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.

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: [email protected] 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.

Hi Nele, About the technical issue, just change the order of your etas (2 and 3) in order to have the 0 FIX at the place of cov1-3, this gives you what is called a band matrix. Hope it will help! Best regards, Elodie Elodie L. Plan, PharmD, MSc, PhDstudent ******************************************* Department of Pharmaceutical Biosciences, Faculty of Pharmacy, Uppsala University Box 591 - 751 24 Uppsala - SWEDEN Office +46 18 4714385 - Fax +46 18 4714003 ----------------------------------------------------

Nele, You'll need to rearrange/reassign your ETAs so that you can have correlation between CL(1) and F1, and CL(2) and F1, but not CL(1) and CL(2). So, put ETA(1) on CL(1), ETA(2) on F1 and ETA(3) on CL(2), then $OMEGA like this: $OMEGA BLOCK(3) 0.1 ;CL(1) 0.01 0.1 ;F1 0 0.01 0.1 ;CL(2) This is the BAND matrix, which is permitted. Mark Sale MD Next Level Solutions, LLC www.NextLevelSolns.com 919-846-9185

Dear Nele, To figure out the error of NONMEM, you can change the sequence of your OMEGAs, $OMEGA BLOCK(3) 0.1 ;CL1 0.01 0.1 ;F1 0 0.01 0.1 ;CL2 Make the corresponding change in the $PK block. Regards, Chenguang

This should do the trick (rename ETAs): $OMEGA BLOCK(3) 0.1 ;CL1 0.01 0.1 ;F1 0 0.01 0.1 ;CL2 (do not FIX anything) Although I am not sure whether you need to estimate F1 for oral data (without IV). You could try to use ETA on V instead of ETA on F1. Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 [email protected] wrote: > 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: [email protected] > 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. >

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

Nele, going by the nonmem user manual, part VIII, p 94 ($OMEGA), "If FIXED appears anywhere among the list of values, the entire block is fixed." I did not see anyone pointing that out yet. This does in fact imply that you need to reorder the sequence of random effects (which can be quite a nuisance if you have a sequence of models and the parameters do not correspond any more across models). Andreas ----- Andreas Krause, PhD Lead Scientist Modeling and Simulation Actelion Pharmaceuticals Ltd / Gewerbestrasse 16 / CH-4123 Allschwil / Switzerland phone +41 61 565 6891 / fax +41 61 565 66 96 andreas.krause nele.plock Sent by: owner-nmusers 04/14/2009 05:08 PM To nmusers cc 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. ---------------------------------------------------------------------- The information of this email and in any file transmitted with it is strictly confidential and may be legally privileged. It is intended solely for the addressee. If you are not the intended recipient, any copying, distribution or any other use of this email is prohibited and may be unlawful. In such case, you should please notify the sender immediately and destroy this email. The content of this email is not legally binding unless confirmed by letter. Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorised to state them to be the views of the sender's company. For further information about Actelion please see our website at http://www.actelion.com

Nele, going by the nonmem user manual, part VIII, p 94 ($OMEGA), "If FIXED appears anywhere among the list of values, the entire block is fixed." I did not see anyone pointing that out yet. This does in fact imply that you need to reorder the sequence of random effects (which can be quite a nuisance if you have a sequence of models and the parameters do not correspond any more across models). Andreas ----- Andreas Krause, PhD Lead Scientist Modeling and Simulation Actelion Pharmaceuticals Ltd / Gewerbestrasse 16 / CH-4123 Allschwil / Switzerland phone +41 61 565 6891 / fax +41 61 565 66 96 [email protected] / www.actelion.com [email protected] Sent by: [email protected] 04/14/2009 05:08 PM To [email protected] cc 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: [email protected] 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. ---------------------------------------------------------------------- The information of this email and in any file transmitted with it is strictly confidential and may be legally privileged. It is intended solely for the addressee. If you are not the intended recipient, any copying, distribution or any other use of this email is prohibited and may be unlawful. In such case, you should please notify the sender immediately and destroy this email. The content of this email is not legally binding unless confirmed by letter. Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorised to state them to be the views of the sender's company. For further information about Actelion please see our website at http://www.actelion.com

