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

Back to the Top

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

Back to the Top

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.

There is more information on our web site www.lapk.org and

demonstration software can be downloaded from www.lapk.org/beta

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

Want to post a follow-up message on this topic? If this link does not work with your browser send a follow-up message to PharmPK@boomer.org with "The Separation Principle" as the subject

PharmPK Discussion List Archive Index page

Copyright 1995-2010 David W. A. Bourne (david@boomer.org)