NONMEM Users Network Archive

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Re: distribution assumption of Eta in NONMEM

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 don’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

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