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Re: distribution assumption of Eta in NONMEM

From: Nick Holford <n.holford>
Date: Mon, 31 May 2010 21:34:33 +0200

Leonid,

I meant by OMEGA(1) the OMEGA value estimated by NONMEM. I suppose I
should have written OMEGA(1,1) to be more precise -- sorry!

Nick

Leonid Gibiansky wrote:
> 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
>>

--
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 - 15:34:33 EDT

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