From: Leonid Gibiansky <*LGibiansky*>

Date: Thu, 05 Nov 2009 06:20:12 -0500

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
*

*> *Subject:* Re: FW: [NMusers] advan8 vs. advan13 (CORRECTION)
*

*>
*

*> 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
*

*>> *Subject:* Re: [NMusers] advan8 vs. advan13 (CORRECTION)
*

*>>
*

*>> 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
*

*>
*

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*

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Received on Thu Nov 05 2009 - 06:20:12 EST

Date: Thu, 05 Nov 2009 06:20:12 -0500

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:

protects from the wrong overflow, it needs to be replaced by

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:

Received on Thu Nov 05 2009 - 06:20:12 EST