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 
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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.
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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
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