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: [email protected] [mailto:[email protected]] On Behalf Of Ethan Wu Sent: Friday, May 28, 2010 2:27 PM To: Serge Guzy; [email protected] 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 <[email protected]> To: Ethan Wu <[email protected]>; [email protected] 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: [email protected] [mailto:[email protected]] On Behalf Of Ethan Wu Sent: Friday, May 28, 2010 9:08 AM To: [email protected] 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.
