PK models for rich and sparse sampling

From: Gordi, Toufigh Toufigh.Gordi@cvt.com Subject: [NMusers] PK models for rich and sparse sampling Date: Fri, May 28, 2004 7:57 pm Dear all, I was recently involved in PK/PD modeling of a compound, where initial modeling on rich data indicated a two-compartment model to describe the data best. Data from a later study with much fewer samples per subject suggested a one-compartment model to be the best model to fit the data to. This is not surprising, since there simply was not enough data available during the early phase of the drug disposition to characterize the two phases of the concentration decline in the latter study the way it was possible in the former study. Interestingly, parameter estimates were quite similar in both models. I would like to hear your comments on how to proceed with the modeling of this compound. Should one fix the estimates from the rich-data model and fit the more complex model to the sparse data or should I use the simpler model in future modeling, which will include PD modeling? In other words, how can I best use the prior information when dealing with the sparsely sampled data? Any reference would be greatly appreciated. I mho, it would be a waste of data NOT to use the more complex model. Toufigh Gordi

From: bvatul bvatul@verizon.net Subject: RE: [NMusers] PK models for rich and sparse sampling Date: Fri, May 28, 2004 10:20 pm Hello Toufigh The best way is to use all the data (rich and sparse) and analyze together using one model. Venkatesh Atul Bhattaram Pharmacometrics OCPB, DPE-1 CDER, FDA.

From: mark.e.sale@gsk.com Subject: RE: [NMusers] PK models for rich and sparse sampling Date: Sun, May 30, 2004 2:12 pm At the risk of making a CLM (Career Limiting Move), I'm going to disagree with the FDA (Food and drug administration). You can see that we at GSK (GlaxoSmithKline) are fond of our TLAs (Three Letter Acronyms). I'll try to avoid TLA speak. Combining the data sets is certainly an option, one we use frequently. But it isn't clear that it is (always) the best. Limitations include computational time. Perhaps more important is the possibility that the rich data set will dominate the estimation methods, resulting in very little being learned from the sparse data set. This would happen particularly if the rich data set is larger. I'd propose considering another methods we've had some success with in constructing very complex models. This is a much more Bayesian approach. Essentially, you use the PRIOR functionality in NONMEM, setting the initial estimates for THETA and OMEGA to a distrib! utions derived from the rich data set. So, if you find that K23 has a mean of 0.5 and a SEE of 0.2 you specify that using PRIOR. In this way, if the second (sparse) data set is uninformative about K23, then the estimates of K23 (including the SEE) are unchanged, but other parameters (for which the sparse data set is informative) will be essentially reestimated, using what you've learned from the first data set. It also adds very little computational time to the analysis. Let me know if you need help for the use of PRIOR hich is not documented in V5, but can be used.) Mark

From:Nick Holford n.holford@auckland.ac.nz Subject: RE: [NMusers] PK models for rich and sparse sampling Date:Sun, May 30, 2004 10:40 pm Mark, IMHO (FLA>TLA) the undocumented PRIOR in NONMEM V is a poor way to use prior information when you have the full data available. Necessarily the estimates from a prior data set are only a limited description of the true prior data. Plus they will be wrong because all models (and especially NONMEM models) are wrong. Plus the use of the (wrong) SEE as the uncertainty of the prior estimate has no strong justification. Using all the prior data is the most informative Bayesian approach I can think of. Note that the NONMEM PRIOR method is not really Bayesian (Gisleskog et al. 2003). The role for NONMEM PRIOR (or other true Bayesian methods using prior parameters) is when you have some estimates from a prior data set but the data itself is no longer available. I suppose execution time might be a problem if you use all the prior data and you only have slow computers :-) Nick Gisleskog PO, Karlsson MO, Beal SL. Use of Prior Information to Stabilize a Population Data Analysis. Journal of Pharmacokinetics & Biopharmaceutics 2003;29(5/6):473-505 -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

From: mark.e.sale@gsk.com Subject: RE: [NMusers] PK models for rich and sparse sampling Date: Mon, May 31, 2004 8:05 am WRT (with regard to) Nicks comments: I don't disagree with combining data sets - we do this very frequently, and is our first choice. My concern was with the unqualified term "best". To elaborate, I think there are two situations when combining has problems: 1. Computational time is limited 2. We have seen that adding a new, sparse data set to a large, rich data sets results in very little change in parameter estimates, in spite of the fact that the post hoc etas for the new individuals are very different from zero. That is, the new data seem different, so the parameters from the first analysis (rich data) seem to not be correct, and yet the overall parameters seem to reflect only the first (rich) data set. The parameters are insensitive to the second data set, and so we are without an adequate description of the second data set. One option is to allow parameters that can be estimated from the second data set (here, presumably CL and V) to vary between data sets, while having common values for those not estimable from the second data set (here, presumably K23 and K32). In the example cited above, this didn't work, CL and V were very poorly estimated from the second data set alone. Another options is ! to! use the mean and SD of the post hoc estimates from the combined data sets to describe the second data set. Another option is the PRIOR method. Mark

From: bvatul bvatul@verizon.net Subject: RE: [NMusers] PK models for rich and sparse sampling Date: Mon, May 31, 2004 9:59 am Mark When I meant "best" I did not say that it is the "only" way to analyse the data. It depends on the other factors which could influence the second study (different population etc). One could always look at the data, understand it and make decisions. Anyways, what I had said was my view and not of the "FDA". Venkatesh Atul Bhattaram Pharmacometrics DPE-1/OCPB CDER, FDA.

