# PharmPK Discussion - The Separation Principle

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• On 23 Nov 2005 at 11:57:11, Jorge Duconge (jduconge.-a-.yahoo.com.mx) sent the message

Hi everyone and happy Thanksgiving Eve,
I wonder if anyone of you could help me understanding what "the
separation principle" means within MAP Bayesian scenario for
population modeling?.
Any hint will be very appreciated,
Best regards,

Jorge Duconge

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• On 23 Nov 2005 at 16:07:14, Roger Jelliffe (jelliffe.-a-.usc.edu) sent the message

Dear Jorge:

The separation principle is well known in areas of
stochastic control, but not so well in the PK community. It states,
basically, that when you seek to control a system by two separate
steps, first getting single point model parameter estimates, and,
second, plan your control (here the dosage regimen to hit the desired
target) the job is almost always done suboptimally, as no specific
performance criterion is being optimized. This is basically what MAP
Bayesian adaptive control does. One only has one value for each model
parameter, and one simply assumes that the regimen will hit the
target exactly. There is no way to estimate the expected error of the
regimen.

On the other hand, if you have a model that has more than
one value for each parameter, like the collection of MAP Bayesian
posteriors in a population model, or a collection of individually
least squares fitted patient parameter values, or probably best yet,
a nonparametric NPML, NPEM, or NPAG population model joint parameter
density (the most likely collection of individual support points
{models} given the data in the population and the error model used),
each of these support points has an estimated set of parameter values
and an estimated probability as well. You can give a candidate
regimen to each of these model support points. This will generate
multiple predictions of future serum concentrations, for example. At
the time you want to hit your target goal, you now have many
predictions, each with a weight according to its probability. It is
easy to calculate the weighted squared error with which the target is
achieved by that regimen. It is then also easy using least squares
fitting to find not parameter values, but the doses that specifically
minimize the weighted squared error with which the target is hit.
This multiple model dosage design gets around the problems of the
separation principle and specifically optimizes the precision of the
dosage regimen. This multiple model dosage design is widely used in
the control of fixed wing aircraft and helicopters, spacecraft, and
missiles. We now have clinical PK software for this dosage design in
the new MM-USCPACK collection of programs. It has population models
for the aminoglycosides, vancomycin, digoxin, and several
antiepileptic drugs. Information is available in

1. Jazwinski AH: Stochastic Processes and Filtering Theory.
Academic Press, San Diego, 1970. This is a good mathematical
description.

2. Jelliffe R, Schumitzky A, Bayard D, Milman M, Van Guilder M,
Wang X, Jiang F, Barbaut X, and Maire P: Model-Based, Goal-Oriented,
Individualized Drug Therapy: Linkage of Population Modeling, New
"Multiple Model" Dosage Design, Bayesian Feedback, and Individualized
Target Goals. Clin. Pharmacokinet. 34: 57-77, 1998.

3. Jelliffe R, Bayard D, Milman M, Van Guilder M, and Schumitzky
A: Achieving Target Goals most Precisely using Nonparametric
Compartmental Models and "Multiple Model" Design of Dosage Regimens.
Therap. Drug Monit. 22: 346-353, 2000.

A related reference is:

4. Bayard D, and Jelliffe R: A Bayesian Approach to Tracking
Patients having Changing Pharmacokinetic Parameters. J. Pharmacokin.
Pharmacodyn. 31 (1): 75-107, 2004.

Very best regards,

Roger Jelliffe

Roger W. Jelliffe, M.D. Professor of Medicine,
Division of Geriatric Medicine,
Laboratory of Applied Pharmacokinetics,
USC Keck School of Medicine
2250 Alcazar St, Los Angeles CA 90033, USA
Phone (323)442-1300, fax (323)442-1302, email= jelliffe.aaa.usc.edu
Our web site= http://www.lapk.org

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