```From:  "atul"
Subject:  [NMusers] When to do transformation of data?
Date:  Tue, April 23, 2002 2:27 am

Hello All

Is there any reference paper which discusses the various methods for transformation of data
and its implication in NONMEM analysis? Could the group share their experience on data
transformations? Especially what aspects of nontransformed data should be looked into
before selecting the suitable transformation of data. In one of the analysis I was observing
that log transformation of data helps in getting better estimates and the analysis is more stable.
The data is after infusion studies in patients who are also on several concomitant medications.
However, I was able to fit the data of healthy subjects data with out any transformation.

What could be the possible reasons for these type of observations?

Venkatesh Atul Bhattaram
Post-doctoral Fellow
University of Florida
Gainesville

*******

From: Steve_Charnick@vpharm.com
Subject: Re: [NMusers] When to do transformation of data?
Date: Tue, 23 Apr 2002 06:49:38 -0400

Atkinson's "Plots, Transformations, and Regression" is an excellent and small text that you could use.

*******

From: Leonid Gibiansky
Subject: Re: [NMusers] When to do transformation of data?
Date: Tue, 23 Apr 2002 09:16:52 -0400

I had an example recently where I exhausted all my options in improving the model, and it still was
not good enough (FO was giving too high estimates for omegas and biased PRED vs. DV plots,
FOCE with interaction OF was strongly dependent on the number of significant digits that I requested and
on the initial guess). Then I was advised to do log-transformation for DV, and it worked like a miracle
and stabilized the model. The main thing (at least, on the paper, I am not so sure about internal
details of the NONMEM algorithm; any thoughts why it could be so helpful ?) is to provide true
exponential error model:
ln(Y)=ln(F) + EPS
is equivalent to
Y=F EXP(EPS)
whereas Y=F EXP(EPS) is approximated by NONMEM as
Y=F(1+EPS)

So if EPS (SIGMA) is large enough, EXP(EPS) is not equal to (1+EPS), and the log-transformed
approximation could be better.

On the other hand, I do not know how to code the error model
Y=F*exp(EPS1) + EPS2
in log-transformed variables.
Any advices on this one ?

Thanks,
Leonid

*******

From: "Hu, Chuanpu"
Subject: RE: [NMusers] When to do transformation of data?
Date: Tue, 23 Apr 2002 10:12:31 -0400

Leonid,

A few years ago I had a similar example, and I made exactly the same
conclusion as yours.
exponential error to the log-transformed structure, because the former
allows negative Y's whereas the latter does not.

Chuanpu

----------------------------------------------------------------
Chuanpu Hu, Ph.D.
Research Modeling and Simulation
Clinical Pharmacology Discovery Medicine
GlaxoSmithKline
Tel: 919-483-8205
Fax: 919-483-6380
----------------------------------------------------------------

*******

From: "Lewis B. Sheiner"
Subject: Re: [NMusers] When to do transformation of data?
Date: Tue, 23 Apr 2002 08:00:34 -0700

But there is a reasonable equivalent model in the log space that Stu
Beal discusses
in the intermediate NONMEM course & by cc of this mail,
I am asking him to share it with nmusers ...

LBS.

_/  _/  _/_/ _/_/_/ _/_/_/ Lewis B Sheiner, MD (lewis@c255.ucsf.edu)
_/  _/ _/    _/     _/      Professor: Lab. Med., Biophmct. Sci.
_/  _/ _/    _/_/_/ _/_/     Mail:    Box 0626, UCSF, SF,CA,94143
_/  _/ _/        _/ _/        Courier: Rm C255, 521
Parnassus,SF,CA,94122
_/_/   _/_/ _/_/_/ _/         415-476-1965 (v), 415-476-2796 (fax)

*******

From: Leonid Gibiansky
Subject: RE: [NMusers] When to do transformation of data?
Date: Tue, 23 Apr 2002 11:21:59 -0400

Chuanpu
I thought about something like the model
ln(Y)=ln(F+EPS1) + EPS2
then
Y=F EPS(2) + EPS1*EXP(EPS2)
I checked that for SD(EPS2) < 0.2 the distribution of EPS1*EXP(EPS2) is
almost normal. For SD(EPS2) = 0.3 the distribution of EPS1*EXP(EPS2) is
very close to normal. For SD(EPS2) = 0.5 the distribution of EPS1*EXP(EPS2)
differs from normal on the tails: deletion of 0.5% of the highest and 0.5%
of the lowest values makes it sufficiently similar to normal.

