Block versus diagonal omega

-------- Original Message -------- Subject: [NMusers] Block versus diagonal omega Date: Wed, 25 Aug 2010 14:20:01 -0500 From: Berg, Alexander K., Pharm.D., Ph.D. <[email protected]> To: <[email protected]> Hello - I was curious if someone from the group could perhaps describe the basis for deciding whether to use a block (variance and covariance) versus diagonal (variance only) form of omega. Specifically, what tests if any can be performed to decide between the two forms and are there certain situations where one is preferred over the other as I often see only the diagonal form used. Any help would be much appreciated - Al Berg, PhD/PharmD Clinical Pharmacology Fellow Mayo Clinic - Rochester [email protected]

________________________________ From: [email protected] [mailto:[email protected]] On Behalf Of Berg, Alexander K., Pharm.D., Ph.D. Sent: Wednesday, 25 August, 2010 21:20 To: [email protected] Subject: [NMusers] Block versus diagonal omega Hello - I was curious if someone from the group could perhaps describe the basis for deciding whether to use a block (variance and covariance) versus diagonal (variance only) form of omega. Specifically, what tests if any can be performed to decide between the two forms and are there certain situations where one is preferred over the other as I often see only the diagonal form used. Any help would be much appreciated - Al Berg, PhD/PharmD Clinical Pharmacology Fellow Mayo Clinic - Rochester [email protected] This message and any attachments are solely for the intended recipient. If you are not the intended recipient, disclosure, copying, use or distribution of the information included in this message is prohibited --- Please immediately and permanently delete.

-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Bioengineering Faculty Search Sent: Wednesday, August 25, 2010 3:59 PM To: [email protected] Subject: Fwd: [NMusers] Block versus diagonal omega Does anyone know how I get OFF this list? Thanks, Janet -------- Original Message -------- Subject: [NMusers] Block versus diagonal omega Date: Wed, 25 Aug 2010 14:20:01 -0500 From: Berg, Alexander K., Pharm.D., Ph.D. <[email protected]> To: <[email protected]> Hello - I was curious if someone from the group could perhaps describe the basis for deciding whether to use a block (variance and covariance) versus diagonal (variance only) form of omega. Specifically, what tests if any can be performed to decide between the two forms and are there certain situations where one is preferred over the other as I often see only the diagonal form used. Any help would be much appreciated - Al Berg, PhD/PharmD Clinical Pharmacology Fellow Mayo Clinic - Rochester [email protected]

From: [email protected] [mailto:[email protected]] On Behalf Of Berg, Alexander K., Pharm.D., Ph.D. Sent: Wednesday, August 25, 2010 12:20 PM To: [email protected] Subject: [NMusers] Block versus diagonal omega Hello - I was curious if someone from the group could perhaps describe the basis for deciding whether to use a block (variance and covariance) versus diagonal (variance only) form of omega. Specifically, what tests if any can be performed to decide between the two forms and are there certain situations where one is preferred over the other as I often see only the diagonal form used. Any help would be much appreciated - Al Berg, PhD/PharmD Clinical Pharmacology Fellow Mayo Clinic - Rochester [email protected] -- The information contained in this email message may contain confidential or legally privileged information and is intended solely for the use of the named recipient(s). No confidentiality or privilege is waived or lost by any transmission error. If the reader of this message is not the intended recipient, please immediately delete the e-mail and all copies of it from your system, destroy any hard copies of it and notify the sender either by telephone or return e-mail. Any direct or indirect use, disclosure, distribution, printing, or copying of any part of this message is prohibited. Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorized to state them to be the views of XOMA.

From: [email protected] [mailto:[email protected]] On Behalf Of Berg, Alexander K., Pharm.D., Ph.D. Sent: Wednesday, August 25, 2010 12:20 PM To: [email protected] Subject: [NMusers] Block versus diagonal omega Hello - I was curious if someone from the group could perhaps describe the basis for deciding whether to use a block (variance and covariance) versus diagonal (variance only) form of omega. Specifically, what tests if any can be performed to decide between the two forms and are there certain situations where one is preferred over the other as I often see only the diagonal form used. Any help would be much appreciated - Al Berg, PhD/PharmD Clinical Pharmacology Fellow Mayo Clinic - Rochester [email protected] The information contained in this email message may contain confidential or legally privileged information and is intended solely for the use of the named recipient(s). No confidentiality or privilege is waived or lost by any transmission error. If the reader of this message is not the intended recipient, please immediately delete the e-mail and all copies of it from your system, destroy any hard copies of it and notify the sender either by telephone or return e-mail. Any direct or indirect use, disclosure, distribution, printing, or copying of any part of this message is prohibited. Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorized to state them to be the views of XOMA.

