target-mediate model: numerical difficulties

Hello NONMEM users, I am working on some target-mediated models. It is necessary to use ADVAN8 because differential equations describe very fast and very slow processes. The models run if I use option SLOW. If I do not use SLOW, different models for different drugs fail. The message is 0PROGRAM TERMINATED BY OBJ ERROR IN NCONTR WITH INDIVIDUAL 4 ID=XXXXXXXX NUMERICAL HESSIAN OF OBJ. FUNC. FOR COMPUTING CONDITIONAL ESTIMATE IS NON POSITIVE DEFINITE MESSAGE ISSUED FROM ESTIMATION STEP AT 0TH ITERATION, UPON EVALUATION OF GRADIENT WITH RESPECT TO OMEGA 0TRY SUBSTANTIALLY INCREASING "INITIAL ESTIMATE OF SIGMA" OR DECREASING "INITIAL ESTIMATE OF OMEGA" I tried to increase sigma, decrease omega, change the initial estimates, use different data and models. Nothing works. Is there a way around it? Option SLOW makes everything too slow. Thanks! Pavel

Dear Pavel, two initial thoughts: 1) Maybe run a sensitivity analysis in simulation mode and assess if you really need to describe the exact time course of the fast process. If not, then one option might be to fix one of the non-influential parameters. 2) Try to find the steady-state solution for the fast process and plug it in either directly as equation into the differential equation block. NONMEM has also special steady-state routines (see SS6 SS9 and ADVAN9 in the NONMEM help) which may be of help for you. Below are two specific and two more general references which seem very relevant. All the best Juergen ----------------------------------------------- Jurgen Bulitta, PhD Infectious Disease - Pharmacometrics University at Buffalo, NY, USA Phone: +1 716 645 2855 ext. 281 Fax: +1 716 645 3693 Email: [EMAIL PROTECTED] ----------------------------------------------- References: Mager DE, Krzyzanski W. Quasi-equilibrium pharmacokinetic model for drugs exhibiting target-mediated drug disposition. Pharm Res. 2005 Oct;22(10):1589-96. Epub 2005 Sep 22. Abraham AK, Krzyzanski W, Mager DE. Partial derivative-based sensitivity analysis of models describing target-mediated drug disposition. AAPS J. 2007 Jun 8;9(2):E181-9. I am sure, you have those two: Mager DE, Jusko WJ. General pharmacokinetic model for drugs exhibiting target-mediated drug disposition. J Pharmacokinet Pharmacodyn. 2001 Dec;28(6):507-32. Mager DE. Target-mediated drug disposition and dynamics. Biochem Pharmacol. 2006 Jun 28;72(1):1-10. Epub 2006 Feb 15. Review -----Ursprüngliche Nachricht----- Von: <[EMAIL PROTECTED]> Gesendet: 19.09.08 21:40:46 An: [email protected] Betreff: [NMusers] target-mediate model: numerical difficulties Hello NONMEM users, I am working on some target-mediated models. It is necessary to use ADVAN8 because differential equations describe very fast and very slow processes. The models run if I use option SLOW. If I do not use SLOW, different models for different drugs fail. The message is 0PROGRAM TERMINATED BY OBJ ERROR IN NCONTR WITH INDIVIDUAL 4 ID=XXXXXXXX NUMERICAL HESSIAN OF OBJ. FUNC. FOR COMPUTING CONDITIONAL ESTIMATE IS NON POSITIVE DEFINITE MESSAGE ISSUED FROM ESTIMATION STEP AT 0TH ITERATION, UPON EVALUATION OF GRADIENT WITH RESPECT TO OMEGA 0TRY SUBSTANTIALLY INCREASING "INITIAL ESTIMATE OF SIGMA" OR DECREASING "INITIAL ESTIMATE OF OMEGA" I tried to increase sigma, decrease omega, change the initial estimates, use different data and models. Nothing works. Is there a way around it? Option SLOW makes everything too slow. Thanks! Pavel