I have not tried this approach, but this might be useful in some cases, at
least to test the presence of additive errors. So what would you say about
NONMEM code ( Y=LOG(DV) ) :

F1=F+EPS1
IF(F1 < 0.001) F1= 0.001
Y=LOG(F1)+EPS2

Will it work and will it be reasonable?
Leonid

*******

From:William Bachman
Subject: RE: [NMusers] When to do transformation of data?
Date: Tue, 23 Apr 2002 11:25 am

Leonid,

don't use F1 or Fn for that matter (reserved words in NONMEM).

Bill

*******

From: Leonid Gibiansky
Subject: RE: [NMusers] When to do transformation of data?
Date: Tue, 23 Apr 2002 11:29:47 -0400

Thanks, Bill,

Lets try
FFF=F+EPS1
IF(FFF < 0.001) FFF= 0.001
Y=LOG(FFF)+EPS2
Leonid

*******

From: "Bachman, William"
Subject: [NMusers] reasonable equivalent model in the log space
Date: Tue, 23 Apr 2002 11:47:30 -0400

Lewis Sheiner writes:

>But there is a reasonable equivalent model in the log space that
Stu
>Beal discusses
>in the intermediate NONMEM course & by cc of this mail,
>I am asking him to share it with nmusers ...

For a description, see "Ways to Fit a PK Model with Some Data
Below the
Quantification Limit", S.L. Beal, JPP, 28, 2001, 481-504.

*******

From: "Hu, Chuanpu"
Subject: RE: [NMusers] When to do transformation of data?
Date: Tue, 23 Apr 2002 13:03:34 -0400

Leonid,

I am skeptical about the properties of this proprosed model. It does not
behave well when F is small, as you surely know. However I thought the
purpose of having the EPS1 term is to allow some error when F is small. In
other words, I am not sure in what cases this approach will be useful.

I guess I should look at Stu's paper first before continuing on this...

Chuanpu

*******

From: Leonid Gibiansky
Subject: RE: [NMusers] When to do transformation of data?
Date: Tue, 23 Apr 2002 13:45:04 -0400

Chuanpu,
In fact, I am not sure that this model behaves badly when F is small. We
always should assume that Y=F+eps is positive (can you imagine negative
concentration ?). Under this assumption I cannot see obvious flows in the
logic. Note however, that I have not tried this model, and thus would not
recommend this model to anyone.

Leonid
*******

From: Unknown
Subject: RE: [NMusers] When to do transformation of data?
Date: Tue, 23 Apr 2002 16:47:24 -0500

Chuanpu and Leonid,

Ken Kowalski and I have been advocating the "log-transform both sides"
approach for a while.  I have found it to do a nice job stabilizing the
residual variability (in epsilon) as assessed by plots of the absolute value
of IWRES versus IPRED.  Also, I have found that the transformation helps
provide better (more reasonable) estimates of the OMEGA matrix, better
estimates of the absorption rate, and I can get convergence of models that
failed with the Y=F*(1+EPS) or Y=F*EXP(EPS) models.  A bonus with the
log-transformation is that you no longer have to worry about invoking the
INTERACTION option.  This is because the transformation orthogonalizes the
individual predictions and the residual error.  Two down sides are as
follows: 1) You have to back transform the results which can require
post-processing  2)  Occasionally the estimation of ALAG can become
problematic with standard first order absorption models.  I believe that the
log-transform has not been frequently used by this audience, because in some
instances, models have observed that a NONMEM run will "lock-up" or fail to
iterate at some point.  I believe that this happens primarily when the
observed (apparent) lag-time (ALAG) is greater in some individuals than
their first PK sampling time point.  If this phenomenon occurs in a
sufficient number of subjects and the ALAG parameter is not bounded above by
the first sampling time, then interaction can estimate the typical ALAG
value greater than the first time point, which can result in a zero
prediction, a problem when taking the log.  If the upper bound is fixed to
the first sampling time point, then the ALAG estimate can iterate to the
bound - this is also unsatisfactory.  In these cases, I have found that a
two-site first order absorption model can circumvent this problem and
perhaps even improve the model's ability to capture Cmax!  In other words,
don't discount the transformation because it cause trouble in estimation.