________________________________ From: [email protected] [mailto:[email protected]] On Behalf Of yhb5442387 Sent: Thursday, 26 August, 2010 11:38 To: nmusers Subject: RE: [NMusers] Block versus diagonal omega Hi Al, Serge's suggestion is available in practise,however when we are considering to add one covariate such as body weight to the parameter-CL,e.g.,the number of off-diagonal elements retained in the base model may be different from the one in the covariate model .As I have noticed,one or above off-diagonal elements could cross the zero cutoff again and should be excluded from the OMEGA block structure.So it is hardly to keep the constructure of OMEGA block same during the model improvment . In my opinion,if all the diagonal elements fall in an acceptable interval,such as the CV of parameter is within 50%,there is no need to insert the off-diagonal element.The off-diagonal element which means covariance between the diagonal paramete,represents the correlation between them.So another way is to refer to the scatter plots between ETAs estimated by the model with diagonal elements .Which off-diagonal element is included depends on the correlation between two ETAs in the scaterr plots. Most frequently,the diagonal elements are enough.Do not be worried about that. By the way, when we discussed the off-diagonal issue,we should not forget the basic purpose of model building-to make the model predictive performance to be in accordance with the observed values as far as possible. Jeroen, Do you mean the off-diagonal elements instead of diagonal elements when you mentioned in the second paragraph,because I would like to believe the the off-digonal elements are more difficult to estimate hongbo ye from nanjing city. 2010-08-26 ________________________________ yhb5442387 ________________________________ 发件人: "Serge Guzy" <[email protected]> 发送时间: 2010-08-26 04:46 主 题: RE: [NMusers] Block versus diagonal omega 收件人: "Berg, Alexander K., Pharm.D., Ph.D." <[email protected]>, <[email protected]> I am not sure there is one single statistical test you can use like we do with covariate selection (forward followed by backward deletion method). The easiest way to deal with this problem would be first to use a stable method like importance sampling assisted by MAP estimation (IMPMAP in NONMEM7) and getting the full variance covariance matrix and correlation matrix. NONMEM7 will give you also like SADAPT the standard errors associated with each correlation coefficient. A way to categorize these correlation coefficients would be to look at each correlation mean +- 2 standard errors and see if it crosses the zero cutoff. If so, you would assume this correlation not to be statistically significant. Once all the not statistically significant correlations are deleted, you have your new blocks to be considered (I guess you have sometimes to change the order of your parameters to define this new block in NONMEM7) and you refit your model with this new blocks. Of course, this is an approximation but at least it allows you ranking the most important correlations based on both their mean but also their corresponding standard errors. A pure diagonal variance covariance matrix will affect the outcome of your subsequent simulations and usually would inflate the response variability across the population as important correlations are may be missing. Serge Guzy; Ph.D President, CEO; POP_PHARM; INC; www.poppharm.com [email protected] 510 684 87 40 From: [email protected] [mailto:[email protected]] On Behalf Of Berg, Alexander K., Pharm.D., Ph.D. Sent: Wednesday, August 25, 2010 12:20 PM To: [email protected] Subject: [NMusers] Block versus diagonal omega Hello - I was curious if someone from the group could perhaps describe the basis for deciding whether to use a block (variance and covariance) versus diagonal (variance only) form of omega. Specifically, what tests if any can be performed to decide between the two forms and are there certain situations where one is preferred over the other as I often see only the diagonal form used. Any help would be much appreciated - Al Berg, PhD/PharmD Clinical Pharmacology Fellow Mayo Clinic - Rochester [email protected] ________________________________ The information contained in this email message may contain confidential or legally privileged information and is intended solely for the use of the named recipient(s). No confidentiality or privilege is waived or lost by any transmission error. If the reader of this message is not the intended recipient, please immediately delete the e-mail and all copies of it from your system, destroy any hard copies of it and notify the sender either by telephone or return e-mail. Any direct or indirect use, disclosure, distribution, printing, or copying of any part of this message is prohibited. Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorized to state them to be the views of XOMA. This message and any attachments are solely for the intended recipient. If you are not the intended recipient, disclosure, copying, use or distribution of the information included in this message is prohibited --- Please immediately and permanently delete.

-------- Original Message -------- Subject: RE: [NMusers] Block versus diagonal omega From: "Elassaiss - Schaap, J. \(Jeroen\)" < [email protected] > Date: Thu, August 26, 2010 3:58 pm To: "yhb5442387" < [email protected] >, "nmusers" < [email protected] > Dear Hongbo, I would rather advocate to include off-diagonal elements if possible. The off-diagonals can trim down the magnitude of the inter-individual variability. And as we often notice that our VPC bands tend to be (initially) rather too wide than too narrow, that can be needed. It is certainly useful when one desires to simulate with the inter-individual variability components. One might want to be careful with basing decisions about off-diagonal elements on posthoc ETAs as shrinkage may induce or mask correlation between the emperical bayesian estimates. Indeed, I ment to indicate that off-diagonal elements are more difficult to estimate. Thank you! Best regards, Jeroen Modeling & Simulation Expert Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3) - DMPK MSD PO Box 20 - AP1112 5340 BH Oss The Netherlands [email protected] T: +31 (0)412 66 9320 F: +31 (0)412 66 2506 www.msd.com From: [email protected] [ mailto: [email protected] ] On Behalf Of yhb5442387 Sent: Thursday, 26 August, 2010 11:38 To: nmusers Subject: RE: [NMusers] Block versus diagonal omega Hi Al, Serge's suggestion is available in practise,however when we are considering to add one covariate such as body weight to the parameter-CL,e.g.,the number of off-diagonal elements retained in the base model may be different from the one in the covariate model .As I have noticed,one or above off-diagonal elements could cross the zero cutoff again and should be excluded from the OMEGA block structure.So it is hardly to keep the constructure of OMEGA block same during the model improvment . In my opinion,if all the diagonal elements fall in an acceptable interval,such as the CV of parameter is within 50%,there is no need to insert the off-diagonal element.The off-diagonal element which means covariance between the diagonal paramete,represents the correlation between them.So another way is to refer to the scatter plots between ETAs estimated by the model with diagonal elements .Which off-diagonal element is included depends on the correlation between two ETAs in the scaterr plots. Most frequently,the diagonal elements are enough.Do not be worried about that. By the way, when we discussed the off-diagonal issue,we should not forget the basic purpose of model building-to make the model predictive performance to be in accordance with the observed values as far as possible. Jeroen, Do you mean the off-diagonal elements instead of diagonal elements when you mentioned in the second paragraph,because I would like to believe the the off-digonal elements are more difficult to estimate hongbo ye from nanjing city. 2010-08-26 yhb5442387 发件人: "Serge Guzy" < [email protected] > 发送时间: 2010-08-26 04:46 主 题: RE: [NMusers] Block versus diagonal omega 收件人: "Berg, Alexander K., Pharm.D., Ph.D." < [email protected] >, < [email protected] > I am not sure there is one single statistical test you can use like we do with covariate selection (forward followed by backward deletion method). The easiest way to deal with this problem would be first to use a stable method like importance sampling assisted by MAP estimation (IMPMAP in NONMEM7) and getting the full variance covariance matrix and correlation matrix. NONMEM7 will give you also like SADAPT the standard errors associated with each correlation coefficient. A way to categorize these correlation coefficients would be to look at each correlation mean +- 2 standard errors and see if it crosses the zero cutoff. If so, you would assume this correlation not to be statistically significant. Once all the not statistically significant correlations are deleted, you have your new blocks to be considered (I guess you have sometimes to change the order of your parameters to define this new block in NONMEM7) and you refit your model with this new blocks. Of course, this is an approximation but at least it allows you ranking the most important correlations based on both their mean but also their corresponding standard errors. A pure diagonal variance covariance matrix will affect the outcome of your subsequent simulations and usually would inflate the response variability across the population as important correlations are may be missing. Serge Guzy; Ph.D President, CEO; POP_PHARM; INC; www.poppharm.com [email protected] 510 684 87 40 From: [email protected] [ mailto: [email protected] ] On Behalf Of Berg, Alexander K., Pharm.D., Ph.D. Sent: Wednesday, August 25, 2010 12:20 PM To: [email protected] Subject: [NMusers] Block versus diagonal omega Hello - I was curious if someone from the group could perhaps describe the basis for deciding whether to use a block (variance and covariance) versus diagonal (variance only) form of omega. Specifically, what tests if any can be performed to decide between the two forms and are there certain situations where one is preferred over the other as I often see only the diagonal form used. Any help would be much appreciated - Al Berg, PhD/PharmD Clinical Pharmacology Fellow Mayo Clinic - Rochester [email protected] The information contained in this email message may contain confidential or legally privileged information and is intended solely for the use of the named recipient(s). No confidentiality or privilege is waived or lost by any transmission error. If the reader of this message is not the intended recipient, please immediately delete the e-mail and all copies of it from your system, destroy any hard copies of it and notify the sender either by telephone or return e-mail. Any direct or indirect use, disclosure, distribution, printing, or copying of any part of this message is prohibited. Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorized to state them to be the views of XOMA. This message and any attachments are solely for the intended recipient. If you are not the intended recipient, disclosure, copying, use or distribution of the information included in this message is prohibited --- Please immediately and permanently delete.

