From:  Yaning Wang 
Subject: [NMusers] Weighting in NONMEM
Date:Mon, 02 Jun 2003 10:26:11 -0400

Hi all:
This may be a little bit distracting from the main question for this
thread (reference to: 99jun022003), but could anyone explain why a weighting like
W=SQRT(THETA(5)**2+THETA(6)**2/F**2) used by Justin
is equivelant to a combination error model as NONMEM guide suggested? What
is the advantage of this form to the standard combination error model?
Any suggestion is appreciated.

--
Yaning Wang
Department of Pharmaceutics
College of Pharmacy
University of Florida
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From:Leonid Gibiansky 
Subject:Re: [NMusers] Weighting in NONMEM
Date:  Mon, 02 Jun 2003 14:17:00 -0400

Yaning,
This error model was suggested by Mats Karlsson (posted 29 April 2002) as 
an error model that combines additive and proportional errors and can be 
used with the log-transformed data:

"To get the same error structure for log-transformed data as the
additive+proportional on the normal scale, I use
Y=LOG(F)+SQRT(THETA(x)**2+THETA(y)**2/F**2)*EPS(1)
with
$SIGMA 1 FIX "

In non-transformed terms
Conc=F*EXP(SQRT(THETA(x)**2+THETA(y)**2/F**2)*EPS(1))
Assuming that EXP(x)=1+x (for small x), you get
Conc=F*(1+SQRT(THETA(x)**2+THETA(y)**2/F**2)*EPS(1))

Variance of this expression
Var(conc)=F**2*(THETA(x)**2+THETA(y)**2/F**2)=
                = F**2*THETA(x)**2+THETA(y)**2

On the other hand, for the error model
Y=F exp(EPS1)+EPS2=F(1+EPS1)+EPS2
variance is equal to
F**2*OMEGA1+OMEGA2

Thus, these models are similar if not identical with
OMEGA1=THETA(x)**2,
OMEGA2=THETA(x)**2,

Leonid
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