RE: BOV
From: "Liang Zhao" zhao.80@osu.edu
Subject: RE: [NMusers] BOV
Date: Wed, September 22, 2004 2:59 pm
Date:
To: "Wang, Yaning" (more)
Cc: "Wang, Yaning"
Priority: Normal
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I have the same doubt as Mike for Yaning's simplified scenario (with BOV is the
same for all occasions). Based on my understanding, the design for both
the simplified scenario and complex scenario is the same as Mike suggested.
In this case, the BSV and BOV are not comfounded and they are all estimable.
Think about the equation system
CL11=CL+a1+b11
....
CLij=CL+ai+bij
There are totally i*j (4*4=16) equations in this case, where i is number
of subjects and j is the number of occasions. By adding constraint equations:
a1+...+a4=0
b11+...+b1j=0
...
bi1+....+bij=0
in total we have i*j+1+j (21 in this case) equations. We know here
CL, a1-ai, b11-bij are all unknowns and there are 21 of them. Solve
the equation system we can get all of the values of unknowns.
Since
ai~N(0, BSV), i=1,..., t, t=4 in this example
bij~N(0, BOV), j=1,..., r, r=4 in this example
BSV and BOV can be further estimated by looking at ai's and bij's.
one step further, since estimation of BSV and BOV does not require the
full information of ai.s and bij's, there is big chance that the clinical
design can be further reduced and you still get information about BSV and BOV.
Even the algorithm to calculate BSV and BOV in NONMEM is carried out different,
degree of freedoms that can be used for parameter estimations will not change,
and I do think more effort should be put in this field of study for potential
fractional clinical designs. If my derivation and reasoning is not making
sense, please point out. It is a very stimulating discussion.
Liang Zhao PhD
Division of Pharmaceutics
The Ohio State Univ.