Van: [email protected] [mailto:[email protected]] Namens Elassaiss - Schaap, J. (Jeroen) Verzonden: August 26, 2010 9:58 PM Aan: yhb5442387; nmusers Onderwerp: RE: [NMusers] Block versus diagonal omega Dear Hongbo, I would rather advocate to include off-diagonal elements if possible. The off-diagonals can trim down the magnitude of the inter-individual variability. And as we often notice that our VPC bands tend to be (initially) rather too wide than too narrow, that can be needed. It is certainly useful when one desires to simulate with the inter-individual variability components. One might want to be careful with basing decisions about off-diagonal elements on posthoc ETAs as shrinkage may induce or mask correlation between the emperical bayesian estimates. Indeed, I ment to indicate that off-diagonal elements are more difficult to estimate. Thank you! Best regards, Jeroen Modeling & Simulation Expert Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3) - DMPK MSD PO Box 20 - AP1112 5340 BH Oss The Netherlands [email protected] T: +31 (0)412 66 9320 F: +31 (0)412 66 2506 www.msd.com ________________________________ From: [email protected] [mailto:[email protected]] On Behalf Of yhb5442387 Sent: Thursday, 26 August, 2010 11:38 To: nmusers Subject: RE: [NMusers] Block versus diagonal omega Hi Al, Serge's suggestion is available in practise,however when we are considering to add one covariate such as body weight to the parameter-CL,e.g.,the number of off-diagonal elements retained in the base model may be different from the one in the covariate model .As I have noticed,one or above off-diagonal elements could cross the zero cutoff again and should be excluded from the OMEGA block structure.So it is hardly to keep the constructure of OMEGA block same during the model improvment . In my opinion,if all the diagonal elements fall in an acceptable interval,such as the CV of parameter is within 50%,there is no need to insert the off-diagonal element.The off-diagonal element which means covariance between the diagonal paramete,represents the correlation between them.So another way is to refer to the scatter plots between ETAs estimated by the model with diagonal elements .Which off-diagonal element is included depends on the correlation between two ETAs in the scaterr plots. Most frequently,the diagonal elements are enough.Do not be worried about that. By the way, when we discussed the off-diagonal issue,we should not forget the basic purpose of model building-to make the model predictive performance to be in accordance with the observed values as far as possible. Jeroen, Do you mean the off-diagonal elements instead of diagonal elements when you mentioned in the second paragraph,because I would like to believe the the off-digonal elements are more difficult to estimate hongbo ye from nanjing city. 2010-08-26 ________________________________ yhb5442387 ________________________________ 发件人: "Serge Guzy" <[email protected]> 发送时间: 2010-08-26 04:46 主 题: RE: [NMusers] Block versus diagonal omega 收件人: "Berg, Alexander K., Pharm.D., Ph.D." <[email protected]>, <[email protected]> I am not sure there is one single statistical test you can use like we do with covariate selection (forward followed by backward deletion method). The easiest way to deal with this problem would be first to use a stable method like importance sampling assisted by MAP estimation (IMPMAP in NONMEM7) and getting the full variance covariance matrix and correlation matrix. NONMEM7 will give you also like SADAPT the standard errors associated with each correlation coefficient. A way to categorize these correlation coefficients would be to look at each correlation mean +- 2 standard errors and see if it crosses the zero cutoff. If so, you would assume this correlation not to be statistically significant. Once all the not statistically significant correlations are deleted, you have your new blocks to be considered (I guess you have sometimes to change the order of your parameters to define this new block in NONMEM7) and you refit your model with this new blocks. Of course, this is an approximation but at least it allows you ranking the most important correlations based on both their mean but also their corresponding standard errors. A pure diagonal variance covariance matrix will affect the outcome of your subsequent simulations and usually would inflate the response variability across the population as important correlations are may be missing. Serge Guzy; Ph.D President, CEO; POP_PHARM; INC; www.poppharm.com [email protected] 510 684 87 40 From: [email protected] [mailto:[email protected]] On Behalf Of Berg, Alexander K., Pharm.D., Ph.D. Sent: Wednesday, August 25, 2010 12:20 PM To: [email protected] Subject: [NMusers] Block versus diagonal omega Hello - I was curious if someone from the group could perhaps describe the basis for deciding whether to use a block (variance and covariance) versus diagonal (variance only) form of omega. Specifically, what tests if any can be performed to decide between the two forms and are there certain situations where one is preferred over the other as I often see only the diagonal form used. Any help would be much appreciated - Al Berg, PhD/PharmD Clinical Pharmacology Fellow Mayo Clinic - Rochester [email protected] ________________________________ The information contained in this email message may contain confidential or legally privileged information and is intended solely for the use of the named recipient(s). No confidentiality or privilege is waived or lost by any transmission error. If the reader of this message is not the intended recipient, please immediately delete the e-mail and all copies of it from your system, destroy any hard copies of it and notify the sender either by telephone or return e-mail. Any direct or indirect use, disclosure, distribution, printing, or copying of any part of this message is prohibited. Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorized to state them to be the views of XOMA. ________________________________ This message and any attachments are solely for the intended recipient. If you are not the intended recipient, disclosure, copying, use or distribution of the information included in this message is prohibited --- Please immediately and permanently delete. ________________________________

