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-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Nick Holford Sent: Monday, May 31, 2010 6:05 PM To: nmusers@globomaxnm.com 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.holf...@auckland.ac.nz http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
