From: "David Nix" <email@example.com>
Subject: Log Normal data
Date: 29 Oct 1997 13:01:58 -0500
Is there any way to force NONMEM to use a log-normal distribution for the intersubject variability involving PK parameters?
The only way that I can come up with is to:
1. Enter concentration data as log transformed values
2. Model Y=Log(F) + EPS(1)
Is this valid?
Is there any way to evaluate whether a log-normal or normal distribution provides the best goodness of fit for a given data set within NONMEM? I assume that if the strategy above is correct, I would not be able to compare objective functions between the analysis of log transformed data and untransformed data. This issue came up because I am working with a data set that was previously analysed as individual subjects. The PK parameters determined by individual analysis is clearly log-normally distributed. Is it acceptable to use a normal distribution for intersubject error in NONMEM?
From: Lewis Sheiner <firstname.lastname@example.org>
Subject: Log Normal data
Date: 29 Oct 1997 14:32:06 -0500
There may besome confusion on David's part or on mine. I am not sure what he means by "intersubject variability involving PK parameters."
I would have thought this was variability modeled by eta. That is, for example, if $PK had
CL = EXP(THETA(1)+ETA(1)
then, under the FOCE mehtod and its variants, indeed, the actual model used by NONMEM would be that CL is distributed log-normally in the population.
The strategy of modeling log(Y) does not automatically say anything about the distribution of the PK parameters; indeed if $PK had
CL = THETA(1) + ETA(1),
and the log(Y) vs log(F) model suggeested by David were used, the assumption would still be that CL is normally distributed, not log-normally!
On the other hand, modeling log(Y) does accomplish a log-normal distribution for the intra-individual noise, and this is often a good idea.
From: email@example.com.EDU (ABoeckmann)
Subject: Log normal data
Date: 29 Oct 1997 18:57:02 -0500
Re: David Nix's email, Stuart Beal offers these remarks.
>Is there any way to force NONMEM to use a log-normal distribution for
>the intersubject variability involving PK parameters?
Use the exponential model for the PK parameters and FOCE.
>The only way that I can come up with is to:
> 1. Enter concentration data as log transformed values
> DV=LN (conc)
> 2. Model Y=Log(F) + EPS(1)
>Is this valid?
This is a valid and useful way to handle intrasubject variability, not intersubject variability (you seem to be asking about the latter with your first question).
>Is there any way to evaluate whether a log-normal or normal
>distribution provides the best goodness of fit for a given data set
To compare goodness of fit results between any two models, plot DV vs. PRED for both models on the same scale and see how they look.
You are right, objective functions from two analyses, one using the observations and the other using the log-transformed observations, cannot be compared.
NONMEM doesn't make distributional assumptions per se. Still, if the "individual analysis" is more or less as you say, one would want to do something to reflect this. As stated above, use the exponential model and FOCE.