-------- Original Message -------- Subject: RE: [NMusers] Block versus diagonal omega From: "Eleveld, DJ" < [email protected] > Date: Fri, August 27, 2010 4:52 am To: "Elassaiss - Schaap, J. (Jeroen)" < [email protected] >, "yhb5442387" < [email protected] >, "nmusers" < [email protected] >  Hi Jeroen, If shrinkage induces correlations (which arent "true") in the posthoc ETAs then the data isnt very informative for at least 1 of the parameters. If this (misleading) correlation causes the researcher to test a model with off-diagonal covariance, I would expect that they would not find a significant drop in objective function, and therefore they would reject the correlation from the model. So, in the end, no harm done (to the model). My thinking is that if the data is not informative about the value of some parameter, then it probably wont be informative about the relationship between that paramater with some other parameter. The concerns about how to handle shrinkage properly simply disappear if you treat the off-diagonal elements like any other parameter, i.e. you require some drop in objective function when you accept a parameter into the model. Best regards, Douglas Eleveld Van: [email protected] [ mailto: [email protected] ] Namens Elassaiss - Schaap, J. (Jeroen) Verzonden: August 26, 2010 9:58 PM Aan: yhb5442387; nmusers Onderwerp: RE: [NMusers] Block versus diagonal omega Dear Hongbo, I would rather advocate to include off-diagonal elements if possible. The off-diagonals can trim down the magnitude of the inter-individual variability. And as we often notice that our VPC bands tend to be (initially) rather too wide than too narrow, that can be needed. It is certainly useful when one desires to simulate with the inter-individual variability components. One might want to be careful with basing decisions about off-diagonal elements on posthoc ETAs as shrinkage may induce or mask correlation between the emperical bayesian estimates. Indeed, I ment to indicate that off-diagonal elements are more difficult to estimate. Thank you! Best regards, Jeroen Modeling & Simulation Expert Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3) - DMPK MSD PO Box 20 - AP1112 5340 BH Oss The Netherlands [email protected] T: +31 (0)412 66 9320 F: +31 (0)412 66 2506 www.msd.com From: [email protected] [ mailto: [email protected] ] On Behalf Of yhb5442387 Sent: Thursday, 26 August, 2010 11:38 To: nmusers Subject: RE: [NMusers] Block versus diagonal omega Hi Al, Serge's suggestion is available in practise,however when we are considering to add one covariate such as body weight to the parameter-CL,e.g.,the number of off-diagonal elements retained in the base model may be different from the one in the covariate model .As I have noticed,one or above off-diagonal elements could cross the zero cutoff again and should be excluded from the OMEGA block structure.So it is hardly to keep the constructure of OMEGA block same during the model improvment . In my opinion,if all the diagonal elements fall in an acceptable interval,such as the CV of parameter is within 50%,there is no need to insert the off-diagonal element.The off-diagonal element which means covariance between the diagonal paramete,represents the correlation between them.So another way is to refer to the scatter plots between ETAs estimated by the model with diagonal elements .Which off-diagonal element is included depends on the correlation between two ETAs in the scaterr plots. Most frequently,the diagonal elements are enough.Do not be worried about that. By the way, when we discussed the off-diagonal issue,we should not forget the basic purpose of model building-to make the model predictive performance to be in accordance with the observed values as far as possible. Jeroen, Do you mean the off-diagonal elements instead of diagonal elements when you mentioned in the second paragraph,because I would like to believe the the off-digonal elements are more difficult to estimate hongbo ye from nanjing city. 2010-08-26 yhb5442387 发件人: "Serge Guzy" < [email protected] > 发送时间: 2010-08-26 04:46 主 题: RE: [NMusers] Block versus diagonal omega 收件人: "Berg, Alexander K., Pharm.D., Ph.D." < [email protected] >, < [email protected] > I am not sure there is one single statistical test you can use like we do with covariate selection (forward followed by backward deletion method). The easiest way to deal with this problem would be first to use a stable method like importance sampling assisted by MAP estimation (IMPMAP in NONMEM7) and getting the full variance covariance matrix and correlation matrix. NONMEM7 will give you also like SADAPT the standard errors associated with each correlation coefficient. A way to categorize these correlation coefficients would be to look at each correlation mean +- 2 standard errors and see if it crosses the zero cutoff. If so, you would assume this correlation not to be statistically significant. Once all the not statistically significant correlations are deleted, you have your new blocks to be considered (I guess you have sometimes to change the order of your parameters to define this new block in NONMEM7) and you refit your model with this new blocks. Of course, this is an approximation but at least it allows you ranking the most important correlations based on both their mean but also their corresponding standard errors. A pure diagonal variance covariance matrix will affect the outcome of your subsequent simulations and usually would inflate the response variability across the population as important correlations are may be missing. Serge Guzy; Ph.D President, CEO; POP_PHARM; INC; www.poppharm.com [email protected] 510 684 87 40 From: [email protected] [ mailto: [email protected] ] On Behalf Of Berg, Alexander K., Pharm.D., Ph.D. Sent: Wednesday, August 25, 2010 12:20 PM To: [email protected] Subject: [NMusers] Block versus diagonal omega Hello - I was curious if someone from the group could perhaps describe the basis for deciding whether to use a block (variance and covariance) versus diagonal (variance only) form of omega. Specifically, what tests if any can be performed to decide between the two forms and are there certain situations where one is preferred over the other as I often see only the diagonal form used. Any help would be much appreciated - Al Berg, PhD/PharmD Clinical Pharmacology Fellow Mayo Clinic - Rochester [email protected] The information contained in this email message may contain confidential or legally privileged information and is intended solely for the use of the named recipient(s). No confidentiality or privilege is waived or lost by any transmission error. If the reader of this message is not the intended recipient, please immediately delete the e-mail and all copies of it from your system, destroy any hard copies of it and notify the sender either by telephone or return e-mail. Any direct or indirect use, disclosure, distribution, printing, or copying of any part of this message is prohibited. Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorized to state them to be the views of XOMA. This message and any attachments are solely for the intended recipient. If you are not the intended recipient, disclosure, copying, use or distribution of the information included in this message is prohibited --- Please immediately and permanently delete.

