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Dear David:
Why do you feel the need to do all this tramsformation? And why do you
assume constant CV? Is that for the lab errors? And if so, why?
I think there are 2 issues here - one concerning the credibility of lab
(serum) assays. The other is to suggest that you might consider a method
such as nonparametric population modeling, in which no parametric
assumptions need to be made about the shape of the distribution of the
parameter values, such as normal, lognormal, etc..
It is useful, and optimal, to give weight to serum level data
according to
its Fisher information - weighting by the reciprocal of the assay variance.
This is usually not done, and people weight by 1/C or 1/Csquared, unity
weighting, and other ways which really are not very realistic, as most
assays do not have a constant CV. This is discussed in part in Ther. Drug
Monit. 15: 380-393, 1993.
The other issue is that of nonparametric population modeling. A useful
reference is by Schumitzky, in Applied Math + Computation, 45: 143-157, 1991.
The bottom line of all this is that one wants to give weight to
each data
point according to its information content, and that one wants to find the
joint probability density that has the greatest likelihood given the doses
and the concentration data. The reason for this is that one wants THEN to
be able to develop the dosage regimen (for the patient, as well as for the
FDA) that MOST PRECISELY hits the desired target therapeutic goal selected
by the clinician for each patient according to his need for the drug. This
precision is provided by the natural link between nonparametric population
modeling and the "Multiple Model" method of dosage design, which can be
done specifically, for example, to minimize the expected value of the
weighted squared error with which a desired target goal is achieved by the
regimen. A useful reference here is by Bayard, Milman, and Schumitzky in
Int. J. Biomed. Computing, 36: 103-115, 1994.
All this is different from most of the approaches currently used, but I
would suggest that it is worthy of your consideration.
Very best regards,
Roger Jelliffe
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Roger W. Jelliffe, M.D.
USC Lab of Applied Pharmacokinetics
CSC 134-B, 2250 Alcazar St, Los Angeles CA 90033
Phone (213)342-1300, Fax (213)342-1302
email=jelliffe.-at-.hsc.usc.edu
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