From: Bauer, Robert <*Robert.Bauer*>

Date: Wed, 4 Nov 2009 23:18:01 -0500

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

On Behalf Of Nick Holford

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). :-)

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

ICON plc made the following annotations.

-------------------------------------------------------------------------=

-----

This e-mail transmission may contain confidential or legally privileged i=

nformation

that is intended only for the individual or entity named in the e-mail ad=

dress. If you

are not the intended recipient, you are hereby notified that any disclosu=

re, copying,

distribution, or reliance upon the contents of this e-mail is strictly pr=

ohibited. If

you have received this e-mail transmission in error, please reply to the =

sender, so that

ICON plc can arrange for proper delivery, and then please delete the mess=

age.

Thank You,

ICON plc

South County Business Park

Leopardstown

Dublin 18

Ireland

Registered number: 145835

Received on Wed Nov 04 2009 - 23:18:01 EST

Date: Wed, 4 Nov 2009 23:18:01 -0500

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

On Behalf Of Nick Holford

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). :-)

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

ICON plc made the following annotations.

-------------------------------------------------------------------------=

-----

This e-mail transmission may contain confidential or legally privileged i=

nformation

that is intended only for the individual or entity named in the e-mail ad=

dress. If you

are not the intended recipient, you are hereby notified that any disclosu=

re, copying,

distribution, or reliance upon the contents of this e-mail is strictly pr=

ohibited. If

you have received this e-mail transmission in error, please reply to the =

sender, so that

ICON plc can arrange for proper delivery, and then please delete the mess=

age.

Thank You,

ICON plc

South County Business Park

Leopardstown

Dublin 18

Ireland

Registered number: 145835

Received on Wed Nov 04 2009 - 23:18:01 EST