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
advan8 vs. advan13 (CORRECTION)
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) EXPP0.0 ;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) EXPP0.0 ;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
Quoted reply history
________________________________
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
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: [email protected]
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
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) EXPP0.0 ;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) EXPP0.0 ;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) EXPP0.0 ;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
>
>
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
Quoted reply history
-----Original Message-----
From: Leonid Gibiansky [mailto:LGibiansky
Sent: Thursday, November 05, 2009 6:20 AM
To: Bauer, Robert
Cc: Nick Holford; nmusers
Subject: Re: FW: [NMusers] advan8 vs. advan13 (CORRECTION)
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) EXPP0.0 ;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) EXPP0.0 ;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) EXPP0.0 ;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
>
>
Dear Bob,
Dear Nick,
Dear Leonid,
Thank you very much for showing us this trick.
Will be happy to try this both-sided protection feature.
In my experience with MC-PEM in S-ADAPT, I did not have
any problems even with the unprotected version of the
code proposed by Bob:
MU_1=THETA(1)
EXPP=MU_1+ETA(1)
EXPW=EXP(-EXPP)
BIO=1/(1.0+EXPW)
I agree that one should take much more care to write
robust / protected code with MC-PEM than with FOCE,
for example.
Best wishes
Juergen
Quoted reply history
-----Original Message-----
From: owner-nmusers
Behalf Of Bauer, Robert
Sent: Thursday, November 05, 2009 9:01 AM
To: Leonid Gibiansky
Cc: Nick Holford; nmusers
Subject: RE: [NMusers] advan8 vs. advan13 (CORRECTION)
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
Subject: Re: FW: [NMusers] advan8 vs. advan13 (CORRECTION)
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) EXPP0.0 ;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) EXPP0.0 ;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) EXPP0.0 ;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
>
>
Juergen (Bob, Nick, Leonid)
FYI: In WinBUGS I also don't get problems with:
> MU_1=THETA(1)
> EXPP=MU_1+ETA(1)
> EXPW=EXP(-EXPP)
> BIO=1/(1.0+EXPW)
Regards
Steve
--
Professor Stephen Duffull
Chair of Clinical Pharmacy
School of Pharmacy
University of Otago
PO Box 913 Dunedin
New Zealand
E: [email protected]
P: +64 3 479 5044
F: +64 3 479 7034
Design software: www.winpopt.com