From: Mats Karlsson <*mats.karlsson*>

Date: Thu, 16 Apr 2009 09:05:00 +0200

Hi Diane,

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. Also, if the underlying model

truly is a mixture model on F, it could be parsimonious, needing mixture

only one parameter only. You can't have IIV on CL, V and relF + off-diagonal

elements without overparameterizing the model. However, although I have

never tried it, I guess that a BLOCK(2) on CL and relative F could work,

provided you have no ETA on V. If you also have an ETA on V all the problems

you mention would be realized. I don't know if Nele has IIV on V, but if so,

she should definitely reduce IIV model size. With respect to the mixture

model, maybe it is possible to reparameterize such that the mixture

component only concerns one ETA.

Best regards,

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

From: Diane R Mould [mailto:drmould

Sent: Wednesday, April 15, 2009 6:16 PM

To: 'Mats Karlsson'; nele.plock

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

Dear All

I am not sure if this topic has been covered before or not, but as its

related to the question below, I thought I would bring it up again.

I have to wonder at the appropriateness of including the IIV term for F in

an omega BLOCK structure in the first place? I can certainly understand

estimating relative bioavailability and even estimating the associated

variability for F, although there are often estimatability issues for an IIV

term for F, even with IV data to help estimate F (or at least using a

reference value for F like one formulation or one occasion).

However because with orally administered drugs, CL is really CL/F then there

is an inherent correlation between CL and F. With F and CL, this

correlation is really in the THETA values so that if the model captures the

correlation at the THETA level, ie allow for larger clearance with larger F

(or vice versa), then the random effects for F and CL may be uncorrelated.

However, if the population model does not capture that correlation at the

THETA level, then correlation will be captured via the random effects,

possibly resulting in an over-parameterized OMEGA matrix. As this latter

situation seems to be very common (e.g. that the correlation between F and

CL etc is picked up in the etas) then one might expect to see high condition

numbers, zero gradients etc when IIV on F is added to the omega BLOCK

structure.

I would guess that as a rule, its probably more appropriate to keep the IIV

term for F out of a BLOCK structure. Can anybody comment on this?

Best regards,

Diane

_____

From: owner-nmusers

Behalf Of Mats Karlsson

Sent: Tuesday, April 14, 2009 2:08 PM

To: nele.plock

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

Dear Nele,

I think you may want to reconsider your model. If you have a negative

correlation between CL and F1, it is likely to be related to high

presystemic metabolism (first-pass) effect. If so, it seems strange to

assume that the F1 distribution would not change between the two

subpopulations. I think you need to have separate CL as well as F1 for the

two subpopulations. Thus I would have CL and F1 described by ETA(1) and

ETA(2) for subpopulation 1 and CL and F1 described by ETA(3) and ETA(4) for

the second subpopulation. If hepatic elimination is responsible for the

correlation, it is probably more parsimonious to use a semi-mechanistic

model with a hepatic compartment (with a single ETA for variation in

metabolic activity). Two examples of implementations of a separate hepatic

compartment are :

Piotrovskij et al. Pharm Res. 1997 Feb;14(2):230-7.

Gordi et al., Br J Clin Pharmacol. 2005 Feb;59(2):189-98

Best regards,

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

From: owner-nmusers

Behalf Of nele.plock

Sent: Tuesday, April 14, 2009 5:09 PM

To: nmusers

Subject: [NMusers] OMEGA BLOCK with mixture model?

Dear all,

I am trying to fit a PK model to oral data. In the data, we observed two

things: First, CL seems to be negatively correlated with F1. Secondly, there

seem to be two subpopulations in the exposure, let's say a large group with

'normal' and a second group with high exposure. I would like to identify the

subpopulations using a mixture model, but keep the correlation between CL

and F1. Now I ran into problems when coding the $OMEGA BLOCK.

I figured the block to be something like:

$OMEGA BLOCK(3)

0.1 ;CL1

0 FIX 0.1 ;CL2

0.01 0.01 0.1 ;F1

The error message that appears is:

a covariance is zero, but the block is not a band matrix

I assume that this means that I am not allowed to fix the correlation

between the two clearance-omegas to zero. However, it would be unreasonable

to allow a correlation, because the omegas belong to different

subpopulations, so there can't be a correlation. On the other hand, I did

not include subpopulations for F1, so how can I keep this correlation to

both CL-subgroups?

Any thoughts on this would be highly appreciated!

Best wishes

Nele

______________________________________________________________

Dr. Nele Plock

Pharmacometrics -- Modeling and Simulation

Nycomed GmbH

Byk-Gulden-Str. 2

D-78467 Konstanz, Germany

Fon: (+49) 7531 / 84 - 4759

Fax: (+49) 7531 / 84 - 94759

mailto: nele.plock

http://www.nycomed.com

County Court: Freiburg, Commercial Register HRB 701257

Chairman Supervisory Board: Charles Depasse

Management Board: Dr. Barthold Piening, Gilbert Rademacher, Dr. Anders

Ullman

----------------------------------------------------------------------

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be contained in this message. If you are not the addressee indicated

in this message, please do not copy or deliver this message to anyone.

In such case, please destroy this message and notify the sender by

reply e-mail. Please advise the sender immediately if you or your

employer do not consent to Internet e-mail for messages of this kind.

