# NONMEM Users Network Archive

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From: Nick Holford <n.holford>
Date: Tue, 03 Nov 2009 08:21:51 +1300

Pavel,

Your model for bioavailability (BIO) (as interpreted by Bob) uses a
random effects model that is based on the normal distribution:

BIO=THETA(1) + ETA(1)

Because there is no constraint on ETA(1) this can lead to negative
values or positive values greater than 1 for individual BIO which is not
realistic.

You could avoid negative individual values of BIO by using this
parameter random effect model which is based on a lognormal distribution:

BIO=THETA(1) * EXP(ETA(1))

However, the lognormal distribution can generate BIO values greater than
1 which once again is not realistic.

So Bob has illustrated how to use a different random effects model based
on the logistic distribution. This will constrain BIO to lie between 0
and 1.

MU_1=THETA(1)
EXPP=MU_1+ETA(1)
BIO=1/(1+EXP(-EXP(EXPP)))

The value of THETA(1) will be a bit harder to interpret because it will
be the logit of bioavailability. You can get a more interpretable value
of THETA(1) with this code:

LBIO=LOG(THETA(1))
MU_1=LBIO/(1-LBIO)
EXPP=MU_1+ETA(1)
BIO=1/(1+EXP(-EXP(EXPP)))

Bob,

I think you can avoid the test for values of EXPW which could cause
overflow by calculating BIO as shown above. This relies on the compiler
rounding large negative values of exp() to a value of zero which is the
usual behaviour.

Best wishes,

Nick

Bauer, Robert wrote:
> Pavel:
> Another thing I noted is that when IMP is used, the lower boundary for
> bioavailability cannot be 0
>
> Typically, Monte Carlo methods try a large number of etas, from
> negative infinity to positive infinity. You may want to remodel your
> bioavailability to something like:
>
> MU_1=THETA(1)
> EXPP=MU_1+ETA(1)
> IE (EXPP>100.0) EXPP=100.0 ;protect against floating overflow
> EXPW=EXP(EXPP)
> BIO=EXPW/(1.0+EXPW)
>
> This way, BIO will always be between 0 and 1, regardless of eta value
> You can now remove the boundaries to the theta.
>
>
>
> *Robert J. Bauer, Ph.D.
> Vice President, Pharmacometrics
> ICON Development Solutions*
>
> *Tel:* (215) 616-6428
> *Mob: *(925) 286-0769
> *Email: Robert.Bauer
> *Web:* www.icondevsolutions.com
>
>
>
>
>
>
>
> ------------------------------------------------------------------------
> *From:* owner-nmusers
> [mailto:owner-nmusers
> *Sent:* Sunday, November 01, 2009 1:57 PM
> *To:* nmusers
>
> Pavel,
>
> The TRANSn option is only meaningful for those ADVANs (i.e. 1-4,11,12)
> which implement a closed form solution of the PK model. TRANS1 does
> nothing except keep the linker happy. Because it is the default it
> need never be explicitly specified for ADVAN5-9,13.
>
> "TRANS1 Dummy, or null, translator; may be used with all ADVAN
> routines. It is the default." NONMEM7 Help
>
> Adding it to those ADVANs which solve ODEs or use matrix exponential
> solutions should make no difference to anything. If you find that
> adding TRANS1 changes the behaviour of ADVAN8 then this is a bug.
>
> Nick
>
>
> nonmem
> > Hello Nonmem Users,
> >
> > When I tried simple simulations and changed advan13 to advan8, some
> concentrations changed. Equations were stiff. Then I added TRANS1 to
> output changed and looked exactly like ADVAN13 output. Do you know
> what happened?
> >
> > (Another thing I noted is that when IMP is used, the lower boundary
> for bioavailability cannot be 0.)
> >
> > Thanks,
> > Pavel
> >
> > ----- Original Message -----
> > From: nonmem
> > Date: Sunday, November 1, 2009 8:34 am
> > To: nmusers
> >
> > > It seems like advan8 has integration difficulties when both LAG
> > > time and variability in Ka are implemented. Method=IMP has
> > > if reporting issues, it keeps running. The objective function
> > > is very low even when bioavailability is almost zero. Removing
> > > LAG and eta of Ka may fix it.
> > >
> > > ----- Original Message -----
> > > From: nonmem
> > > Date: Sunday, November 1, 2009 12:04 am
> > > To: nmusers
> > >
> > > > Hello NONMEM users,
> > > >
> > > > Because advan13 was recomended for both stiff and nonstiff
> > > > differential equations, I used it for stiff differential
> > > > equations. It appeared that some results looked too sensitive
> > > > to a parameters representing a "slow" processes. I did not
> > > > observe it with nonmem6. When I used advan8, the objective
> > > > function changed from 10228.853 (the final value; diagnostic
> > > > plots looked good) to 5512.594 (the first value; I im still
> > > > waiting for the final value of the objective function).
> > > >
> > > > Does it mean that advan13 should be used with caution when the
> > > > equations are stiff or advan13 cannot replace advan8?
> > > >
> > > > Thanks,
> > > > Pavel
> > > >
> > >
>
> --
> Nick Holford, Professor Clinical Pharmacology
> Dept Pharmacology & Clinical Pharmacology
> University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
> Zealand
> n.holford
> mobile: +64 21 46 23 53
> http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
>
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--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
n.holford
mobile: +64 21 46 23 53
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford

Received on Mon Nov 02 2009 - 14:21:51 EST

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