It is precisely these issues that could be an indication that the standard
absorption model is unsatisfactory! Of course, not discounting that the
sampling design may also not be sufficient.

Matt

*******

From: Peter Wright
Subject: RE: [NMusers] When to do transformation of data?
Date: Wed, 24 Apr 2002 10:51:21 -0700

On the topic of data transformation I have a quick question for the group

If I want to fit a model to data transformed to natural log can I do
this just in the error block

e.g.
Y1   = LOG(F) + EPS(1)
Y     = EXP(Y1)
IPRE  = F
IRES  = DV-IPRE
IWRE  = IRES/IPRE

or must I actually transform the data?

Peter Wright
UCSF

*******

From:  Mats Karlsson
Subject: Re: [NMusers] When to do transformation of data?
Date: Mon, 29 Apr 2002 06:03:48 +0200

Hi,

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

THETA(x) and THETA(y) will have the same meaning as on the untransformed scale
with

Y=F+SQRT(THETA(y)**2+THETA(x)**2*F**2)*EPS(1)
with
\$SIGMA 1 FIX

As for zero predictions with lag-time models, you would have to condition this
LOG(F)-variance model. Alternatively, compared to a lag-time model, I have not
seen worse behaviour with a chain of transit compartments (all with the same rate
constant) and often better (lower OFV, more stable). A chain of transit
compartments will not predict a zero concentration. The only drawback is
sometimes longer runtimes. I usually use 3-5 compartments in the chain. If you
want really lag-time like behaviour (still without zero predictions), you could
increase that further.

In general with log-transformation, I have found that run-times can be both
considerably longer and considerably shorter than without transformation. I have
not seen a pattern that allows me to make a prediction which will happen. Maybe
someone has an explanation.

Best regards,
Mats

Mats Karlsson, PhD
Professor of Pharmacometrics
Div. of Pharmacokinetics and Drug Therapy
Dept. of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
SE-751 24 Uppsala
Sweden
phone +46 18 471 4105
fax   +46 18 471 4003
mats.karlsson@farmbio.uu.se

*******
From:  "atul"
Subject:  [NMusers] When to do transformation of data?
Date:  April 29, 2002

Dr Karlsson/nmusers

What aspects of non-transformed data runs do you look into before deciding
to transform the data? I am trying to look into literature if anybody has
discussed this specifically while doing analysis in NONMEM? Could you
suggest to me any reference which has looked into these aspects and
compared the results? How does this impact any model validation or qualification?

Atul

*******

From: Mats Karlsson [Mats.Karlsson@farmbio.uu.se]
Subject: Re: [NMusers] When to do transformation of data?
Sent: Monday, April 29, 2002 2:38 PM

Dear ATul,

I would often try it regardless of diagnostics, but a skewed distribution of
WRES (more high outliers than low) is usually a sign  that transformation
will
improve things.

Best regards,
Mats

Mats Karlsson, PhD
Professor of Pharmacometrics
Div. of Pharmacokinetics and Drug Therapy
Dept. of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
SE-751 24 Uppsala
Sweden
phone +46 18 471 4105
fax   +46 18 471 4003
mats.karlsson@farmbio.uu.se

*******

From: "Kowalski, Ken"
Subject: RE: [NMusers] When to do transformation of data?
Date: Mon, 29 Apr 2002 16:16:15 -0400

Atul,

diagnostic that might suggest the need for a log-transformation is when a
concordance plot of PRED vs OBS shows bias but a plot of IPRED vs OBS does
not.  You can think of the log-transformation as providing a geometric mean
prediction rather than an arithmetic mean prediction.  The geometric mean is
a better measure of central tendency when the data are right-skewed.

A good discussion on this topic can be found in

Carroll & Ruppert, Transformations and Weighting in Regression, Chapman &
Hall, NY (1988).

They devote a whole chapter to the "transform-both-sides" approach.
Although the text is devoted to linear and nonlinear fixed effects models,
many of the results are relevant for mixed effects models as well.

Ken

```