Iterative Two Stage Bayesian in NONMEM

From: drfreedman@drfreedmaninc.com Subject: [NMusers] Iterative Two Stage Bayesian in NONMEM Date: Wed, May 4, 2005 7:01 am Colleagues Can we code Iterative Two Stage Bayesian in NONMEM by iterating on the parameters and covariance matrix found by the Standard Two Stage approach? Will it be sufficient to insert the estimates into the control stream for the next iteration (e.g., by nmctl from WFN) rather than rely on PRIOR? Immanuel Freedman, PhD, MIEEE (619) 884-1347

From: "Nick Holford" n.holford@auckland.ac.nz Subject: Re: [NMusers] Iterative Two Stage Bayesian in NONMEM Date: Wed, May 4, 2005 9:44 am Immanuel, I'm not familiar with the ITSB. Do you mean using using sets of individual parameters obtained by fitting one individual at a time along with the covariance matrix of the estimate to weight the individual parameter estimates so that you can come up with a more sophisticated set of Two Stage Population means and variances? I am more familiar with the subject of your second question. The WFN nmctl procedure can be a convenient way to transfer final parameter estimates into the original control stream but in its usual form it does not use the information in the covariance matrix of the estimate. However, if you want to use the undocumented PRIOR subroutine in NONMEM V 1.1 you can use nmctl with the 'b' option to extract the covariance matrix of the estimate and format the control stream to include the covariance matrix of the estimate. I have no idea if this would help with ITSB but it can be a convenient way of performing a frequentist prior estimation procedure (see Gisleskog et al 2003). 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.

From: "Wang, Yaning" WangYA@cder.fda.gov Subject: RE: [NMusers] Iterative Two Stage Bayesian in NONMEM Date: Thu, May 5, 2005 8:34 am Immanuel, In my opinion, when you use the parameters and covariance matrix found by the Standard Two Stage approach as the initials for THETA and OMEGA in NONMEM and use FOCE estimation method, NONMEM is already dosing Iterative Two Stage Bayesian automatically. During each iteration, the values that are tried for population parameters are used as the prior to get the MAP Bayesian estimates for each individual (ETAs). These ETAs are then used to get the marginal likelihood for the population parameters. Then the objective function is re-defined around these ETAs. The gradient vector and the Hessian matrix based on this objective function will lead to the next set of values that will be tried for population parameters. Another iteration starts... Maybe the only problem is that the updating process of the population parameters is not taking means (for THETA) and SDs (for OMEGA) based on individual Bayesian estimates, but following the Quasi-Newton search pathway. Yaning Wang, Ph.D. Pharmacometrician Office of Clinical Pharmacology and Biopharmaceutics Center of Drug Research and Evaluation Food and Drug Administration Office: 301-827-9763 _______________________________________________________