[NMusers] OMEGA priors using modes of inverse Wishart matrix

[Joachim Grevel]

Dear NMusers,

Our NONMEM User Guides are full of good advice and they are searchable. Yet
when I tried to find out whether any of the estimation methods could be
enticed to give me the “inverse Wishart matrix” needed to specify PRIORS for
OMEGAs, I found no help. Leonid G. mentions the inverse Wishart matrix in
his historic contributions to NMusers, but again I could not find out how to
obtain it. If it does not happen in NONMEM, is there a tool in R that can
give me that matrix?

Your help is greatly appreciated,

 

Joachim

 

Joachim Grevel, PhD

Scientific Director

BAST Inc Limited

BioCity Nottingham

Pennyfoot Street

Nottingham, NG1 1GF

Tel: +44 (0)115 8120497

 

Re: [NMusers] OMEGA priors using modes of inverse Wishart matrix

[Tim Bergsma]

Joachim,

Please see the CRAN package "metrumrg".  Look for the function
"riwish", written by Leonid Gibiansky.  Any errors are mine
(maintainer).

-Tim

Tim Bergsma, PhD
Metrum Research Group LLC
Tariffville, CT
860-930-9931

On Wed, Feb 22, 2012 at 7:53 AM, Joachim Grevel  wrote:
> Dear NMusers,
>
> Our NONMEM User Guides are full of good advice and they are searchable. Yet
> when I tried to find out whether any of the estimation methods could be
> enticed to give me the “inverse Wishart matrix” needed to specify PRIORS for
> OMEGAs, I found no help. Leonid G. mentions the inverse Wishart matrix in
> his historic contributions to NMusers, but again I could not find out how to
> obtain it. If it does not happen in NONMEM, is there a tool in R that can
> give me that matrix?
>
> Your help is greatly appreciated,
>
>
>
> Joachim
>
>
>
> Joachim Grevel, PhD
>
> Scientific Director
>
> BAST Inc Limited
>
> BioCity Nottingham
>
> Pennyfoot Street
>
> Nottingham, NG1 1GF
>
> Tel: +44 (0)115 8120497
>
>

RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

[Joachim Grevel]

Dear Coen,

 

There I do have the answer: with MCMC Bayesian in NONMEM 7.1 you have to use
NWPRI according to the guide.

 

Dear Nidal,

 

What I try to do is that: use an existing very well defined popPK model
(2500 conc in 200 patients) to obtain individual PK parameters in only 20
additional patients that have sparse sampling (2 to 4 conc per patient). I
was planning to use informative priors rather than add 80 conc  to a bulk of
2500 conc. What do you think?

 

Thanks to all, specifically Tim!

 

Joachim

 

From: Coen van Hasselt [mailto:coen.vanhass...@slz.nl] 
Sent: 22 February 2012 14:03
To: jgre...@o2.co.uk
Subject: Re: [NMusers] OMEGA priors using modes of inverse Wishart matrix

 

Dear Joachim,

I have always wondered about this particular question myself as well..
Thanks for asking at NMusers.

Another thing related to the PRIORs I was wondering about: you can either
use NWPRI (i.e. with the inverse wishart for OMEGA's), or TNPRI, which uses
a multivariate normal for the OMEGA's. Do you have any idea when to use
either of these two possible implementations ?

Thanks,
Coen

>>> "Joachim Grevel" 02/22/12 2:11 PM >>>



Dear NMusers,

Our NONMEM User Guides are full of good advice and they are searchable. Yet
when I tried to find out whether any of the estimation methods could be
enticed to give me the ?inverse Wishart matrix? needed to specify PRIORS for
OMEGAs, I found no help. Leonid G. mentions the inverse Wishart matrix in
his historic contributions to NMusers, but again I could not find out how to
obtain it. If it does not happen in NONMEM, is there a tool in R that can
give me that matrix?

Your help is greatly appreciated,

 

Joachim

 

Joachim Grevel, PhD

Scientific Director

BAST Inc Limited

BioCity Nottingham

Pennyfoot Street

Nottingham, NG1 1GF

Tel: +44 (0)115 8120497

 

RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

[Mats Karlsson]

Dear Joachim,

 

The IW distribution is not something you get from NONMEM, you have to give
the degrees of freedom of the IW prior distribution. Normally this is at or
below the number of subjects in you previous study depending the information
about the parameter per subject.