Hi, It is indeed a nuisance to have to renumber all the ETAs if you have a complex model and you change the sequence of $OMEGA. You can of course choose to use the awk script which comes with WFN ( http://wfn.sourceforge.net ) translate an extended NM-TRAN control stream, which uses parameter names for THETA, ETA and EPS (or ERR) references in the abbreviated code, into a standard NM-TRAN format with all the renumbering taken care of automatically. This awk script can be used with any installation of NONMEM that runs an operating system that has a version of awk available. It is not necessary to use WFN. Typically a one or two line change is needed in your favourite script for running NONMEM to allow the translation to take place. Nick [email protected] wrote: > Nele, > > going by the nonmem user manual, part VIII, p 94 ($OMEGA), "If FIXED appears anywhere among the list of values, the entire block is fixed." > > I did not see anyone pointing that out yet. > > This does in fact imply that you need to reorder the sequence of random effects (which can be quite a nuisance if you have a sequence of models and the parameters do not correspond any more across models). > > Andreas > > ----- > > Andreas Krause, PhD > Lead Scientist Modeling and Simulation > > Actelion Pharmaceuticals Ltd / Gewerbestrasse 16 / CH-4123 Allschwil / Switzerland > > phone +41 61 565 6891 / fax +41 61 565 66 96 > [email protected] / www.actelion.com > > *[email protected]* > Sent by: [email protected] > > 04/14/2009 05:08 PM > > To > [email protected] > cc > > 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: [email protected] > 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. > ---------------------------------------------------------------------- > > The information of this email and in any file transmitted with it is strictly > confidential and may be legally privileged. > It is intended solely for the addressee. If you are not the intended recipient, > any copying, distribution or any other use of this email is prohibited and may > be unlawful. In such case, you should please notify the sender immediately and > destroy this email. > The content of this email is not legally binding unless confirmed by letter. > > Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorised to state them to be the views of the sender's company. For further information about Actelion please see our website at http://www.actelion.com -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand [email protected] tel:+64(9)923-6730 fax:+64(9)373-7090 mobile: +33 64 271-6369 (Apr 6-Jul 17 2009) http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford

If you want both CL1 and CL2 to be correlated with F (i.e. allow Omega(CL1,F) and Omega(CL2,F) to be free in the objective function optimization), then I don't think there is any simple reordering of the random effects that will allow the correlation between CL1 and CL2 to be fixed to zero - i.e. the element Omega(CL1,CL2) must also be free. The reason for the Nonmem manual entry part VIII, p 94 ($OMEGA), "If FIXED appears anywhere among the list of values, the entire block is fixed." that Andreas pointed out is that internally Nonmem parameterizes the Omega matrix by its Cholesky factor elements, not the elements of the Omega matrix itself. The Cholesky factor has the same block diagonal structure as the Omega matrix, but due to the 'fill-in' phenomenon during a factorization, an internal zero element inside an Omega block will not necessarily be preserved as a zero in the Cholesky factor. So there is no way to force an internal element in an Omega block to be zero. Robert H. Leary, PhD Fellow Pharsight - A Certara(tm) Company 5625 Dillard Dr., Suite 205 Cary, NC 27511 Phone/Voice Mail: (919) 852-4625, Fax: (919) 859-6871 Email: [email protected] This email message (including any attachments) is for the sole use of the intended recipient and may contain confidential and proprietary information. Any disclosure or distribution to third parties that is not specifically authorized by the sender is prohibited. If you are not the intended recipient, please contact the sender by reply email and destroy all copies of the original message.

Dear all, There is an undocumented option in NONMEM called Band, allowing to fix at least one correlation to zero in a block(n). In the specific case you just have to put zero as initial estimate for Omega (CL1,CL2). It should work I used it in the past with NONMEM V! Hope this helps. Christian **************************************************************************** ******************************************* Christian Laveille Senior Consultant Exprimo NV Tel: +33 474 68 81 84 Mob: +33 610 55 31 09 Fax: +33 959 106 261 Email: [email protected] Web: www.exprimo.com http://www.exprimo.com/ This e-mail is confidential. It is also privileged or otherwise protected by work product immunity or other legal rules. The information is intended to be for use of the individual or entity named above. If you are not the intended recipient, please be aware that any disclosure, copying, distribution or use of the contents of this information is prohibited. You should therefore delete this message from your computer system. If you have received the message in error, please notify us by reply e-mail. The integrity and security of this message cannot be guaranteed on the Internet. Thank you for your co-operation. _____

