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 
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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


_______________________________________________________

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 
_______________________________________________________

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

_______________________________________________________