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pertain to the sender's employer and its products and services

represent the opinion of the sender and do not necessarily represent

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----------------------------------------------------------------------

Received on Thu Apr 16 2009 - 03:05:00 EDT

Date: Thu, 16 Apr 2009 09:05:00 +0200

Hi Diane,

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. Also, if the underlying model

truly is a mixture model on F, it could be parsimonious, needing mixture

only one parameter only. You can't have IIV on CL, V and relF + off-diagonal

elements without overparameterizing the model. However, although I have

never tried it, I guess that a BLOCK(2) on CL and relative F could work,

provided you have no ETA on V. If you also have an ETA on V all the problems

you mention would be realized. I don't know if Nele has IIV on V, but if so,

she should definitely reduce IIV model size. With respect to the mixture

model, maybe it is possible to reparameterize such that the mixture

component only concerns one ETA.

Best regards,

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

From: Diane R Mould [mailto:drmould

Sent: Wednesday, April 15, 2009 6:16 PM

To: 'Mats Karlsson'; nele.plock

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

Dear All

I am not sure if this topic has been covered before or not, but as its

related to the question below, I thought I would bring it up again.

I have to wonder at the appropriateness of including the IIV term for F in

an omega BLOCK structure in the first place? I can certainly understand

estimating relative bioavailability and even estimating the associated

variability for F, although there are often estimatability issues for an IIV

term for F, even with IV data to help estimate F (or at least using a

reference value for F like one formulation or one occasion).

However because with orally administered drugs, CL is really CL/F then there

is an inherent correlation between CL and F. With F and CL, this

correlation is really in the THETA values so that if the model captures the

correlation at the THETA level, ie allow for larger clearance with larger F

(or vice versa), then the random effects for F and CL may be uncorrelated.

However, if the population model does not capture that correlation at the

THETA level, then correlation will be captured via the random effects,

possibly resulting in an over-parameterized OMEGA matrix. As this latter

situation seems to be very common (e.g. that the correlation between F and

CL etc is picked up in the etas) then one might expect to see high condition

numbers, zero gradients etc when IIV on F is added to the omega BLOCK

structure.

I would guess that as a rule, its probably more appropriate to keep the IIV

term for F out of a BLOCK structure. Can anybody comment on this?

Best regards,

Diane

_____

From: owner-nmusers

Behalf Of Mats Karlsson

Sent: Tuesday, April 14, 2009 2:08 PM

To: nele.plock

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

Dear Nele,

I think you may want to reconsider your model. If you have a negative

correlation between CL and F1, it is likely to be related to high

presystemic metabolism (first-pass) effect. If so, it seems strange to

assume that the F1 distribution would not change between the two

subpopulations. I think you need to have separate CL as well as F1 for the

two subpopulations. Thus I would have CL and F1 described by ETA(1) and

ETA(2) for subpopulation 1 and CL and F1 described by ETA(3) and ETA(4) for

the second subpopulation. If hepatic elimination is responsible for the

correlation, it is probably more parsimonious to use a semi-mechanistic

model with a hepatic compartment (with a single ETA for variation in

metabolic activity). Two examples of implementations of a separate hepatic

compartment are :

Piotrovskij et al. Pharm Res. 1997 Feb;14(2):230-7.

Gordi et al., Br J Clin Pharmacol. 2005 Feb;59(2):189-98

Best regards,

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

From: owner-nmusers

Behalf Of nele.plock

Sent: Tuesday, April 14, 2009 5:09 PM

To: nmusers

Subject: [NMusers] OMEGA BLOCK with mixture model?

Dear all,

I am trying to fit a PK model to oral data. In the data, we observed two

things: First, CL seems to be negatively correlated with F1. Secondly, there

seem to be two subpopulations in the exposure, let's say a large group with

'normal' and a second group with high exposure. I would like to identify the

subpopulations using a mixture model, but keep the correlation between CL

and F1. Now I ran into problems when coding the $OMEGA BLOCK.

I figured the block to be something like:

$OMEGA BLOCK(3)

0.1 ;CL1

0 FIX 0.1 ;CL2

0.01 0.01 0.1 ;F1

The error message that appears is:

a covariance is zero, but the block is not a band matrix

I assume that this means that I am not allowed to fix the correlation

between the two clearance-omegas to zero. However, it would be unreasonable

to allow a correlation, because the omegas belong to different

subpopulations, so there can't be a correlation. On the other hand, I did

not include subpopulations for F1, so how can I keep this correlation to

both CL-subgroups?

Any thoughts on this would be highly appreciated!

Best wishes

Nele

______________________________________________________________

Dr. Nele Plock

Pharmacometrics -- Modeling and Simulation

Nycomed GmbH

Byk-Gulden-Str. 2

D-78467 Konstanz, Germany

Fon: (+49) 7531 / 84 - 4759

Fax: (+49) 7531 / 84 - 94759

mailto: nele.plock

http://www.nycomed.com

County Court: Freiburg, Commercial Register HRB 701257

Chairman Supervisory Board: Charles Depasse

Management Board: Dr. Barthold Piening, Gilbert Rademacher, Dr. Anders

Ullman

----------------------------------------------------------------------

Proprietary or confidential information belonging to Nycomed Group may

be contained in this message. If you are not the addressee indicated

in this message, please do not copy or deliver this message to anyone.

In such case, please destroy this message and notify the sender by

reply e-mail. Please advise the sender immediately if you or your

employer do not consent to Internet e-mail for messages of this kind.

Opinions, conclusions and other information in this message that

pertain to the sender's employer and its products and services

represent the opinion of the sender and do not necessarily represent

or reflect the views and opinions of the employer.

----------------------------------------------------------------------

Received on Thu Apr 16 2009 - 03:05:00 EDT