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-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Nick Holford Sent: Friday, May 28, 2010 3:51 PM To: nmusers@globomaxnm.com 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 <g...@xoma.com><mailto:g...@xoma.com> To: Ethan Wu <ethan.w...@yahoo.com><mailto:ethan.w...@yahoo.com>; nmusers@globomaxnm.com<mailto:nmusers@globomaxnm.com> 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-nmus...@globomaxnm.com<mailto:owner-nmus...@globomaxnm.com> [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Ethan Wu Sent: Friday, May 28, 2010 9:08 AM To: nmusers@globomaxnm.com<mailto:nmusers@globomaxnm.com> 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: n.holf...@auckland.ac.nz<mailto:n.holf...@auckland.ac.nz> http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
