From: Leonid Gibiansky <*LGibiansky*>

Date: Mon, 31 May 2010 13:23:42 -0400

Nick, Mats

I would guess that nonmem should inflate variance (for this example)

trying to fit the observed uniform (-0.5, 0.5) into some normal N(0, ?).

This example (if I read it correctly) shows that Nonmem somehow

estimates variance without making distribution assumption.

Nick, you mentioned:

"the mean estimate of OMEGA(1) was 0.0827"

does it mean that Nonmem-estimated OMEGA was close to 0.0827 or you

refer to the variances of estimated ETAs?

Thanks

Leonid

--------------------------------------

Leonid Gibiansky, Ph.D.

President, QuantPharm LLC

web: www.quantpharm.com

e-mail: LGibiansky at quantpharm.com

tel: (301) 767 5566

Mats Karlsson wrote:

*> Nick,
*

*>
*

*>
*

*>
*

*> It has been showed over and over again that empirical Bayes estimates,
*

*> when individual data is rich, will resemble the true individual
*

*> parameter regardless of the underlying distribution. Therefore I donâ€™t
*

*> understand what you think this exercise contributes.
*

*>
*

*>
*

*>
*

*> Best regards,
*

*>
*

*> Mats
*

*>
*

*>
*

*>
*

*> Mats Karlsson, PhD
*

*>
*

*> Professor of Pharmacometrics
*

*>
*

*> Dept of Pharmaceutical Biosciences
*

*>
*

*> Uppsala University
*

*>
*

*> Box 591
*

*>
*

*> 751 24 Uppsala Sweden
*

*>
*

*> phone: +46 18 4714105
*

*>
*

*> fax: +46 18 471 4003
*

*>
*

*>
*

*>
*

*> *From:* owner-nmusers *

*> [mailto:owner-nmusers *

*> *Sent:* Monday, May 31, 2010 6:05 PM
*

*> *To:* nmusers *

*> *Cc:* 'Marc Lavielle'
*

*> *Subject:* Re: [NMusers] distribution assumption of Eta in NONMEM
*

*>
*

*>
*

*>
*

*> Hi,
*

*>
*

*> I tried to see with brute force how well NONMEM can produce an empirical
*

*> Bayes estimate when the ETA used for simulation is uniform. I attempted
*

*> to stress NONMEM with a non-linear problem (the average DV is 0.62). The
*

*> mean estimate of OMEGA(1) was 0.0827 compared with the theoretical value
*

*> of 0.0833.
*

*>
*

*> The distribution of 1000 EBEs of ETA(1) looked much more uniform than
*

*> normal.
*

*> Thus FOCE show no evidence of normality being imposed on the EBEs.
*

*>
*

*> $PROB EBE
*

*> $INPUT ID DV UNIETA
*

*> $DATA uni1.csv ; 100 subjects with 1 obs each
*

*> $THETA 5 ; HILL
*

*> $OMEGA 0.083333333 ; PPV_HILL = 1/12
*

*> $SIGMA 0.000001 FIX ; EPS1
*

*>
*

*> $SIM (1234) (5678 UNIFORM) NSUB=10
*

*> $EST METHOD=COND MAX=9990 SIG=3
*

*> $PRED
*

*> IF (ICALL.EQ.4) THEN
*

*> IF (NEWIND.LE.1) THEN
*

*> CALL RANDOM(2,R)
*

*> UNIETA=R-0.5 ; U(-0.5,0.5) mean=0, variance=1/12
*

*> HILL=THETA(1)*EXP(UNIETA)
*

*> Y=1.1**HILL/(1.1**HILL+1)
*

*> ENDIF
*

*> ELSE
*

*>
*

*> HILL=THETA(1)*EXP(ETA(1))
*

*> Y=1.1**HILL/(1.1**HILL+1) + EPS(1)
*

*> ENDIF
*

*>
*

*> REP=IREP
*

*>
*

*> $TABLE ID REP HILL UNIETA ETA(1) Y
*

*> ONEHEADER NOPRINT FILE=uni.fit
*

*>
*

*> I realized after a bit more thought that my suggestion to transform the
*

*> eta value for estimation wasn't rational so please ignore that senior
*

*> moment in my earlier email on this topic.
*

*>
*

*> 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 Mon May 31 2010 - 13:23:42 EDT

Date: Mon, 31 May 2010 13:23:42 -0400

Nick, Mats

I would guess that nonmem should inflate variance (for this example)

trying to fit the observed uniform (-0.5, 0.5) into some normal N(0, ?).

This example (if I read it correctly) shows that Nonmem somehow

estimates variance without making distribution assumption.

Nick, you mentioned:

"the mean estimate of OMEGA(1) was 0.0827"

does it mean that Nonmem-estimated OMEGA was close to 0.0827 or you

refer to the variances of estimated ETAs?

Thanks

Leonid

--------------------------------------

Leonid Gibiansky, Ph.D.

President, QuantPharm LLC

web: www.quantpharm.com

e-mail: LGibiansky at quantpharm.com

tel: (301) 767 5566

Mats Karlsson wrote:

Received on Mon May 31 2010 - 13:23:42 EDT