On 8/30/2010 1:41 PM, Hu, Chuanpu [CNTUS] wrote: > *From:* Hu, Chuanpu [CNTUS] > *Sent:* Monday, August 30, 2010 8:46 AM > *To:* 'Mark Sale' > *Cc:* 'nmusers' > *Subject:* RE: [NMusers] Block versus diagonal omega > > Mark, > > Nice thought – the test can be conducted, but the devil is in the > details. This has to do with the intricacies of the role alternative > hypothesis plays in hypothesis testing: > > For the original parameterization testing OMEGA, the hypothesis test is > > H0: OMEGA=0, vs. H1: OMEGA>0 > > For the THETA parameterization testing OMEGA, the hypothesis test is > > H0: THETA=0, vs. H1: THETA<>0 > > So without getting into the math, the intuitive argument is that the > alternative hypotheses in the 2 situations are different, therefore it > is logical that the testing criteria must change. The world of math does > not contain contradictions even though it may appear so at times. J > > Chuanpu > > *From:* Mark Sale [mailto:[email protected]] > *Sent:* Sunday, August 29, 2010 9:19 AM > *To:* Hu, Chuanpu [CNTUS] > *Cc:* nmusers > *Subject:* RE: [NMusers] Block versus diagonal omega > > Chuanpu, > Do I extrapolate correctly then that: > > V = THETA(1)*EXP(THETA(2)*ETA(1)) > . > . > . > $OMEGA > (1,FIXED). > > Can be tested (THETA(2) <> 0), since it is not a truncated distribution? > might be an interesting exercise to do this with LRT and compare to the > randomization test with the usual specification. > > Mark > > --- On *Fri, 8/27/10, Hu, Chuanpu [CNTUS] /<[email protected]>/* wrote: > > From: Hu, Chuanpu [CNTUS] <[email protected]> > Subject: RE: [NMusers] Block versus diagonal omega > To: "Mark Sale - Next Level Solutions" <[email protected]>, > "Eleveld,DJ" <[email protected]> > Cc: "nmusers" <[email protected]> > Date: Friday, August 27, 2010, 4:33 PM > > Theoretically, the NONMEM objective function drop for adding a diagonal > element follows a mixture chi-square distribution, from which follows > that using the “usual” chi-square distribution would be conservative. > This has to do with 0 being on the boundary of possible values. (See > Pinheiro and Bates, Mixed Effects Models in S and S-PLUS, Springer, > 2000.) As this boundary issue does not apply to off-diagonal elements, > the “usual” chi-square distribution should be fine (with the usual > statistical asymptotic caveats). > > I’d like to mention that, while the “find the best fit” mindset may be > suitable for the typical exploratory setting, the p-values from repeated > (e.g., stepwise) tests are not statistically interpretable. To have > valid p-values, confirmatory analyses would be needed, which in my mind > deserves a wider use. J > > Chuanpu > > ~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~* > > Chuanpu Hu, Ph.D. > > Director, Pharmacometrics > > Pharmacokinetics > > Biologics Clinical Pharmacology > > Janssen Pharmaceutical Companies of Johnson & Johnson > > C-3-3 > > 200 Great Valley Parkway > > Malvern, PA 19355 > > Tel: 610-651-7423 > > Fax: (610) 993-7801 > > E-mail: [email protected] </mc/[email protected]> > > ~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*

