Re: [Fwd: Simulations]
Date: Mon, 22 Nov 1999 15:26:26 -0800 (PST)
From: ABoeckmann <alison@c255.ucsf.edu>
Subject: Re: [Fwd: Simulations]
Comment from Stuart Beal...
As a habit, I do not read NM-Users mail, and therefore have not read any mail described as "Eliane's e-mail". The following comments are simply meant as follow ups to some pointed comments recently made by Jeff Wald.
>1.) NONMEM always reports the variance of a normally-distributed eta. When
> using a parameter model of the form p=theta*exp(eta), then
> Var(eta) is APPROXIMATELY (CV(p))**2. That
> approximation is pretty good for small CV's. For example when
> sqrt(Var(eta)) = 0.1 then CV = 0.10025. However, when sqrt(Var(eta)) gets
> large the approximation isn't so good. This is illustrated here using the
> values from Eliane's manuscript:
>
>Parameter sqrt(Var(eta)) CV
>CL 0.56 0.607
>V 0.604 0.664
>ka 0.991 1.29
The approximation has nothing to do with normality, nor, really, does that which NONMEM reports. It is the so-called exact value (given in Jeff's table, but not given in NONMEM output) which depends on a normally distributed eta. For more information about the approximation (and the exact value), see my memos to NM-Users entitled "Computation of CV's from OMEGA" dated September 26,27, 1997, which may be found in the NM-Users Archive ( http://www.phor.com/nonmem/nm/index.html).
>2.) The same model structure as NONMEM could have been used with normal
> distributions for log(p) and then translated to p. This approach is
> succinct in PTD through use of the exponentiated normal distribtion
> component. Alternately, a parameter modeled as p=theta*exp(eta) in
> NONMEM would be:
>
>mean(p) = theta*exp(Var(eta)/2)
>sd(p) = mean(p)*sqrt(exp(Var(eta))-1)
It is not clear to me what is being asserted here. Perhaps, it is being asserted that a technique might be used that involves computing the mean and sd of a parameter given be p=theta*exp(eta) using the two above formulas. I think this would be a bad idea. These formulas do rely on normality, and should not be generally trusted in population data analysis.
Stu Beal