From: Steve Duffull sduffull@pharmacy.uq.edu.au Subject: RE: [NMusers] PK models for rich and sparse sampling Date: Tue, 1 Jun 2004 09:41:51 +1000 Hi Mark When you used informative priors as indicated below (and in previous threads): >Another option is the PRIOR method. How do you set up your prior on your between-subject variance? I am guessing that NONMEM uses an inverse Wishart for the prior on OMEGA, which means that you will need to specify your degrees of freedom in some manner. Since you only have your dense data as your "prior" then you will not have enough information to determine the uncertainty in your omega estimate (unless you use your SE's here which is likely to be risky due to assumed normality). If you do use your SE's then how do you go about figuring out your dof (?), unfortunately the Wishart is annoyingly tricky and there is not a linear relationship between dof and inverse precision. Regards Steve ========================================= Stephen Duffull School of Pharmacy University of Queensland Brisbane 4072 Australia Tel +61 7 3365 8808 Fax +61 7 3365 1688 University Provider Number: 00025B Email: sduffull@pharmacy.uq.edu.au www: http://www.uq.edu.au/pharmacy/sduffull/duffull.htm PFIM: http://www.uq.edu.au/pharmacy/sduffull/pfim.htm MCMC PK example: http://www.uq.edu.au/pharmacy/sduffull/MCMC_eg.htm

From: Paul Hutson prhutson@pharmacy.wisc.edu Subject: RE: [NMusers] PK models for rich and sparse sampling Date: Tue, June 1, 2004 10:11 am Mark: The use of PRIOR at GSK and by others (DM) suggests that it is a powerful tool that increases the Bayesian modelling capacity of NONMEM. Although I have a copy, it is unclear to me that its use would be acceptable to reviewers in a manuscript, since it is not a documented subroutine. Have any others been successful in using PRIOR in manuscripts? More importantly (Bill), is there any hope in obtaining "official" recognition and documentation of PRIOR? Paul Paul Hutson, Pharm.D. Associate Professor (CHS) UW School of Pharmacy 777 Highland Avenue Madison, WI 53705-2222 Tel: (608) 263-2496 FAX: (608) 265-5421 Pager: (608) 265-7000, #7856

From: mark.e.sale@gsk.com Subject: RE: [NMusers] PK models for rich and sparse sampling Date: Tue, June 1, 2004 10:28 am I think someone (likely Nick), has pointed out that this has been in the literature. Gisleskog PO. Karlsson MO. Beal SL. Use of prior information to stabilize a population data analysis. Journal of Pharmacokinetics & Pharmacodynamics. 29(5-6):473-505, 2002 Dec. I don't see a problem with publishing it, I don't think we have yet, but certainly intend to. And you're right, we have found it to be a very powerful tool for constructing very large, complex models that otherwise would not be stable (like PBPK models). Mark

From: Bachman, William (MYD) bachmanw@iconus.com Subject: RE: [NMusers] PK models for rich and sparse sampling Date: Tue, June 1, 2004 10:42 am There will be no official recognition or documentation of PRIOR for NONMEM V by UCSF. The PRIOR functionality is still being tested for NONMEM 6. There is no committment from UCSF, at this time, to include PRIOR or documentation for it. nmconsult@globomaxnm.com GloboMax The Strategic Pharmaceutical Development Division of ICON plc 7250 Parkway Drive, Suite 430 Hanover, MD 21076 Voice: (410) 782-2205 FAX: (410) 712-0737

From: mark.e.sale@gsk.com Subject: RE: [NMusers] PK models for rich and sparse sampling Date: Tue, 1 Jun 2004 06:46:34 -0400 My understanding is that NONMEM does use an inverse Wishart for OMEGA (and Normal for THETA). I've found that while there isn't any good way to determine the appropriate DF for OMEGA (or so I've been told by smart people), once you get beyond about 5 DF, the result isn't very sensitive to the choice (I usually use about 20). We have played a little with relating DF for inverse Wishart with SEE for OMEGA (using Monte Carlo simulation, to get DF for the sampling optimisation work), but not yet completely satisfactory. But, I think a little more work and this will be possible. Bottom line is that I don't think it matters (much), it you have at least 5 DF. Mark

From: Steve Duffull sduffull@pharmacy.uq.edu.au Subject: RE: [NMusers] PK models for rich and sparse sampling Date: Tue, June 1, 2004 6:12 pm Mark... Re: Wishart... > once you get beyond about 5 DF, the result isn't very sensitive to the choice (I usually use about 20) We generally simulate from the Wishart and compare nonparametric intervals (say 25th and 75th percentiles) on the simulated OMEGA's vs what we think seems reasonable (e.g. from prior analyses). The choice of dof with the Wishart is also linked to its dimensionality - so a dof of 5 has a different meaning for a OMEGA matrix of rank of 2 vs one with a rank of 5. Steve ========================================Stephen Duffull School of Pharmacy University of Queensland Brisbane 4072 Australia Tel +61 7 3365 8808 Fax +61 7 3365 1688 University Provider Number: 00025B Email: sduffull@pharmacy.uq.edu.au www: http://www.uq.edu.au/pharmacy/sduffull/duffull.htm PFIM: http://www.uq.edu.au/pharmacy/sduffull/pfim.htm MCMC PK example: http://www.uq.edu.au/pharmacy/sduffull/MCMC_eg.htm

From:mark.e.sale@gsk.com Subject: RE: [NMusers] PK models for rich and sparse sampling Date: Wed, June 2, 2004 9:08 pm Steve, Have to confess that I hadn't thought it that far through. But, we did realize that it will be difficult to use Monte Carlo simulation to match df with SEE for OMEGA when each omega has a different SEE. Compromises will have to be made. Mark _______________________________________________________