 

In addition to User's Guides, you may find useful info in Gisleskog et al J
Pharmacokinet Pharmacodyn. 2002 Dec;29(5-6):473-505.

 

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

 

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On
Behalf Of Joachim Grevel
Sent: 22 February 2012 15:24
To: 'Coen van Hasselt'; nmusers
Subject: RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

 

Dear Coen,

 

There I do have the answer: with MCMC Bayesian in NONMEM 7.1 you have to use
NWPRI according to the guide.

 

Dear Nidal,

 

What I try to do is that: use an existing very well defined popPK model
(2500 conc in 200 patients) to obtain individual PK parameters in only 20
additional patients that have sparse sampling (2 to 4 conc per patient). I
was planning to use informative priors rather than add 80 conc  to a bulk of
2500 conc. What do you think?

 

Thanks to all, specifically Tim!

 

Joachim

 

From: Coen van Hasselt [mailto:coen.vanhass...@slz.nl] 
Sent: 22 February 2012 14:03
To: jgre...@o2.co.uk
Subject: Re: [NMusers] OMEGA priors using modes of inverse Wishart matrix

 

Dear Joachim,

I have always wondered about this particular question myself as well..
Thanks for asking at NMusers.

Another thing related to the PRIORs I was wondering about: you can either
use NWPRI (i.e. with the inverse wishart for OMEGA's), or TNPRI, which uses
a multivariate normal for the OMEGA's. Do you have any idea when to use
either of these two possible implementations ?

Thanks,
Coen

>>> "Joachim Grevel" 02/22/12 2:11 PM >>>

Dear NMusers,

Our NONMEM User Guides are full of good advice and they are searchable. Yet
when I tried to find out whether any of the estimation methods could be
enticed to give me the ?inverse Wishart matrix? needed to specify PRIORS for
OMEGAs, I found no help. Leonid G. mentions the inverse Wishart matrix in
his historic contributions to NMusers, but again I could not find out how to
obtain it. If it does not happen in NONMEM, is there a tool in R that can
give me that matrix?

Your help is greatly appreciated,

 

Joachim

 

Joachim Grevel, PhD

Scientific Director

BAST Inc Limited

BioCity Nottingham

Pennyfoot Street

Nottingham, NG1 1GF

Tel: +44 (0)115 8120497

 

RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

[Ayyappa Chaturvedula]

Joachim,

I found the following also useful in calculating df from IW distribution.

Dansirikul C, Morris RG, Tett SE, Duffull SB.
A Bayesian approach for population pharmacokinetic modelling of sirolimus. Br J 
Clin Pharmacol. 2006 Oct;62(4):420-34.


Regards,
Ayyappa


From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On 
Behalf Of Mats Karlsson
Sent: Wednesday, February 22, 2012 9:58 AM
To: 'Joachim Grevel'; 'Coen van Hasselt'; 'nmusers'
Subject: RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

Dear Joachim,

The IW distribution is not something you get from NONMEM, you have to give the 
degrees of freedom of the IW prior distribution. Normally this is at or below 
the number of subjects in you previous study depending the information about 
the parameter per subject.

In addition to User's Guides, you may find useful info in Gisleskog et al J 
Pharmacokinet Pharmacodyn. 2002 Dec;29(5-6):473-505.

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

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On 
Behalf Of Joachim Grevel
Sent: 22 February 2012 15:24
To: 'Coen van Hasselt'; nmusers
Subject: RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

Dear Coen,

There I do have the answer: with MCMC Bayesian in NONMEM 7.1 you have to use 
NWPRI according to the guide.

Dear Nidal,

What I try to do is that: use an existing very well defined popPK model (2500 
conc in 200 patients) to obtain individual PK parameters in only 20 additional 
patients that have sparse sampling (2 to 4 conc per patient). I was planning to 
use informative priors rather than add 80 conc  to a bulk of 2500 conc. What do 
you think?

Thanks to all, specifically Tim!

Joachim

From: Coen van Hasselt 
[mailto:coen.vanhass...@slz.nl]
Sent: 22 February 2012 14:03
To: jgre...@o2.co.uk
Subject: Re: [NMusers] OMEGA priors using modes of inverse Wishart matrix

Dear Joachim,

I have always wondered about this particular question myself as well.. Thanks 
for asking at NMusers.

