RE: BOV
From: "Wang, Yaning" WangYA@cder.fda.gov
Subject: RE: [NMusers] BOV
Date: Wed, September 22, 2004 9:57 pm
Dear all:
First of all, I have to appologize for giving the wrong comments, especially
to Ken. If Ken had done the derivation, he would not have missed this. Then
I would like to say individual BOVj is estimable even if there is no
replicates of occasions within a subject (Just my personal opinion based on
my own derivation, I may be wrong).
In my previous derivation, I had to admit that I didn't try hard enough to
get the estimates for BOVj. Once I saw BSV could not be estimated by Nick's
proposal (SD2avg), I stopped and assumed BOVj certainly could not be
estimated by his next step. But Nick's intuition is right. If BSV is
estimated by SD2avg-BOVavghat/r (unbiased for BSV as shown in my detailed
derivation), the estimate (BSVhat) can then be used to estimate BOVj based
on Nick's logic. Define CLjavg as the mean CL across subjects for occassion
j. If SD2j={sum(i,t)(CLij-CLjavg)^2}/(t-1), then BOVjhat=SD2j-BSVhat.
BOVjhat is also an unbiased estimate for BOVj (see the derivation).
Detailed derivation can be found here.
http://www.geocities.com/wangyaning2004/unequalbov.pdf
Summary of the derivation
CLij=CL+ai+bij, CL is the true CL for the whole population, ai is the random
subject effect, bij is the random occasion effect within a subject.
ai~N(0, BSV), i=1,..., t,
bij~N(0, BOVj), j=1,..., r, N=t*r
BOVavghat={sum (i,t) sum (j,r) (CLij-CLavgi)^2}/(N-t) (unbiased estimate)
SD2avg={sum(i,t)(CLavgi-CLavgall)^2}/(t-1)
BSVhat=SD2avg-BOVavghat/r (unbiased estimate)
SD2j={sum(i,t)(CLij-CLjavg)^2}/(t-1)
BOVjhat=SD2j-BSVhat (unbiased estimate)
This is really an exciting discussion. I learned a lot. Again, my appologies
for sending the previous misleading comments. Thanks to Matts and Nick for
holding the right belief.
Yaning Wang, PhD
Pharmacometrician
OCPB, CDER, FDA