From: Nick Holford <*n.holford*>

Date: Thu, 05 Nov 2009 12:42:44 +1300

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

Received on Wed Nov 04 2009 - 18:42:44 EST

Date: Thu, 05 Nov 2009 12:42:44 +1300

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

Received on Wed Nov 04 2009 - 18:42:44 EST