-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Leonid Gibiansky Sent: Monday, August 30, 2010 2:48 PM To: Hu, Chuanpu [CNTUS] Cc: [email protected] Subject: Re: FW: [NMusers] Block versus diagonal omega Chuanpu, In all stable problems that I tried, parametrization ETA() $OMEGA 0.1 ; estimated was equivalent (in terms of the estimated value and objective function) to THETA(*)*ETA() $OMEGA 1 FIXED Also, H0: THETA=0, vs. H1: THETA<>0 is the same as H0: OMEGA=0, vs. H1: OMEGA>0 since OMEGA=THETA^2 In theta-form, the problem has two identical solution THETA()=SQRT(OMEGA) and THETA()= -SQRT(OMEGA) Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 On 8/30/2010 1:41 PM, Hu, Chuanpu [CNTUS] wrote: > *From:* Hu, Chuanpu [CNTUS] > *Sent:* Monday, August 30, 2010 8:46 AM > *To:* 'Mark Sale' > *Cc:* 'nmusers' > *Subject:* RE: [NMusers] Block versus diagonal omega > > Mark, > > Nice thought - the test can be conducted, but the devil is in the > details. This has to do with the intricacies of the role alternative > hypothesis plays in hypothesis testing: > > For the original parameterization testing OMEGA, the hypothesis test is > > H0: OMEGA=0, vs. H1: OMEGA>0 > > For the THETA parameterization testing OMEGA, the hypothesis test is > > H0: THETA=0, vs. H1: THETA<>0 > > So without getting into the math, the intuitive argument is that the > alternative hypotheses in the 2 situations are different, therefore it > is logical that the testing criteria must change. The world of math does > not contain contradictions even though it may appear so at times. J > > Chuanpu > > *From:* Mark Sale [mailto:[email protected]] > *Sent:* Sunday, August 29, 2010 9:19 AM > *To:* Hu, Chuanpu [CNTUS] > *Cc:* nmusers > *Subject:* RE: [NMusers] Block versus diagonal omega > > Chuanpu, > Do I extrapolate correctly then that: > > V = THETA(1)*EXP(THETA(2)*ETA(1)) > . > . > . > $OMEGA > (1,FIXED). > > Can be tested (THETA(2) <> 0), since it is not a truncated distribution? > might be an interesting exercise to do this with LRT and compare to the > randomization test with the usual specification. > > > Mark > > > --- On *Fri, 8/27/10, Hu, Chuanpu [CNTUS] /<[email protected]>/* wrote: > > > From: Hu, Chuanpu [CNTUS] <[email protected]> > Subject: RE: [NMusers] Block versus diagonal omega > To: "Mark Sale - Next Level Solutions" <[email protected]>, > "Eleveld,DJ" <[email protected]> > Cc: "nmusers" <[email protected]> > Date: Friday, August 27, 2010, 4:33 PM > > Theoretically, the NONMEM objective function drop for adding a diagonal > element follows a mixture chi-square distribution, from which follows > that using the "usual" chi-square distribution would be conservative. > This has to do with 0 being on the boundary of possible values. (See > Pinheiro and Bates, Mixed Effects Models in S and S-PLUS, Springer, > 2000.) As this boundary issue does not apply to off-diagonal elements, > the "usual" chi-square distribution should be fine (with the usual > statistical asymptotic caveats). > > I'd like to mention that, while the "find the best fit" mindset may be > suitable for the typical exploratory setting, the p-values from repeated > (e.g., stepwise) tests are not statistically interpretable. To have > valid p-values, confirmatory analyses would be needed, which in my mind > deserves a wider use. J > > Chuanpu > > ~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~* > > Chuanpu Hu, Ph.D. > > Director, Pharmacometrics > > Pharmacokinetics > > Biologics Clinical Pharmacology > > Janssen Pharmaceutical Companies of Johnson & Johnson > > C-3-3 > > 200 Great Valley Parkway > > Malvern, PA 19355 > > Tel: 610-651-7423 > > Fax: (610) 993-7801 > > E-mail: [email protected] </mc/[email protected]> > > ~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~* > Notice: This e-mail message, together with any attachments, contains information of Merck & Co., Inc. (One Merck Drive, Whitehouse Station, New Jersey, USA 08889), and/or its affiliates Direct contact information for affiliates is available at http://www.merck.com/contact/contacts.html) that may be confidential, proprietary copyrighted and/or legally privileged. It is intended solely for the use of the individual or entity named on this message. If you are not the intended recipient, and have received this message in error, please notify us immediately by reply e-mail and then delete it from your system.