Another thing related to the PRIORs I was wondering about: you can either use 
NWPRI (i.e. with the inverse wishart for OMEGA's), or TNPRI, which uses a 
multivariate normal for the OMEGA's. Do you have any idea when to use either of 
these two possible implementations ?

Thanks,
Coen

>>> "Joachim Grevel" 02/22/12 2:11 PM >>>
Dear NMusers,
Our NONMEM User Guides are full of good advice and they are searchable. Yet 
when I tried to find out whether any of the estimation methods could be enticed 
to give me the ?inverse Wishart matrix? needed to specify PRIORS for OMEGAs, I 
found no help. Leonid G. mentions the inverse Wishart matrix in his historic 
contributions to NMusers, but again I could not find out how to obtain it. If 
it does not happen in NONMEM, is there a tool in R that can give me that matrix?
Your help is greatly appreciated,

Joachim

Joachim Grevel, PhD
Scientific Director
BAST Inc Limited
BioCity Nottingham
Pennyfoot Street
Nottingham, NG1 1GF
Tel: +44 (0)115 8120497

RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

[Stephen Duffull]

Hi

An appropriate value for dof of the IW is difficult to determine.  While it can 
be set at n-1 from a prior this is somewhat arbitrary.  It is not in this sense 
like a t-distn where we calculate dof in this manner.

You would have to get a feeling for the degree of spread in your deviates given 
your guess at OMEGA(0) and dof.  This can be done by simulation or in special 
circumstances by direct calculation.

Steve
--

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On 
Behalf Of Mats Karlsson
Sent: Thursday, 23 February 2012 3:58 a.m.
To: 'Joachim Grevel'; 'Coen van Hasselt'; 'nmusers'
Subject: RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

Dear Joachim,

The IW distribution is not something you get from NONMEM, you have to give the 
degrees of freedom of the IW prior distribution. Normally this is at or below 
the number of subjects in you previous study depending the information about 
the parameter per subject.

In addition to User's Guides, you may find useful info in Gisleskog et al J 
Pharmacokinet Pharmacodyn. 2002 Dec;29(5-6):473-505.

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

From: owner-nmus...@globomaxnm.com 
[mailto:owner-nmus...@globomaxnm.com] On Behalf Of Joachim Grevel
Sent: 22 February 2012 15:24
To: 'Coen van Hasselt'; nmusers
Subject: RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

Dear Coen,

There I do have the answer: with MCMC Bayesian in NONMEM 7.1 you have to use 
NWPRI according to the guide.

Dear Nidal,

What I try to do is that: use an existing very well defined popPK model (2500 
conc in 200 patients) to obtain individual PK parameters in only 20 additional 
patients that have sparse sampling (2 to 4 conc per patient). I was planning to 
use informative priors rather than add 80 conc  to a bulk of 2500 conc. What do 
you think?

Thanks to all, specifically Tim!

Joachim

From: Coen van Hasselt 
[mailto:coen.vanhass...@slz.nl]
Sent: 22 February 2012 14:03
To: jgre...@o2.co.uk
Subject: Re: [NMusers] OMEGA priors using modes of inverse Wishart matrix

Dear Joachim,

I have always wondered about this particular question myself as well.. Thanks 
for asking at NMusers.

Another thing related to the PRIORs I was wondering about: you can either use 
NWPRI (i.e. with the inverse wishart for OMEGA's), or TNPRI, which uses a 
multivariate normal for the OMEGA's. Do you have any idea when to use either of 
these two possible implementations ?

Thanks,
Coen

>>> "Joachim Grevel" 02/22/12 2:11 PM >>>
Dear NMusers,
Our NONMEM User Guides are full of good advice and they are searchable. Yet 
when I tried to find out whether any of the estimation methods could be enticed 
to give me the ?inverse Wishart matrix? needed to specify PRIORS for OMEGAs, I 
found no help. Leonid G. mentions the inverse Wishart matrix in his historic 
contributions to NMusers, but again I could not find out how to obtain it. If 
it does not happen in NONMEM, is there a tool in R that can give me that matrix?
Your help is greatly appreciated,

Joachim

Joachim Grevel, PhD
Scientific Director
BAST Inc Limited
BioCity Nottingham
Pennyfoot Street
Nottingham, NG1 1GF
Tel: +44 (0)115 8120497

FW: [NMusers] OMEGA priors using modes of inverse Wishart matrix

[Mats Karlsson]

Hi again,

 

We use a formula to come up with a suitable number of subjects (N) for
degrees of freedom (df) for IW distribution. It is based on the assumption
that you know the SE of the variance estimate that you want to use as a
prior. 

