Re: distribution assumption of Eta in NONMEM

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:* [email protected] [ [email protected] ] On Behalf Of Nick Holford [ [email protected] ] > > *Sent:* Friday, May 28, 2010 2:50 PM > *To:* [email protected] > *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 <[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. > > -- > 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: [email protected] > http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford > _________________________________________________________________ >