RE: Problem with HESSIAN
Hi Jacob,
You could try to replace that part with:
DEL = 0.01
IPRED= FX
W = SQRT(THETA(8)**2*FX**2 + (1-TYP)*THETA(9)**2 + TYP*THETA(10)**2)
IRES = DV-IPRED
IWRES= IRES/(W+DEL)
Reason:
1) as long as theta9/10 combination is not zero, the square root does not need
protection.
2) comparing against a floating number is never a good idea, because of the
mantra (residual part of a floating number that is not defined). Nonmem/fortran
mostly seem to do a good job at it nevertheless. However I do not expect the
result to be guaranteed to protect the division.
Does this help?
Jeroen
Jeroen Elassaiss-Schaap, PhD
Modeling & Simulation Expert
Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3)
Early Clinical Research and Experimental Medicine
Schering-Plough Research Institute
T: +31 41266 9320
Quoted reply history
-----Original Message-----
From: [email protected] [mailto:[email protected]] On
Behalf Of Brogren, Jacob
Sent: Thursday, 25 June, 2009 10:12
To: Nmusers (E-mail)
Subject: [NMusers] Problem with HESSIAN
Hi all,
surely a trivial, but still, problem:
I get
"HESSIAN OF POSTERIOR DENSITY IS NON-POSITIVE-DEFINITE DURING SEARCH"
when trying to run the model (model1 below).
I managed to run the ADVAN4 version (model2 below) and got successful
minimization and plausible estimates, but now when I want to restate the model
as defferential equations the problem occurs. What I could find out from
nmusers was that this has something to do with predictions being zero (right?).
I try to "protect" with the DEL variable (see code).
Any suggestions?
==========================================================================
Model 1
==========================================================================
$PROB Restate model using $DES
$INPUT ID DAT2=DROP TIME EVID AMT DV MDV UVOL CMT DOSE FOOD OCC AGE CREA CLCR
TYP
$DATA ../data/data5.csv IGNORE=@
$SUBS ADVAN6 TOL=3
$MODEL COMP=DEPOT ; 1. Absorption
COMP=CENTRAL ; 2. Central
COMP=PERIPH ; 3. Peripheral
COMP=URINE ; 4. Urine (output)
$PK
TVF1 = 1
TVLG = THETA(1)
TVKA = THETA(2)
TVCL = THETA(3)
TCLR = THETA(4)
TVV2 = THETA(5)
TVQ = THETA(6)
TVV3 = THETA(7)
ALAG1 = TVLG
KA = TVKA
F1 = TVF1*EXP(ETA(1))
CL = TVCL
CLR = TCLR
V2 = TVV2
Q = TVQ
V3 = TVV3
S2 = V2
S4 = UVOL
$DES
K23 = Q/V2
K32 = Q/V3
K24 = CLR/V2
K20 = (CL-CLR)/V2
DADT(1) = - KA*A(1)
DADT(2) = KA*A(1) - K23*A(2) + K32*A(3) - K20*A(2) - K24*A(2)
DADT(3) = K23*A(2) - K32*A(3)
DADT(4) = K24*A(2)
$ERROR
CP = A(2)/S2
CUR = A(4)/S4
FX = (1-TYP)*CP + TYP*CUR
DEL = 0
IF (FX.EQ.0) DEL=1
IPRED= FX
W = SQRT(THETA(8)**2*FX**2 + (1-TYP)*THETA(9)**2 + TYP*THETA(10)**2 + DEL)
IRES = DV-IPRED
IWRES= IRES/W
Y = IPRED + ERR(1)*W
$THETA
(0,...) ; ALAG1 (lag time)
(0,...) ; KA
(0,...) ; CL
(0,...) ; CLR
(0,...) ; V2
(0,...) ; Q
(0,...) ; V3
(0,...) ; proportional error
(0,...) ; additive error (plasma)
(0,...) ; additive error (urine)
$OMEGA 0.09
$SIGMA 1 FIX
$EST PRINT=1 MAXEVAL=9999 METHOD=1 INTER POSTHOC
$COV PRINT=E
==========================================================================
Model 2
==========================================================================
$PROB Renal data included
$INPUT ID DAT2=DROP TIME EVID AMT DV MDV UVOL CMT DOSE FOOD OCC AGE CREA CLCR
TYP
$DATA ../data/data4.csv IGNORE=@
$SUBS ADVAN4 TRANS4
$PK
TVF1 = 1
TVLG = THETA(1)
TVKA = THETA(2)
TVCL = THETA(3)
TCLR = THETA(4)
TVV2 = THETA(5)
TVQ = THETA(6)
TVV3 = THETA(7)
ALAG1 = TVLG*EXP(ETA(1))
KA = TVKA
F1 = TVF1
CL = TVCL
CLR = TCLR