 

.  How to choose N?

.  We know 0 < N < Nsubj

.  Guesstimate N

.  Closer to 0 if sparse info per subject

.  Closer to Nsubj if rich info per subject

.  If we know SE of omega, we can do better!

.  Calculate how many subjects with perfect information our SE
corresponds to and then use that N for calculation of df

.  For a variance (omega^2): SE=omega^2*SQRT(2/(N-1))

.  Rearrange to: N=2*omega^4/SE^2+1

.  N   = Estimate of N

.  Omega^2  = Variance estimate (from output of previous model)

.  SE = Standard error of Omega^2 (from output f
previous)

 

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

 

From: Bauer, Robert [mailto:robert.ba...@iconplc.com] 
Sent: 23 February 2012 00:10
To: Mats Karlsson
Cc: chee ng
Subject: FW: [NMusers] OMEGA priors using modes of inverse Wishart matrix

 

Mats:

I think the general formula you gave me in your slides for degrees of
freedom for a prior OMEGA is quite useful to others, as noted below.  Is
this something you could share with nmusers?

 

 

Robert J. Bauer, Ph.D.

Vice President, Pharmacometrics, R&D

ICON Development Solutions

7740 Milestone Parkway

Suite 150

Hanover, MD 21076

Tel: (215) 616-6428

Mob: (925) 286-0769

Email: robert.ba...@iconplc.com

Web: www.iconplc.com  

 

 

  _  

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On
Behalf Of Stephen Duffull
Sent: Wednesday, February 22, 2012 1:09 PM
To: Mats Karlsson; 'Joachim Grevel'; 'Coen van Hasselt'; 'nmusers'
Subject: RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

Hi

 

An appropriate value for dof of the IW is difficult to determine.  While it
can be set at n-1 from a prior this is somewhat arbitrary.  It is not in
this sense like a t-distn where we calculate dof in this manner.

 

You would have to get a feeling for the degree of spread in your deviates
given your guess at OMEGA(0) and dof.  This can be done by simulation or in
special circumstances by direct calculation.

 

Steve

--

 

 

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On
Behalf Of Mats Karlsson
Sent: Thursday, 23 February 2012 3:58 a.m.
To: 'Joachim Grevel'; 'Coen van Hasselt'; 'nmusers'
Subject: RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

 

Dear Joachim,

 

The IW distribution is not something you get from NONMEM, you have to give
the degrees of freedom of the IW prior distribution. Normally this is at or
below the number of subjects in you previous study depending the information
about the parameter per subject.

 

In addition to User's Guides, you may find useful info in Gisleskog et al J
Pharmacokinet Pharmacodyn. 2002 Dec;29(5-6):473-505.

 

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

 

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On
Behalf Of Joachim Grevel
Sent: 22 February 2012 15:24
To: 'Coen van Hasselt'; nmusers
Subject: RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

 

Dear Coen,

 

There I do have the answer: with MCMC Bayesian in NONMEM 7.1 you have to use
NWPRI according to the guide.

 

Dear Nidal,

 

What I try to do is that: use an existing very well defined popPK model
(2500 conc in 200 patients) to obtain individual PK parameters in only 20
additional patients that have sparse sampling (2 to 4 conc per patient). I
was planning to use informative priors rather than add 80 conc  to a bulk of
2500 conc. What do you think?

 

Thanks to all, specifically Tim!

 

Joachim

 

From: Coen van Hasselt [mailto:coen.vanhass...@slz.nl] 
Sent: 22 February 2012 14:03
To: jgre...@o2.co.uk
Subject: Re: [NMusers] OMEGA priors using modes of inverse Wishart matrix

 

Dear Joachim,

I have always wondered about this particular question myself as well..
Thanks for asking at NMusers.

Another thing related to the PRIORs I was wondering about: you can either
use NWPRI (i.e. with the inverse wishart for OMEGA's), or TNPRI, which uses
a multivariate normal for the OMEGA's. Do you have any idea when to use
either of these two possible implementations ?

Thanks,
Coen

>>> "Joachim Grevel" 02/22/12 2:11 PM >>>

Dear NMusers,

Our NONMEM User Guides are full of good advice and they are searchable. Yet
when I tried to