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RE: Linear VS LTBS

From: Mats Karlsson <mats.karlsson>
Date: Mon, 24 Aug 2009 01:13:23 +0200



Pls see below.


Best regards,



Mats Karlsson, PhD

Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences

Uppsala University

Box 591

751 24 Uppsala Sweden

phone: +46 18 4714105

fax: +46 18 471 4003


From: owner-nmusers
Behalf Of Nick Holford
Sent: Sunday, August 23, 2009 11:02 PM
To: Leonid Gibiansky
Cc: nmusers
Subject: Re: [NMusers] Linear VS LTBS



This is what I wanted to bring to the attention of nmusers:

"Of course, I agree that overparameterisation could be a cause of
convergence problems but I would not agree that this is often the reason. "

If you can provide some evidence that over-paramerization is *often* the
cause of convergence problems then I will be happy to consider it.

What kind of evidence did you have in mind?

My experience with NM7 beta has not convinced me that the new methods are
helpful compared to FOCE. They require much longer run times and currently
mysterious tuning parameters to do anything useful.

Truly exponential error is never the truth. This is a model that is wrong
and IMHO not useful. You cannot get sensible optimal designs from models
that do not have an additive error component.

All models are wrong and I see no reason why the exponential error model
would be different although I think it is better than the proportional error
for most situations. It seems that you assume that whenever TBS is used,
only an additive error (on the transformed scale) is used. Is that why you
say it is wrong? Or is it because you believe in negative concentrations?


Why would you not be able to get sensible information from models that don't
have an additive error component? (You can of course have a residual error
magnitude that increases with decreasing concentrations without having to
have an additive error; this regardless of whether you use the untransformed
or transformed scale).


Leonid Gibiansky wrote:

Hi Nick,

You are once again ignoring the actual evidence that NONMEM VI will fail to
converge or not complete the covariance step for over-parametrized problems

Sure, there are cases when it doesn't converge even if the model is
reasonable, but it does not mean that we should ignore these warning signs
of possible ill-parameterization. I think that the group is already tired of
our once-a-year discussions on the topic, so, let's just agree to disagree
one more time :)

Nonmem VII unlike earlier versions will provide you with the standard errors
even for non-converging problems. Also, you will always be able to use
Bayesian or SAEM, and never worry about convergence, just stop it at any
point and do VPC to confirm that the model is good :)

Yes, indeed, I observed that FOCEI with non-transformed variables was always
or nearly always equivalent to FOCEI in log-transformed variables. Still,
truly exponential error cannot be described in original variables, so I
usually try both in the first several models, and then decide which of them
to use fro model development.


Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
e-mail: LGibiansky at
tel: (301) 767 5566

Nick Holford wrote:


You are once again ignoring the actual evidence that NONMEM VI will fail to
converge or not complete the covariance step more or less at random. If you
bootstrap simulated data in which the model is known and not
overparameterised it has been shown repeatedly that NONMEM VI will sometimes
converge and do the covariance step and sometimes fail to converge.

Of course, I agree that overparameterisation could be a cause of convergence
problems but I would not agree that this is often the reason.

Bob Bauer has made efforts in NONMEM 7 to try to fix the random termination
behaviour and covariance step problems by providing additional control over
numerical tolerances. It remains to be seen by direct experiment if NONMEM 7
is indeed less random than NONMEM VI.

BTW in this discussion about LTBS I think it is important to point out that
the only systematic study I know of comparing LTBS with untransformed models
was the one you reported at the 2008 PAGE meeting
( My understanding of your results was
that there was no clear advantage of LTBS if INTER was used with
non-transformed data:
"Models with exponential residual error presented in the log-transformed
performed similar to the ones fitted in original variables with INTER
option. For problems with
residual variability exceeding 40%, use of INTER option or
log-transformation was necessary to
obtain unbiased estimates of inter- and intra-subject variability."