Hi Pavel, In addition to Juergen suggestions, here are couple of recent references that describe how you can directly check whether you need the full TMDD model or can use some simpler approximations. To check it, you need at least one set of TMDD parameter estimates (it looks like you get one with the SLOW option). You can compare the TMDD model predictions with the predictions of corresponding simpler approximations (with the parameters directly computed using TMDD parameters). If simpler models provide the same predictions as more complicated models, you can safely use them (within the dose/concentration range of your data) Leonid Gibiansky, Ekaterina Gibiansky,Tarundeep Kakkar, Peiming Ma, Approximations of the Target-Mediated Drug Disposition Model and Identifiability of Model Parameters, PAGE 17 (2008) Abstract 1269 [www.page-meeting.org/?abstract=1269] http://www.quantpharm.com/pdf_files/PAGE_2008_Poster_1269_web.pdf Leonid Gibiansky, Tarundeep Kakkar, Peiming Ma, Application of Identifiability Analysis Algorithm to Population PK of the Drug with Target-Mediated Drug Disposition, PAGE 17 (2008) Abstract 1271 [www.page-meeting.org/?abstract=1271] http://www.quantpharm.com/pdf_files/PAGE_2008_Poster_1271_web.pdf Regards, Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 Jurgen Bulitta wrote: > Dear Pavel, > > two initial thoughts: > > 1) Maybe run a sensitivity analysis in simulation > mode and assess if you really need to describe the > > exact time course of the fast process. If not, then one option might be to fix one of the non-influential parameters. > > 2) Try to find the steady-state solution for the fast > process and plug it in either directly as equation into > the differential equation block. NONMEM has also > > special steady-state routines (see SS6 SS9 and ADVAN9 in the NONMEM help) which may be of help for you. > > Below are two specific and two more general references > which seem very relevant. > > All the best > Juergen > > ----------------------------------------------- > > Jurgen Bulitta, PhD Infectious Disease - Pharmacometrics > > University at Buffalo, NY, USA > Phone: +1 716 645 2855 ext. 281 > > Fax: +1 716 645 3693 Email: [EMAIL PROTECTED] > > ----------------------------------------------- > > References: > > Mager DE, Krzyzanski W. > Quasi-equilibrium pharmacokinetic model for drugs exhibiting target-mediated > drug disposition. > Pharm Res. 2005 Oct;22(10):1589-96. Epub 2005 Sep 22. > > Abraham AK, Krzyzanski W, Mager DE. > Partial derivative-based sensitivity analysis of models describing > target-mediated drug disposition. > AAPS J. 2007 Jun 8;9(2):E181-9. > > I am sure, you have those two: > > Mager DE, Jusko WJ. > General pharmacokinetic model for drugs exhibiting target-mediated drug > disposition. > J Pharmacokinet Pharmacodyn. 2001 Dec;28(6):507-32. > > Mager DE. > Target-mediated drug disposition and dynamics. > Biochem Pharmacol. 2006 Jun 28;72(1):1-10. Epub 2006 Feb 15. Review > > -----Ursprüngliche Nachricht----- > Von: <[EMAIL PROTECTED]> > Gesendet: 19.09.08 21:40:46 > An: [email protected] > Betreff: [NMusers] target-mediate model: numerical difficulties > > Hello NONMEM users, > > I am working on some target-mediated models. It is necessary to use ADVAN8 because differential equations describe very fast and very slow processes. The models run if I use option SLOW. If I do not use SLOW, different models for different drugs fail. The message is > > 0PROGRAM TERMINATED BY OBJ > ERROR IN NCONTR WITH INDIVIDUAL 4 ID=XXXXXXXX > NUMERICAL HESSIAN OF OBJ. FUNC. FOR COMPUTING CONDITIONAL ESTIMATE > IS NON POSITIVE DEFINITE > MESSAGE ISSUED FROM ESTIMATION STEP > AT 0TH ITERATION, UPON EVALUATION OF GRADIENT WITH RESPECT TO OMEGA > 0TRY SUBSTANTIALLY INCREASING "INITIAL ESTIMATE OF SIGMA" > OR DECREASING "INITIAL ESTIMATE OF OMEGA" > > I tried to increase sigma, decrease omega, change the initial estimates, use different data and models. Nothing works. Is there a way around it? Option SLOW makes everything too slow. > > Thanks! > Pavel