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 _____

I think Christian is referring to this feature of NONMEM 5 (from the NONMEM 5 Supplement guide): "Changes to NONMEM Inputs Band Symmetric Matrices An initial estimate of a diagonal block of ether the OMEGA or SIGMA matrices may have a band symmetric form, in which case the final estimate has the same form." With these structures for (e.g.) OMEGA BLOCK(3), the 0's are preserved: x 0x 00x x xx 0xx No need to FIX the off-diag (off-band) 0's. So it is not actually undocumented. Unfortunately, the OMEGA entry in on-line help was not updated with this feature. It will be included in the NONMEM 7 help. On Wed, 15 Apr 2009 15:47:35 +0200, "Christian Laveille" <[email protected]> said: > Dear all, > > > > There is an undocumented option in NONMEM called Band, allowing to fix at > least one correlation to zero in a block(n). > > In the specific case you just have to put zero as initial estimate for > Omega > (CL1,CL2). > > It should work I used it in the past with NONMEM V! > > > > Hope this helps. > > > > Christian > > **************************************************************************** > ******************************************* > > Christian Laveille > > Senior Consultant > > Exprimo NV > > > > Tel: +33 474 68 81 84 > > Mob: +33 610 55 31 09 > > Fax: +33 959 106 261 > > Email: [email protected] > > Web: www.exprimo.com http://www.exprimo.com/ > > > > This e-mail is confidential. It is also privileged or otherwise protected > by > work product immunity or other legal rules. The information is intended > to > be for use of the individual or entity named above. If you are not the > intended recipient, please be aware that any disclosure, copying, > distribution or use of the contents of this information is prohibited. > You > should therefore delete this message from your computer system. If you > have > received the message in error, please notify us by reply e-mail. The > integrity and security of this message cannot be guaranteed on the > Internet. > Thank you for your co-operation. > > > > _____ >

Dear all, thank you for all your responses, and it seems to me the topic has raised quite some discussions. Especially the point Diane brought up seemed to be a very reasonable thought to me, and I will definitely try and see if this changes anything with respect to model stability, and if I can omit the correlation between the omegas. Also, thanks for all the tips how to correctly code the OMEGA BLOCK. Best regards 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 drmould 15.04.2009 18:16 Please respond to drmould To mats.karlsson nmusers cc 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

Dear all, thank you for all your responses, and it seems to me the topic has raised quite some discussions. Especially the point Diane brought up seemed to be a very reasonable thought to me, and I will definitely try and see if this changes anything with respect to model stability, and if I can omit the correlation between the omegas. Also, thanks for all the tips how to correctly code the OMEGA BLOCK. Best regards 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: [email protected] 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 [email protected] 15.04.2009 18:16 Please respond to [email protected] To [email protected], Nele Plock/DEKON/AP/alt...@altana-mail, [email protected] cc 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

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

Nele, I dont agree that with this assertion "I know that in a one-compartment model, NONMEM would not be able to differentiate between IIV on volume or IIV on F1" If you use this approach (similar to that suggested by Mats) $OMEGA 0.5 ; BSV_F1 $OMEGA BLOCK(2) .5 ; BSV_CL 0 .5 ; BSV_V ; Note zero covariance between CL and V $PK F1=EXP(BSV_F1) ; relative 'bioavailability, protein binding, etc.' CL=POP_CL*EXP(BSV_CL) V=POP_CL*EXP(BSV_V) then you can in theory identy the 3 BSV components. This is because anything that causes between subject variability in F1 (which can be differences in bioavailability, protein binding, dose error) will affect CL and V identically. If there is an additonal uncorrelated source of BSV for CL e.g. renal function, and BSV for V e.g. partition into fat, then this can be identified. The $PK code above is equivalent to this: CL=POP_CL*EXP(BSV_F1 + BSV_CL) V=POP_CL*EXP(BSV_F1 + BSV_V) Nick [email protected] wrote: > Dear Mats, > > thank you, that is exactly what I am trying now (as I have IIV on central volume). I will now only include the diagonal elements of the omega matrix, and have included the correlation in the thetas as CL/F. > > Let's see how this works. > > One question out of curiosity: I know that in a one-compartment model, NONMEM would not be able to differentiate between IIV on volume or IIV on F1. But with more compartments, this should work, shouldn't it, even if I only have oral data? > > 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: [email protected] > 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 > > *[email protected]* > > 16.04.2009 09:05 > > To > > [email protected] , Nele Plock/DEKON/AP/alt...@altana-mail, [email protected] > > cc > > Subject > RE: [NMusers] OMEGA BLOCK with mixture model? > > 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: [email protected] ] * > > Sent:* Wednesday, April 15, 2009 6:16 PM* > To:* 'Mats Karlsson'; [email protected]; [email protected]* > 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:* [email protected] [ mailto: [email protected] ] *On Behalf Of *Mats Karlsson* > > Sent:* Tuesday, April 14, 2009 2:08 PM* > To:* [email protected]; [email protected]* > 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:* [email protected] [ mailto: [email protected] ] *On Behalf Of * [email protected] * > > Sent:* Tuesday, April 14, 2009 5:09 PM* > To:* [email protected]* > 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: [email protected] > 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. > ---------------------------------------------------------------------- > > ---------------------------------------------------------------------- > 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. > ---------------------------------------------------------------------- -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand [email protected] tel:+64(9)923-6730 fax:+64(9)373-7090 mobile: +33 64 271-6369 (Apr 6-Jul 17 2009) http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford

