RE: FW: advan8 vs. advan13 (CORRECTION)

-----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 > >