Post-hoc distributions

From: "Bonate, Peter, HMR/US" <Peter.Bonate@hmrag.com> Subject: Post-hoc distributions Date: Wed, 7 Oct 1998 16:03:01 -0500 Maybe someone can explain something to me. Assume that you specify in your structural model that a parameter is log-normal distributed. Then you use first order estimation to get your post-hoc estimates for that parameter. Shouldn't the distribution of the post-hocs be log-normal as well? I have noticed that sometimes they are dramatically different. Thanks. PETER L. BONATE, PhD. Population Pharmacokinetics Hoechst Marion Roussel POB 9627 (F4-M3112) Kansas City, MO 64134 phone: 816-966-3723 fax: 816-966-6999

From: lewis@c255.ucsf.EDU (LSheiner) Subject: Re: Post-hoc distributions Date: Wed, 7 Oct 1998 18:02:11 -0700 When you say "specify in your structural model that a parameter is log-normal distributed." I assume you mean you write something like (*) CL = TVCL*EXP(ETA(1)). [Of course, FO estimates OMEGA according to the model: CL = TVCL*(1+ETA(1)).] The post-hoc etas are indeed computed using (*). The distribution of the post-hoc etas is usually driven by the data, not the log normal "prior" (although this does influence them to be more log-normally distributed than, for example, they might be if a non-parametric prior were used)). If they appear not to be log normally distributed, then your assumption that they are so distributed may be poor. On the other hand, with, say, only 25-50 individuals, it is extremely difficult to rule in or out any particular distributional form, and before you conclude you have a problem, you might want to see if the observed distribution of post-hoc etas deviates significantly from log normal using some appropriate test (such as KS). LBS.