# RE: distribution assumption of Eta in NONMEM

From: Mats Karlsson <mats.karlsson>
Date: Mon, 31 May 2010 18:35:59 +0200

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
On Behalf Of Nick Holford
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

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 - 12:35:59 EDT

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