From: Nick Holford <*n.holford*>

Date: Mon, 31 May 2010 18:05:06 +0200

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 - 12:05:06 EDT

Date: Mon, 31 May 2010 18:05:06 +0200

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 - 12:05:06 EDT