V2 = TVV2
Q = TVQ
V3 = TVV3
F0 = CLR/CL
S2 = V2
S0 = UVOL
$ERROR
DEL = 0
IF (F.EQ.0) DEL=1
IPRED=F
W = SQRT(THETA(8)**2*FX**2 + (1-TYP)*THETA(9)**2 + TYP*THETA(10)**2 + DEL)
IRES = DV-IPRED
IWRES= IRES/W
Y = F + ERR(1)*W
$THETA
(0,...) ; ALAG1 (lag time)
(0,...) ; KA
(0,...) ; CL
(0,...) ; CLR
(0,...) ; V2
(0,...) ; Q
(0,...) ; V3
(0,...) ; proportional error (plasma)
(0,...) ; additive error (plasma)
(0,...) ; additive error (urine)
$OMEGA 0.09
$SIGMA 1 FIX
$EST PRINT=1 MAXEVAL=9999 METHOD=1 INTER POSTHOC
$COV PRINT=E
==============================================================================
Data file (data5.csv) for ADVAN6 model. First ID. ([...]=masked data)
==============================================================================
ID DAT2 TIME EVID AMT DV MDV UVOL CMT
[...] TYP
101 1973-07-10 08:19 2 . . 1 . 4
[...] 1
101 1973-07-10 08:21 0 . . 1 . 2
[...] 0
101 1973-07-10 08:30 1 10000 . 1 . 1
[...] 0
101 1973-07-10 08:46 0 . [...] 0 . 2
[...] 0
101 1973-07-10 09:01 0 . [...] 0 . 2
[...] 0
101 1973-07-10 09:17 0 . [...] 0 . 2
[...] 0
101 1973-07-10 09:31 0 . [...] 0 . 2
[...] 0
101 1973-07-10 10:01 0 . [...] 0 . 2
[...] 0
101 1973-07-10 10:31 0 . [...] 0 . 2
[...] 0
101 1973-07-10 11:01 0 . [...] 0 . 2
[...] 0
101 1973-07-10 11:31 0 . [...] 0 . 2
[...] 0
101 1973-07-10 12:30 0 . [...] 0 . 2
[...] 0
101 1973-07-10 14:14 0 . [...] 0 0.6 4
[...] 1
101 1973-07-10 14:14 2 . . 1 . -4
[...] 1
101 1973-07-10 14:14 2 . . 1 . 4
[...] 1
101 1973-07-10 14:31 0 . [...] 0 . 2
[...] 0
101 1973-07-10 17:30 0 . . 1 . 2
[...] 0
101 1973-07-10 20:30 0 . . 1 . 2
[...] 0
101 1973-07-10 20:44 0 . [...] 0 0.8 4
[...] 1
101 1973-07-10 20:44 2 . . 1 . -4
[...] 1
101 1973-07-10 20:44 2 . . 1 . 4
[...] 1
101 1973-07-11 08:31 0 . . 1 . 2
[...] 0
101 1973-07-11 08:51 0 . [...] 0 0.7 4
[...] 1
101 1973-07-11 08:51 2 . . 1 . -4
[...] 1
[...]
==============================================================================
Data file (data4.csv) for ADVAN4 model. First ID. ([...]=masked data)
==============================================================================
ID DAT2 TIME EVID AMT DV MDV UVOL CMT
[...] TYP
101 1973-07-10 08:19 2 . . 1 . 4
[...] 1
101 1973-07-10 08:21 0 . . 1 . 2
[...] 0
101 1973-07-10 08:30 1 10000 . 1 . 1
[...] 0
101 1973-07-10 08:46 0 . [...] 0 . 2
[...] 0
101 1973-07-10 09:01 0 . [...] 0 . 2
[...] 0
101 1973-07-10 09:17 0 . [...] 0 . 2
[...] 0
101 1973-07-10 09:31 0 . [...] 0 . 2
[...] 0
101 1973-07-10 10:01 0 . [...] 0 . 2
[...] 0
101 1973-07-10 10:31 0 . [...] 0 . 2
[...] 0
101 1973-07-10 11:01 0 . [...] 0 . 2
[...] 0
101 1973-07-10 11:31 0 . [...] 0 . 2
[...] 0
101 1973-07-10 12:30 0 . [...] 0 . 2
[...] 0
101 1973-07-10 14:14 0 . [...] 0 0.6 -4
[...] 1
101 1973-07-10 14:14 2 . . 1 . 4
[...] 1
101 1973-07-10 14:31 0 . [...] 0 . 2
[...] 0
101 1973-07-10 17:30 0 . . 1 . 2
[...] 0
101 1973-07-10 20:30 0 . . 1 . 2
[...] 0
101 1973-07-10 20:44 0 . [...] 0 0.5 -4
[...] 1
101 1973-07-10 20:44 2 . . 1 . 4
[...] 1
101 1973-07-11 08:31 0 . . 1 . 2
[...] 0
101 1973-07-11 08:51 0 . [...] 0 0.7 -4
[...] 1
[...]
====================================================================
Best regards
Jacob
-------------------------------------------------
Jacob Brogren MSc Pharm
Senior Research Scientist
Pharmacometrics
Clinical Pharmacology and DMPK
AstraZeneca R&D Södertälje
SE-151 85 Södertälje Sweden
Tel. +46 8 553 236 33
Fax +46 8 553 274 91
[email protected]
www.astrazeneca.com
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