# NONMEM Users Network Archive

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From: Bauer, Robert <Robert.Bauer>
Date: Thu, 5 Nov 2009 09:01:23 -0500

Leonid:
Agreed.

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

-----Original Message-----
From: Leonid Gibiansky [mailto:LGibiansky
Sent: Thursday, November 05, 2009 6:20 AM
To: Bauer, Robert
Cc: Nick Holford; nmusers

Bob,

You seems to protect only from positive x=infinity overflow
Do we also need to worry about negatives x=-infinity?

If yes, we also need lines:
IF (EXPP<-100.0) EXPP=-100.0 ;protect against floating overflow

If not, then the second part of the code:
> EXPP=MU_1+ETA(1)
> IF (EXPP>100.0) EXPP=100.0 ;protect against floating overflow
> EXPW=EXP(-EXPP)
protects from the wrong overflow, it needs to be replaced by
> IF (EXPP<-100.0) EXPP=-100.0 ;protect against floating overflow

Leonid

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

Bauer, Robert wrote:
> Nick:
> Because EXPP could be highly negative, then EXP(-EXPP) has the
potential
> to result in floating overflow. So, a filtering line would still be
good.
> **
> Using the logit code, the theta(1) would indeed be more easily
> interpretable. However, as you say, your theta would need to be
> constrained between 0 and 1
>
> But, if we wish to retain linear mu modeling, something that is good
to
> do for importance sampling, and sometimes essential for SAEM, then
> the parameterization I originally recommended would be most suitable:
.
>
> 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)
>
> or
> MU_1=THETA(1)
> EXPP=MU_1+ETA(1)
> IE (EXPP>100.0) EXPP=100.0 ;protect against floating overflow
> EXPW=EXP(-EXPP)
> BIO=1/(1.0+EXPW)
>
> would be best. Furthermore, theta(1) itself may be negative infinity
to
> positive infinity, so no boundaries are necessary to theta(1). All of

> these factors make the analysis particularly amenable to Gibbs
sampling
> when doing BAYES analysis as well. Otherwise, non-linear mu/theta
> relationships and boundary imposing means Metropolis-Hastings sampling

> must be done, a less efficient process.
>
> When the analysis is done, the final result thetas could be
transformed
> to more meaningful values:
>
> Thetap(1)=1/(1+exp(-theta(1)))
>
> and reported in that fashion. The transformation patterns after the
> individual subject parameter BIO and its relationship to theta.
> An appropriate propagation of errors algorithm would be used to
> transform the standard errors as well.
>
>
> *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:* Wednesday, November 04, 2009 10:40 PM
> *To:* nmusers
>
> Peiming,
>
> Thank you for pointing out my mistake again!
>
> Perhaps next time you should make the correction and send it to
nmusers :-)
>
> MU_1=LOG(THETA(1)/(1-THETA(1)) ; logit of population bioavailability
>
> EXPP=MU_1+ETA(1) ; add random effect
>
> BIO=1/(1+EXP(-EXPP)) ; individual bioavailability
>
>
>
> Nick
>
> Ma, Peiming wrote:
>>
>> Unfortunately, Nick, you have an extra EXP: the denominator of BIO
>> should be just 1 + EXP(-EXPP). J
>>
>> Cheers,
>>
>>
------------------------------------------------------------------------
>>
>> *From:* owner-nmusers
>> [mailto:owner-nmusers
>> *Sent:* Wednesday, November 04, 2009 3:43 PM
>> *To:* nmusers
>>
>> Hi,
>>
>> Thanks to Peiming Ma and Thuy Vu for pointing out an error in my
>> attempt to transform bioavailability into its logit.
>>
>> The logit transformation of a probability is ln(P/(1-P)) i.e. the log

>> of the odds ratio. The reverse transform is correct i.e. exp(logit)
is
>> the odds ratio and P is then OR/(1+OR) (or 1/1+exp(-logit)).
>>
>> If THETA(1) is the bioavailability then this is (I hope) the correct
>> transformation of THETA(1) and reverse transform to get the
>> individual bioavailability with a random effect constrained to be
>> within 0 and 1.
>>
>> MU_1=LOG(THETA(1)/(1-THETA(1)) ; logit of population =
bioavailability
>>
>> EXPP=MU_1+ETA(1) ; add random effect
>>
>> BIO=1/(1+EXP(-EXP(EXPP))) ; individual bioavailability
>>
>>
>> Nick
>>
>> --
>> Nick Holford, Professor Clinical Pharmacology
>> Dept Pharmacology & Clinical Pharmacology
>> University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New
Zealand
>> tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
>> email: n.holford
>> http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
>
> --
> Nick Holford, Professor Clinical Pharmacology
> Dept Pharmacology & Clinical Pharmacology
> University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New
Zealand
> tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
> email: n.holford
> http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
>
> ICON plc made the following annotations.
>
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