From: Stephen Duffull <*stephen.duffull*>

Date: Fri, 17 Apr 2009 09:15:11 +1200

Mats

Thanks for your succinct summary.

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

acted from a BLOCK and estimated as a separate DIAG variance term. The cor=

relation 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 ha=

ve 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.)

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

red this possibility.

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

tive correlation). I think parsimony might be more important with NONMEM u=

sing gradient search algorithms than SAEM algorithms. If a later version o=

f NONMEM includes different search algorithms then perhaps some of difficul=

ties that we have here and that Nele had in her example will be less of an =

issue.

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 Thu Apr 16 2009 - 17:15:11 EDT

Date: Fri, 17 Apr 2009 09:15:11 +1200

Mats

Thanks for your succinct summary.

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

acted from a BLOCK and estimated as a separate DIAG variance term. The cor=

relation 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 ha=

ve 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.)

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

red this possibility.

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

tive correlation). I think parsimony might be more important with NONMEM u=

sing gradient search algorithms than SAEM algorithms. If a later version o=

f NONMEM includes different search algorithms then perhaps some of difficul=

ties that we have here and that Nele had in her example will be less of an =

issue.

Steve

--

Received on Thu Apr 16 2009 - 17:15:11 EDT