Do you know of any other systematic studies comparing LTBS with no


Leonid Gibiansky wrote:

Large RSE, inability to converge, failure of the covariance step are often
caused by the over-parametrization of the model. If you already have
bootstrap, look at the scatter-plot matrix of parameters versus parameters
(THATA1 vs THETA2, .., THETA1 vs OMEGA1, ...), these are very informative
plots. If you have over-parametrization on the population level, it will be
seen in these plots as strong correlations of the parameter estimates.

Also, look on plots of ETAs vs ETAs. If you see strong correlation (close to
1) there, it may indicate over-parametrization on the individual level (too
many ETAs in the model).

For random effect with a very large RSE on the variance, I would try to
remove it and see what happens with the model: often, this (high RSE) is the
indication that the error effect is not needed.

Also, try combined error model (on log-transformed variables):

  Y = LOG(IPRED) + W1*EPS(1)


Why concentrations were on LOQ? Was it because BQLs were inserted as LOQ?
Then this is not a good idea.

Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
e-mail: LGibiansky at
tel: (301) 767 5566

Indranil Bhattacharya wrote:

Hi Joachim, thanks for your suggestions/comments.
When using LTBS I had used a different error model and the error block is
shown below
IPRED = -5
IF (F.GT.0) IPRED = LOG(F) ;log transforming predicition
IWRES=IRES/W ;Uniform Weighting
Y = IPRED + ERR(1)
I also performed bootsrap on both LTBS and non-LTBS models and the non-LTBS
CI were much more tighter and the precision was greater than non-LTBS.
I think the problem plausibly is with the fact that when fitting the
non-transformed data I have used the proportional + additive model while
using LTBS the exponential model (which converts to additional model due to
LTBS) was used. The extra additive component also may be more important in
the non-LTBS model as for some subjects the concentrations were right on
I tried the dual error model for LTBS but does not provide a CV%. So I am
currently running a bootstrap to get the CI when using the dual error model
with LTBS.

On Fri, Aug 21, 2009 at 3:01 AM, Grevel, Joachim

    Hi Neil,
         1. When data are log-transformed the $ERROR block has to change:
    additive error becomes true exponential error which cannot be
    achieved without log-transformation (Nick, correct me if I am wrong).
         2. Error cannot "go away". You claim your structural model (THs)
    remained unchanged. Therefore the "amount" of error will remain the
    same as well. If you reduce BSV you may have to "pay" for it with
    increased residual variability.
         3. Confidence intervals of ETAs based on standard errors produced
    during the covariance step are unreliable (many threads in NMusers).
    Do bootstrap to obtain more reliable C.I..
         These are my five cents worth of thought in the early morning,
         Good luck,


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        -----Original Message-----

        *From:* owner-nmusers
        *Sent:* 20 August 2009 17:07
        *To:* nmusers
        *Subject:* [NMusers] Linear VS LTBS

        Hi, while data fitting using NONMEM on a regular PK data set
        and its log transformed version I made the following observations
                   - PK parameters (thetas) were generally similar between
        regular and when using LTBS.
        -ETA on CL was similar
        -ETA on Vc was different between the two runs.
        - Sigma was higher in LTBS (51%) than linear (33%)
                 Now using LTBS, I would have expected to see the ETAs
        or actually decrease and accordingly I observed that the eta
        values decreased showing less BSV. However the %RSE for ETA on
        VC changed from 40% (linear) to 350% (LTBS) and further the
        lower 95% CI bound has a negative number for ETA on Vc (-0.087).
                 What would be the explanation behind the above observations

        regarding increased %RSE using LTBS and a negative lower bound
        for ETA on Vc? Can a negative lower bound in ETA be considered
        as zero?
        Also why would the residual vriability increase when using LTBS?
                 Please note that the PK is multiexponential (may be this is


        -- Indranil Bhattacharya

Indranil Bhattacharya


Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
mobile: +64 21 46 23 53

Received on Sun Aug 23 2009 - 19:13:23 EDT

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