From: Mats Karlsson <*mats.karlsson*>

Date: Sun, 19 Apr 2009 10:01:08 +0200

Hi Steve,

See below.

Mats Karlsson, PhD

Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences

Uppsala University

Box 591

751 24 Uppsala Sweden

phone: +46 18 4714105

fax: +46 18 471 4003

-----Original Message-----

From: Stephen Duffull [mailto:stephen.duffull

Sent: Thursday, April 16, 2009 11:15 PM

To: Mats Karlsson; drmould

nmusers

Subject: RE: [NMusers] OMEGA BLOCK with mixture model?

Mats

Thanks for your succinct summary.

For point 1. In a more general sense I think a covariance term can be

extracted from a BLOCK and estimated as a separate DIAG variance term. The

correlation need not be positive, albeit the variance will be positive.

This is not possible with F in NONMEM due to constraints on its value.

*>>Sure, I was just referring to modeling F1
*

For point 3. I have occasionally compared DIAG(3) with BLOCK(2) and var(F)

was indeed estimated to be greater than cov(CL/F, V/F) and if var(F) had

have been the estimate of cov(CL/F, V/F) then the matrix would not have been

positive definite. (This is only a n=1 experience.)

*>> Normally, OFV and parameter estimates are the same from the two runs with
*

BLOCK2 and DIAG3, with COV(CL/F,V/F) being equal to VAR(F1). If that was not

the case for your runs, it seems they had ended up in different minima.

Rerunning with new initial estimates would likely bring them to the same

minimum.

I like your thoughts on using a mixture on F in NONMEM, I had never

considered this possibility.

I agree with your points on parsimony as well (under the assumption of

positive correlation). I think parsimony might be more important with

NONMEM using gradient search algorithms than SAEM algorithms. If a later

version of NONMEM includes different search algorithms then perhaps some of

difficulties that we have here and that Nele had in her example will be less

of an issue.

