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

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

_____

The information contained in this email message may contain confidential or

legally privileged information and is intended solely for the use of the

named recipient(s). No confidentiality or privilege is waived or lost by any

transmission error. If the reader of this message is not the intended

recipient, please immediately delete the e-mail and all copies of it from

your system, destroy any hard copies of it and notify the sender either by

telephone or return e-mail. Any direct or indirect use, disclosure,

distribution, printing, or copying of any part of this message is

prohibited. Any views expressed in this message are those of the individual

sender, except where the message states otherwise and the sender is

authorized to state them to be the views of XOMA.

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