM, FOCE, BAYES, etc.?

Nick

Bob Leary wrote:
> Nick -
> a slight correction. Not all distributions have a variance - the most
> familiar and important example
> is the Cauchy distribution (1/pi) *1/(1+x^2) - the variance integral
> is infinite.
>
> This is actually a significant distribution in physics,
> representing the shape of certain spectral
> lines. It is also related to the Poisson kernel in solving Laplace
> equations.
>
> Bob
> ------------------------------------------------------------------------
>
>
> *From:* owner-nmusers
> Behalf Of Nick Holford [n.holford
> *Sent:* Friday, May 28, 2010 2:50 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 <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
>> [mailto:owner-nmusers
>> *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
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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 - 03:40:29 EDT

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