-------- Original Message -------- Subject: Re: FW: [NMusers] Block versus diagonal omega From: Leonid Gibiansky < [email protected] > Date: Mon, August 30, 2010 2:47 pm To: "Hu, Chuanpu [CNTUS]" < [email protected] > Cc: [email protected] Chuanpu, In all stable problems that I tried, parametrization ETA() $OMEGA 0.1 ; estimated was equivalent (in terms of the estimated value and objective function) to THETA(*)*ETA() $OMEGA 1 FIXED Also, H0: THETA=0, vs. H1: THETA<>0 is the same as H0: OMEGA=0, vs. H1: OMEGA>0 since OMEGA=THETA^2 In theta-form, the problem has two identical solution THETA()=SQRT(OMEGA) and THETA()= -SQRT(OMEGA) Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 On 8/30/2010 1:41 PM, Hu, Chuanpu [CNTUS] wrote: > *From:* Hu, Chuanpu [CNTUS] > *Sent:* Monday, August 30, 2010 8:46 AM > *To:* 'Mark Sale' > *Cc:* 'nmusers' > *Subject:* RE: [NMusers] Block versus diagonal omega > > Mark, > > Nice thought – the test can be conducted, but the devil is in the > details. This has to do with the intricacies of the role alternative > hypothesis plays in hypothesis testing: > > For the original parameterization testing OMEGA, the hypothesis test is > > H0: OMEGA=0, vs. H1: OMEGA>0 > > For the THETA parameterization testing OMEGA, the hypothesis test is > > H0: THETA=0, vs. H1: THETA<>0 > > So without getting into the math, the intuitive argument is that the > alternative hypotheses in the 2 situations are different, therefore it > is logical that the testing criteria must change. The world of math does > not contain contradictions even though it may appear so at times. J > > Chuanpu > > *From:* Mark Sale [ mailto: [email protected] ] > *Sent:* Sunday, August 29, 2010 9:19 AM > *To:* Hu, Chuanpu [CNTUS] > *Cc:* nmusers > *Subject:* RE: [NMusers] Block versus diagonal omega > > Chuanpu, > Do I extrapolate correctly then that: > > V = THETA(1)*EXP(THETA(2)*ETA(1)) > . > . > . > $OMEGA > (1,FIXED). > > Can be tested (THETA(2) <> 0), since it is not a truncated distribution? > might be an interesting exercise to do this with LRT and compare to the > randomization test with the usual specification. > > > Mark > > > --- On *Fri, 8/27/10, Hu, Chuanpu [CNTUS] /< [email protected] >/* wrote: > > > From: Hu, Chuanpu [CNTUS] < [email protected] > > Subject: RE: [NMusers] Block versus diagonal omega > To: "Mark Sale - Next Level Solutions" < [email protected] >, > "Eleveld,DJ" < [email protected] > > Cc: "nmusers" < [email protected] > > Date: Friday, August 27, 2010, 4:33 PM > > Theoretically, the NONMEM objective function drop for adding a diagonal > element follows a mixture chi-square distribution, from which follows > that using the “usual” chi-square distribution would be conservative. > This has to do with 0 being on the boundary of possible values. (See > Pinheiro and Bates, Mixed Effects Models in S and S-PLUS, Springer, > 2000.) As this boundary issue does not apply to off-diagonal elements, > the “usual” chi-square distribution should be fine (with the usual > statistical asymptotic caveats). > > I’d like to mention that, while the “find the best fit” mindset may be > suitable for the typical exploratory setting, the p-values from repeated > (e.g., stepwise) tests are not statistically interpretable. To have > valid p-values, confirmatory analyses would be needed, which in my mind > deserves a wider use. J > > Chuanpu > > ~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~* > > Chuanpu Hu, Ph.D. > > Director, Pharmacometrics > > Pharmacokinetics > > Biologics Clinical Pharmacology > > Janssen Pharmaceutical Companies of Johnson & Johnson > > C-3-3 > > 200 Great Valley Parkway > > Malvern, PA 19355 > > Tel: 610-651-7423 > > Fax: (610) 993-7801 > > E-mail: [email protected] < /mc/ [email protected] > > > ~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~* >

On 8/30/2010 4:22 PM, Hu, Chuanpu [CNTUS] wrote: > Mark, Leonid et al, > > I guess my previous message was not clear. (And by the way, I have used > something similar to the THETA-parameterization and observed the same > NONMEM OBJF values, as should be.) The question is what distribution the > NONMEM objective function difference follows. The proof of it being > chi-square with 1 df requires certain mathematical “regularity > conditions” that the THETA parameterization would violate (otherwise its > distribution would not be a mixture chi-squire!). So, the hypothesis > test based on OMEGA-parameterization is valid (with mixture > chi-squared), and the test based on THETA-parameterization is invalid. > > Chuanpu > > *From:* [email protected] > [mailto:[email protected]] *On Behalf Of *Mark Sale - Next > Level Solutions > *Sent:* Monday, August 30, 2010 3:55 PM > *Cc:* [email protected] > *Subject:* RE: FW: [NMusers] Block versus diagonal omega > > Chuanpu, > > My experience is the same as Leonid's. I get the same OBJ, the same > (transformed) parameters, with H(null) and H(alt). Hence my confusion, I > get the same numbers, but one test of hypothesis is not valid (or > perhaps conservative) and the other may be (noting that the distribution > for THETA only makes sense if THETA is constrainted to be >0 or < 0, a > distribution that crosses 0 seems meaningless to me). > > But, I'm usually not all that interested in testing hypotheses WRT > OMEGA, and I'm pleased to learn that: > > 1. If you do a test of hypothesis it is conservative > > 2. AIC/BIC seem to still be valid indicators of "preference" WRT > -2Loglikelihood change. > > Mark Sale MD > Next Level Solutions, LLC > www.NextLevelSolns.com http://www.NextLevelSolns.com > 919-846-9185 > > A carbon-neutral company > > See our real time solar energy production at: > > http://enlighten.enphaseenergy.com/public/systems/aSDz2458 > > -------- Original Message -------- > Subject: Re: FW: [NMusers] Block versus diagonal omega > From: Leonid Gibiansky <[email protected] > <mailto:[email protected]>> > Date: Mon, August 30, 2010 2:47 pm > To: "Hu, Chuanpu [CNTUS]" <[email protected] <mailto:[email protected]>> > Cc: [email protected] <mailto:[email protected]> > > Chuanpu, > > In all stable problems that I tried, parametrization > > ETA() > $OMEGA > 0.1 ; estimated > > was equivalent (in terms of the estimated value and objective > function) to > > THETA(*)*ETA() > $OMEGA > 1 FIXED > > Also, > > H0: THETA=0, vs. H1: THETA<>0 > > is the same as > > H0: OMEGA=0, vs. H1: OMEGA>0 > > since OMEGA=THETA^2 > > In theta-form, the problem has two identical solution > > THETA()=SQRT(OMEGA) and THETA()= -SQRT(OMEGA) > > Leonid > > -------------------------------------- > Leonid Gibiansky, Ph.D. > President, QuantPharm LLC > web: www.quantpharm.com http://www.quantpharm.com > e-mail: LGibiansky at quantpharm.com http://quantpharm.com > tel: (301) 767 5566

