# Problem with HESSIAN

From: Brogren, Jacob <Jacob.Brogren>
Date: Thu, 25 Jun 2009 10:11:38 +0200

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=

\$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(2) = KA*A(1) - K23*A(2) + K32*A(3) - K20*A(2) - 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

\$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=

\$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)

\$OMEGA 0.09

\$SIGMA 1 FIX

\$EST PRINT=1 MAXEVAL=9999 METHOD=1 INTER POSTHOC

\$COV PRINT=E
==========================
==========================
==========================
===
==========================
==========================
==========================
===
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
[...]
==========================
==========================
==========================
===
==========================
==========================
==========================
===
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
jacob.brogren
www.astrazeneca.com

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Received on Thu Jun 25 2009 - 04:11:38 EDT

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