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RE: [NMusers] $PRIOR with normal for OMEGA?

From: Mats Karlsson <Mats.Karlsson_at_farmbio.uu.se>
Date: Fri, 11 Nov 2016 07:36:13 +0000

Hi Mark,

As I’m sure you know NONMEM has the TNPRI functionality for that. If you want to use it without the TNPRI functionality, you can estimate OMEGA as THETA and use a multivariate normal for that. If you have off-diagonal elements, you may want to do a Cholesky transformation (you can get that automatically in PsN).

As Andy writes there are pros and cons with different priors. While IW has a better shape to its prior for variances, it is problematic that there is no correlation between the typical value estimates and their variances.

Best regards,
Mats


Mats Karlsson, PhD
Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
75124 Uppsala

Phone: +46 18 4714105
Fax + 46 18 4714003
www.farmbio.uu.se/research/researchgroups/pharmacometrics/<http://www.farmbio.uu.se/research/researchgroups/pharmacometrics/>

From: owner-nmusers_at_globomaxnm.com [mailto:owner-nmusers_at_globomaxnm.com] On Behalf Of Gewitz, Andrew
Sent: Friday, November 11, 2016 6:53 AM
To: Mark Sale
Cc: nmusers_at_globomaxnm.com
Subject: Re: [NMusers] $PRIOR with normal for OMEGA?

Mark,

Without getting too technical, recall that the inverse wishart is a distribution on matrices, and is naturally conjugate to the multivariate normal distribution (i.e. on vectors of random variables.) Generally, this is chosen because posterior computations are simplified and it is easy to sample from this posterior distribution.

What you're suggesting is the Matrix Normal distribution. Since it is not conjugate to the multivariate normal, posterior computations can cause headaches. So while it is *possible* to use such a distribution as a prior, it is cumbersome to work with in practice and requires thinking about some things like correlation and scale in non straightforward ways.




--------------
Andy Gewitz, PhD
Bioengineering and Therapeutic Sciences
University of California, San Francisco

On Nov 10, 2016, at 7:57 PM, Mark Sale <msale_at_nuventra.com<mailto:msale_at_nuventra.com>> wrote:

Is it possible to use a normal prior for OMEGA? The default is inverse Wishart, but I'd be interested in using Normal (insuring that it is positive definite) Any ideas?

thanks





Mark Sale M.D.
Vice President, Modeling and Simulation
Nuventra Pharma Sciences, Inc.
2525 Meridian Parkway, Suite 280
Durham, NC 27713
Phone (919)-973-0383
msale_at_nuventra.com<msale_at_kinetigen.com>
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Received on Fri Nov 11 2016 - 02:36:13 EST

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