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: [email protected] P: +64 3 479 5044 F: +64 3 479 7034 Design software: www.winpopt.com

Mats, Another difference between BLOCK(2) and DIAG(3) is that they provide different number of ETAs for the individual fit. I am a bit surprised that one-compartment model with random effects on CL, V, and F is identifiable (even with diagonal OMEGA). Indeed, for each subject, this model has 3 free parameters. The only thing that allows to identify them separately is the distributional assumption. It could be rather week so I would expect higher variance values with DIAG(3) versus BLOCK(2). How often have you used ETAs on CL, V, and F in the same one-compartment model (without IV arm)? Is it always stable (or at least as stable as BLOCK(2))? Thanks Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 Mats Karlsson wrote: > 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 >

Nick, In your code example for the estimation of a 'relative bioavailability' wouldn't it be necessary to use a logit transformation to keep F1 between 0 and 1? Something like: F1 = 1/(1+exp(BSV_F1)) Regards, Andreas. ____________________________ Andreas Lindauer Department of Clinical Pharmacy Institute of Pharmacy University of Bonn An der Immenburg 4 D-53121 Bonn phone: + 49 228 73 5781 fax: + 49 228 73 9757

Andreas, Thanks for the suggestion. However, I think its only necessary to enforce 0 to 1 boundaries on the individual value of F1 when one is modelling absolute bioavailability. In this example I gave the individual 'apparent' bioavailability can be due to a variety of differences from the implicit mean of 1 (e.g. actual bioavailability, protein binding, dose errors, etc). The only constraint required is that F1 be non-negative. This is taken care of by the use of EXP transformation of ETA. Nick andreas lindauer wrote: > Nick, > > In your code example for the estimation of a 'relative bioavailability' wouldn't it be necessary to use a logit transformation to keep F1 between 0 and 1? Something like: F1 = 1/(1+exp(BSV_F1)) > > Regards, Andreas. > > ____________________________ > > Andreas Lindauer > > Department of Clinical Pharmacy > > Institute of Pharmacy > > University of Bonn > > An der Immenburg 4 > > D-53121 Bonn > > phone: + 49 228 73 5781 > > fax: + 49 228 73 9757 -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand [email protected] tel:+64(9)923-6730 fax:+64(9)373-7090 mobile: +33 64 271-6369 (Apr 6-Jul 17 2009) http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford

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

Hi Mats, Thanks for sharing your experience: very interesting and unexpected (at least to me) findings. I always used either CL-V or F-CL OMEGAs, but never F-CL-V for oral studies. Mechanistically and for covariate model development, F-CL-V structure looks very attractive. Thanks Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 Mats Karlsson wrote: > Hi Leonid, > > Pls 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 >

Dear NMusers, I have a question also related to omega blocks. Would it be okay to have two such blocks? In my model for instance correlation between eta 1, 2, and 3 seem biologically plausible, as is a correlation between eta 4 and 5. Correlations between 1, 2, or 3 and eta 4 or 5 is highly unlikely. Could this be coded as follows (I used arbitrary initial estimates for the omegas): $OMEGA BLOCK(3) 0.1 ;eta 1 0.1 0.1 ;eta2 0.1 0.1 0.1 ;eta3 $OMEGA BLOCK(2) 0.1 ;eta4 0.1 0.1 ;eta5 Thank you for your input, Elke Krekels > >

Dear NMusers, I have a question also related to omega blocks. Would it be okay to have two such blocks? In my model for instance correlation between eta 1, 2, and 3 seem biologically plausible, as is a correlation between eta 4 and 5. Correlations between 1, 2, or 3 and eta 4 or 5 is highly unlikely. Could this be coded as follows (I used arbitrary initial estimates for the omegas): $OMEGA BLOCK(3) 0.1 ;eta 1 0.1 0.1 ;eta2 0.1 0.1 0.1 ;eta3 $OMEGA BLOCK(2) 0.1 ;eta4 0.1 0.1 ;eta5 Thank you for your input, Elke Krekels