*>> Agree
*

Steve

--

*> -----Original Message-----
*

*> From: Mats Karlsson [mailto:mats.karlsson *

*> Sent: Thursday, 16 April 2009 11:07 p.m.
*

*> To: Stephen Duffull; drmould *

*> nele.plock *

*> Subject: RE: [NMusers] OMEGA BLOCK with mixture model?
*

*>
*

*> Hi Steve,
*

*>
*

*> For a one-compartment model I think these are differences:
*

*>
*

*> 1) DIAG(3) is more restrictive than BLOCK(2) in the sense
*

*> that only positive correlation between CL/F and V/F can be estimated
*

*> 2) DIAG(3) is less restrictive than BLOCK(2) in the sense
*

*> that different transformations can be used for F
*

*> 3) DIAG(3) provides an EBE that can be used for diagnostic
*

*> purposes (DIAG(3) and BLOCK(2) would give the same estimates
*

*> for the same model so I don't understand your comment of
*

*> var(F) being higher than cov(CL/F,V/F))
*

*> 4) DIAG(3) may facilitate covariate model building (although
*

*> this is minor as you with BLOCK(2) can put the same
*

*> relationship in in two places)
*

*> 5) If there truly is a mixture in F1, then I think DIAG(3)
*

*> has a advantages over BLOCK(2) in number of parameters (two
*

*> fewer) needed to describe the variability model
*

*> 6) If some additional assumptions can be reliably made, such
*

*> as all variability in F1 is truly in bioavailability and
*

*> bioavailability is restricted to be between 0 and 1, some
*

*> additional info may be extracted from the data for example by .
*

*>
*

*> I would not rank any of these as major differences (expect
*

*> possibly the mixture aspect which I've never tried).
*

*>
*

*> For two- or three-compartment models the advantages are that
*

*> if indeed the main covariance structure between CL/F, V1/F,
*

*> Q/F, V2/F is a joint positive correlation due to variability
*

*> in bioavailability, fu etc, then a DIAG(5) is more
*

*> parsimonious than a BLOCK(4).
*

*>
*

*> Mats
*

*>
*

*> Mats Karlsson, PhD
*

*> Professor of Pharmacometrics
*

*> Dept of Pharmaceutical Biosciences
*

*> Uppsala University
*

*> Box 591
*

*> 751 24 Uppsala Sweden
*

*> phone: +46 18 4714105
*

*> fax: +46 18 471 4003
*

*>
*

*>
*

*> -----Original Message-----
*

*> From: Stephen Duffull [mailto:stephen.duffull *

*> Sent: Thursday, April 16, 2009 10:13 AM
*

*> To: Mats Karlsson; drmould *

*> nele.plock *

*> Subject: RE: [NMusers] OMEGA BLOCK with mixture model?
*

*>
*

*> Mats
*

*>
*

*> > With oral data only I would normally model with BLOCK(2) on
*

*> CL/F and
*

*> > V/F or a DIAG(3) on CL/F, V/F and relative F. The latter
*

*> may have some
*

*> > advantages for diagnostics, covariate model building etc.
*

*>
*

*> I have often seen these two options considered. I am unclear
*

*> as to the advantages of DIAG(3) over BLOCK(2)? In theory it
*

*> would seem that they should be identical. In practice it
*

*> seems that DIAG(3) is more relaxed since it is not required
*

*> that the variance of relative F if reassigned to the
*

*> covariance of (CL/F, V/F) [under BLOCK(2)] yields a positive
*

*> definite matrix.
*

*>
*

*> I presume an advantage wrt covariate model building would be
*

*> access to the EBEs of F_i. However, given the variance of
*

*> F_i may exceed the covariance of (CL/F, V/F) then I wonder if
*

*> this is a real advantage or an artefact of numerical procedures?
*

*>
*

*> I am keen to learn more about real advantages of application
*

*> of DIAG(3) as an alternative to BLOCK(2).
*

*>
*

*> Steve
*

*> --
*

*> Professor Stephen Duffull
*

*> Chair of Clinical Pharmacy
*

*> School of Pharmacy
*

*> University of Otago
*

*> PO Box 913 Dunedin
*

*> New Zealand
*

*> E: stephen.duffull *

*> P: +64 3 479 5044
*

*> F: +64 3 479 7034
*

*>
*

*> Design software: www.winpopt.com
*

*>
*

*>
*

Received on Sun Apr 19 2009 - 04:01:08 EDT

Date: Sun, 19 Apr 2009 10:01:08 +0200

Hi Steve,

See below.

Mats Karlsson, PhD

Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences

Uppsala University

Box 591

751 24 Uppsala Sweden

phone: +46 18 4714105

fax: +46 18 471 4003

-----Original Message-----

From: Stephen Duffull [mailto:stephen.duffull

Sent: Thursday, April 16, 2009 11:15 PM

To: Mats Karlsson; drmould

nmusers

Subject: RE: [NMusers] OMEGA BLOCK with mixture model?

Mats

Thanks for your succinct summary.

For point 1. In a more general sense I think a covariance term can be

extracted from a BLOCK and estimated as a separate DIAG variance term. The

correlation need not be positive, albeit the variance will be positive.

This is not possible with F in NONMEM due to constraints on its value.

For point 3. I have occasionally compared DIAG(3) with BLOCK(2) and var(F)

was indeed estimated to be greater than cov(CL/F, V/F) and if var(F) had

have been the estimate of cov(CL/F, V/F) then the matrix would not have been

positive definite. (This is only a n=1 experience.)

BLOCK2 and DIAG3, with COV(CL/F,V/F) being equal to VAR(F1). If that was not

the case for your runs, it seems they had ended up in different minima.

Rerunning with new initial estimates would likely bring them to the same

minimum.

I like your thoughts on using a mixture on F in NONMEM, I had never

considered this possibility.

I agree with your points on parsimony as well (under the assumption of

positive correlation). I think parsimony might be more important with

NONMEM using gradient search algorithms than SAEM algorithms. If a later

version of NONMEM includes different search algorithms then perhaps some of

difficulties that we have here and that Nele had in her example will be less

of an issue.

Steve

--

Received on Sun Apr 19 2009 - 04:01:08 EDT