-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Leonid Gibiansky Sent: Monday, August 30, 2010 8:05 PM To: Hu, Chuanpu [CNTUS] Cc: Mark Sale - Next Level Solutions; [email protected] Subject: Re: FW: [NMusers] Block versus diagonal omega Chuanpu, These two problems (in OMEGA and THETA parametrizations) are identical (in a sense that they provide same parameter values and OF). Moreover, one can propose the third parametrization: SQRT(THETA())*ETA() $OMEGA 1 FIXED with THETA() > 0 being the variance of the random effect (rather than SD). The tests based on them are either all valid, or all invalid. I have not seen anybody going into that level of "rigorousness" as to analyze conditions when the OF follows theoretical chi^2 distribution (for each specific model parameter). If so, we can use the same test for variances as well. The fact that we can does not imply that we should: in my experience, the number and the structure of random effects is defined mostly by the amount of individual data and stability of the problem (that is related to the amount of data). It may also be defined by the estimation method: newer methods allow (or even require) more complex OMEGA structure. Thanks Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 On 8/30/2010 4:22 PM, Hu, Chuanpu [CNTUS] wrote: > Mark, Leonid et al, > > I guess my previous message was not clear. (And by the way, I have > used something similar to the THETA-parameterization and observed the > same NONMEM OBJF values, as should be.) The question is what > distribution the NONMEM objective function difference follows. The > proof of it being chi-square with 1 df requires certain mathematical > “regularity conditions” that the THETA parameterization would violate > (otherwise its distribution would not be a mixture chi-squire!). So, > the hypothesis test based on OMEGA-parameterization is valid (with > mixture chi-squared), and the test based on THETA-parameterization is invalid. > > Chuanpu

________________________________ From: [email protected] [mailto:[email protected]] On Behalf Of Berg, Alexander K., Pharm.D., Ph.D. Sent: Thursday, 02 September, 2010 22:40 To: [email protected] Subject: RE: [NMusers] Block versus diagonal omega Everyone - Thank you all for your assistance in answering my question regarding the block versus diagonal omega structure. The answers that you all provided have been a great help thus far and are much appreciated. As a follow-up, I was curious if someone could point me towards a reference that would help me to figure out how to restructure the covariance into different omega blocks. Specifically, I would like to understand the basis and proper method for restructuring the omega block so that I may remove selected covariance terms when simplifying from a completely unstructured block to a more parsimonious one. Thanks again for your help and time - Al Berg This message and any attachments are solely for the intended recipient. If you are not the intended recipient, disclosure, copying, use or distribution of the information included in this message is prohibited --- Please immediately and permanently delete.

On 02/09/2010 22:39, Berg, Alexander K., Pharm.D., Ph.D. wrote: > Everyone - > > Thank you all for your assistance in answering my question regarding the block versus diagonal omega structure. The answers that you all provided have been a great help thus far and are much appreciated. As a follow-up, I was curious if someone could point me towards a reference that would help me to figure out how to restructure the covariance into different omega blocks. Specifically, I would like to understand the basis and proper method for restructuring the omega block so that I may remove selected covariance terms when simplifying from a completely unstructured block to a more parsimonious one. Thanks again for your help and time - > > Al Berg -- ------------------------------------------------ Paolo Denti, PhD Post-Doctoral Fellow Division of Clinical Pharmacology Department of Medicine University of Cape Town K45 Old Main Building Groote Schuur Hospital Observatory, Cape Town 7925 South Africa phone: +27 21 404 7719 fax: +27 21 448 1989 email:[email protected]

________________________________ From: [email protected] [mailto:[email protected]] On Behalf Of Paolo Denti Sent: Friday, September 03, 2010 7:44 AM To: nmusers Subject: Re: [NMusers] Block versus diagonal omega Hi Al, as far as I can tell, if you have a BLOCK matrix in NONMEM, the only elements that you can fix to zero (without fixing the whole block) are the ones in the lower corner of the matrix. You can have lower triangular matrices of zeros as large as all of yours off-diagonal elements (in which case the matrix would become diagonal). To do this, you just set the initial estimate of those element to exactly zero. Don't write FIX anywhere in the block, or else NONMEM is going fix the values of the whole block. Some examples would be $OMEGA BLOCK(3) a b c 0 d e or $OMEGA BLOCK(4) a b c 0 d e 0 0 f g or $OMEGA BLOCK(4) a b c d e f 0 g h j Obviously, unless you are lucky, the zeros won't be where you want them to be with the numbering you chose for the ETAs, so you might need to change the order and bring all the zeros to the lower triangle. Lots of fun! ;) Some matrices can't be obtained this way unless you sacrifice some additional correlations, I fear. Or at least I can't see how. Like the one below: $OMEGA BLOCK(4) a b c d e f 0 0 g h The only way I can think to obtain exactly this one (someone else can maybe help here) is to calculate the Cholesky factor of your matrix so that you can rewrite it the whole thing in your code using only thetas. In that way you would be able free to fix whatever you want to any value. Hope this is not too confusing... Greetings from Cape Town, Paolo On 02/09/2010 22:39, Berg, Alexander K., Pharm.D., Ph.D. wrote: Everyone - Thank you all for your assistance in answering my question regarding the block versus diagonal omega structure. The answers that you all provided have been a great help thus far and are much appreciated. As a follow-up, I was curious if someone could point me towards a reference that would help me to figure out how to restructure the covariance into different omega blocks. Specifically, I would like to understand the basis and proper method for restructuring the omega block so that I may remove selected covariance terms when simplifying from a completely unstructured block to a more parsimonious one. Thanks again for your help and time - Al Berg -- ------------------------------------------------ Paolo Denti, PhD Post-Doctoral Fellow Division of Clinical Pharmacology Department of Medicine University of Cape Town K45 Old Main Building Groote Schuur Hospital Observatory, Cape Town 7925 South Africa phone: +27 21 404 7719 fax: +27 21 448 1989 email: [email protected]