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RE: FW: advan8 vs. advan13 (CORRECTION)

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

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

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