t-distribution in NONMEM?

4 messages 2 people Latest: Jul 25, 2003

t-distribution in NONMEM?

From: Yaning Wang Date: July 23, 2003 technical
From: "WANG,YANING" <yaning@ufl.edu> Subject: [NMusers] t-distribution in NONMEM? Date: Wed, 23 Jul 2003 01:43:26 -0400 (EDT) Dear NONMEM users: According to NONMEM user guide, normal distribution is only used for demonstration convenience and not the only distribution available for data analysis. Has anyone tried other distributions for modeling, such as t-distribution to make the model more robust to outliers? How can this be done? Any input is appreciated! Thanks in advance. Yaning Wang Department of Pharmaceutics College of Pharmacy University of Florida

RE: t-distribution in NONMEM?

From: Vladimir Piotrovskij Date: July 24, 2003 technical
From: VPIOTROV@PRDBE.jnj.com Subject: RE: [NMusers] t-distribution in NONMEM? Date: Thu, 24 Jul 2003 15:25:04 +0200 Yaning, To the best of my knowledge, you cannot use t-distribution in NONMEM. At least, I cannot recall any easy way to do it for estimation. There is, however, an approach that allows to improve the fit in case of heavily tailed distributions of observations. It is based on the assumption that the study population is not homogeneous, but includes groups of individuals which differ in their residual variability. This can be implemented using $MIX option of NONMEM. An example can be found in the NONMEM users archive ( http://www.cognigencorp.com/nonmem/nm/99aug102000.html). This is also applicable to the situation of heavy-tailed distribution of PK parameters, say, CL. Best regards, Vladimir ----------------------------------------------------------------- Vladimir Piotrovsky, Ph.D. Research Fellow, Advanced PK-PD Modeling & Simulation Global Clinical Pharmacokinetics and Clinical Pharmacology (ext. 5463/151) Johnson & Johnson Pharmaceutical Research & Development Turnhoutseweg 30 B-2340 Beerse Belgium

t-distribution =scaled mixture of normal distributions

From: Yaning Wang Date: July 24, 2003 technical
From: "WANG,YANING" <yaning@ufl.edu> Subject: [NMusers] t-distribution =scaled mixture of normal distributions Date: Thu, 24 Jul 2003 10:52:28 -0400 (EDT) Dear Dr. Piotrovsky: Thanks for your response. It seems that NONMEM has to turn to the original way of dealing with t-distribution--scaled mixture of normal distributions (to be exact, scaled by a gamma distribution). Maybe it is easier to explain the results in terms of a heterogeneous population with different normal distributions rather than a general t-distribution with a degree of freedom. Is this the reason why NONMEM doesn't have t-distribution which is quite common in most of other softwares? Thanks Yaning Wang Department of Pharmaceutics College of Pharmacy University of Florida

RE: t-distribution =scaled mixture of normal distributions

From: Vladimir Piotrovskij Date: July 25, 2003 technical
From: VPIOTROV@PRDBE.jnj.com Subject: [NMusers] RE: t-distribution =scaled mixture of normal distributions Date: Fri, 25 Jul 2003 10:22:14 +0200 Dear Yaning, I am not sure about other softwares. The two nonlinear mixed-effects program I used myself: nlme (in S-PLUS of R) and WinNonMix, are based on the normality assumption. As to NONMEM, the idea I introduced 3 years ago about the mixture of normals at the level of the residual error had no connection to the t-distribution. Moreover, the residual error distribution with an individual is still normal, and I do not know how to make it t-distributed. Best regards, Vladimir ----------------------------------------------------------------- Vladimir Piotrovsky, Ph.D. Research Fellow, Advanced PK-PD Modeling & Simulation Global Clinical Pharmacokinetics and Clinical Pharmacology (ext. 5463/151) Johnson & Johnson Pharmaceutical Research & Development Turnhoutseweg 30 B-2340 Beerse Belgium _______________________________________________________