OMEGA priors using modes of inverse Wishart matrix

On Wed, Feb 22, 2012 at 7:53 AM, Joachim Grevel <[email protected]> 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 > >

From: [email protected] [mailto:[email protected]] 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:[email protected]] Sent: 22 February 2012 14:03 To: [email protected] 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

From: [email protected] [mailto:[email protected]] 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: [email protected] [mailto:[email protected]] 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:[email protected]]<mailto:[mailto:[email protected]]> Sent: 22 February 2012 14:03 To: [email protected]<mailto:[email protected]> 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

From: [email protected] [mailto:[email protected]] 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: [email protected]<mailto:[email protected]> [mailto:[email protected]] 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:[email protected]]<mailto:[mailto:[email protected]]> Sent: 22 February 2012 14:03 To: [email protected]<mailto:[email protected]> 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

From: Bauer, Robert [mailto:[email protected]] 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: [email protected] Web: www.iconplc.com http://www.iconplc.com/ _____ From: [email protected] [mailto:[email protected]] 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: [email protected] [mailto:[email protected]] 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: [email protected] [mailto:[email protected]] 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:[email protected]] Sent: 22 February 2012 14:03 To: [email protected] 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

From: [email protected] [mailto:[email protected]] On Behalf Of Mats Karlsson Sent: 23 February 2012 05:55 To: [email protected] Subject: FW: [NMusers] OMEGA priors using modes of inverse Wishart matrix 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:[email protected]] 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: [email protected] Web: www.iconplc.com http://www.iconplc.com/ _____ From: [email protected] [mailto:[email protected]] 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: [email protected] [mailto:[email protected]] 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: [email protected] [mailto:[email protected]] 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:[email protected]] Sent: 22 February 2012 14:03 To: [email protected] 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

From: [email protected] [mailto:[email protected]] On Behalf Of Stephen Duffull Sent: 22 February 2012 17:46 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: [email protected] [mailto:[email protected]] 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: [email protected] [mailto:[email protected]] 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:[email protected]] Sent: 22 February 2012 14:03 To: [email protected] 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

From: [email protected] [mailto:[email protected]] On Behalf Of Joachim Grevel Sent: den 23 februari 2012 18:20 To: [email protected] Subject: RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix Many thanks to all of you who responded so quickly and comprehensively. For those looking into this exchange in the future through the NMuser archive: Look at Mats' and Tim's response first then at all the others. There is not a single answer. I for my part will employ several techniques with sensitivity analysis, before I chose a model that gives me the most useful individual parameters for my new small data set of interest. Joachim From: [email protected] [mailto:[email protected]] On Behalf Of Mats Karlsson Sent: 23 February 2012 05:55 To: [email protected] Subject: FW: [NMusers] OMEGA priors using modes of inverse Wishart matrix 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