# Re: FW: transit model

From: justin.wilkins
Date: Fri, 5 Sep 2008 13:38:28 +0200

Dear Dirk (and all),

This is a tricky one. After we got our heads together to look at it, we
realized that it's a bit more complex than it appears. The reason why we
use greater-than or equal to (T.GE.TDOS) instead of (T.GT.TDOS) is to get
around an issue with NONMEM. The easiest way to explain why is through an
example - given multiple dosing every 12 hours, and observations at 1, 2,
4, and 8 h post-dose, time after dose (TAD) will need to be set to 0 at
every 12-hourly dosing event - so at this point, TAD==0 and TDOS==1=
2.
However, in order to integrate between 8 h and 12 h in this scheme, NONMEM =

will use a TDOS value of 12 h here, resulting in negative values of TAD
over the 8-12h period - which will clearly produce undesirable results.
Using the IF-THEN structure with (T.GE.TDOS) is a cheat to overcome this.

However, as Sebastien pointed out, another assumption is introduced by
doing it this way - the dose is assumed to be fully absorbed by the last
observation event, in this case 8 h (as opposed to the time of the next
dose, 12 h). This may have fairly problematic consequences, especially
where you have a series of dosing events without observations between
them. We think the best way to tackle this will be to add dummy
observation records (using EVID==2) at inter-dose troughs (e.g. 11.9 h)=

between each successive dose event - another method might be to leverage
NONMEM VI's very helpful model event time (MTIME) variable to take care of =

this.

Hope this was helpful!

Best

Justin Wilkins
Novartis Pharma AG
PH346, MODELING & SIMULATION
CHBS, WSJ-027.1.084
Novartis Pharma AG
Lichtstrasse 35
CH-4056 Basel
Switzerland
Phone: +41 61 324 6549
Fax: +41 61 324 3039
Mobile: +41 76 561 0949
Email : justin.wilkins

Sébastien Bihorel <sbihorel
Sent by: owner-nmusers
27/08/2008 15:59

To
Garmann Dirk <Dirk.Garmann
cc
nmusers
Subject
Re: [NMusers] FW: transit model

(Sorry for the spelling mistakes)

Dirk,

This absorption model can correctly accommodate multiple dosing only if
the absorption of dose n is complete when dose n+1 is given ! Since the
input is hard-coded and reset at each dose, you have to make sure that
your estimates for MTT and NN provide this complete absorption. Otherwise, =

a part of each dose never enters the system.

I don't really understand how you implemented the transit model but you
may refer to the following code (for Wings for NONMEM) that worked just
fine for me. The frame time for the input function has to start at zero,
so I used a time transform based on a dosing interval of 24h. A column DAY =

is included in the dataset to calculate the new time MYT.

Hope it helps.

Sebastien Bihorel

\$PROBLEM Simulation Transit model
\$INPUT ID DOSE DAY TI24 TIME AMT RATX CMT EVID DVID DV MDV
\$DATA ../Data/Simulation.csv IGNORE=#

\$SIM (32047023) NSUB=1

\$THETA (0,6.) ; POP_CL
\$THETA (0,100.) ; POP_V2
\$THETA (0,18.) ; POP_MTT
\$THETA (0.00001,3.) ; POP_n
\$THETA (0,6.) ; POP_TABS

\$OMEGA BLOCK(2)
0.1 ; BSVCL
0.01 0.1 ; BSVV2

\$OMEGA BLOCK(3)
0.1 ; BSVMTT
0.01 0.1 ; BSVN
0.01 0.01 0.1 ; BSVTABS

\$SIGMA 0.1 ;cvcp
\$SIGMA 0.05 ;sdcp

\$MODEL COMP = (ABS) ; absorption compartment
COMP = (CEN) ; central compartment

;\$ABBREVIATED DERIV2=NOCOMMON

\$PK
"FIRST
" COMMON /PRCOMG/ IDUM1,IDUM2,IMAX,IDUM4,IDUM5
" INTEGER IDUM1,IDUM2,IMAX,IDUM4,IDUM5
" IMAX=1000000

IF(AMT.GT.0.AND.CMT.EQ.1)PODO=AMT; oral dose

F1 = 0.
F2 = 0.

ECL = EXP(BSVCL)
EV2 = EXP(BSVV2)
EMTT = EXP(BSVMTT)
ENB = EXP(BSVN)
ETAB = EXP(BSVTABS)

CL = POP_CL * ECL
V = POP_V2 * EV2
MTT = (POP_MTT * EMTT)/60
NB = POP_n * ENB
TABS = POP_TABS * ETAB
KA = LOG(2)/(TABS/60)

KTR = (NB+1)/MTT ; transit rate constant
LNFA = 0.5*LOG(2*3.14159*NB)+NB*LOG(NB)-NB+LOG(1.+1./(12.*NB)) ;
logarithmic transformation of 2nd Stirling approximation

S2 = V
BIO =1.

\$DES
MYT = T -(DAY-1)*24

IF (MYT.LT.0.001) THEN
INPU = 0.
ELSE
INPU = EXP(LOG(BIO*PODO)+LOG(KTR)+NB*LOG(KTR*MYT)-KTR*MYT-LNFA)
ENDIF

\$ERROR

CP=A(2)
Y=CP*(1+CVCP)+SDCP

\$TABLE ID DAY TIME AMT CMT EVID DVID Y
CL V MTT NB TABS ECL EV2 EMTT ENB ETAB
FILE=k0ka1l.fit

Garmann Dirk a écrit :
Dear NONMEM users,

I try to fit a dataset with a high variability in TLAG. With the standard
approaches it was not possible to get successful runs (variability in Tlag =

is always modeled as zero, but their is clearly a high variability)

Therefore I used the transit model, published by Justin Wilkins/Radoika
Savic. For single dose studies it works well (improved fit/successful
runs). Next , I included a multiple drug study and adapted the model. The =

model works, but I have some questions regarding the code (see below in
red). It would be very nice if someone can help to enhance my
understanding.
Thank you in advance
Dirk

\$MODEL NCOMP=3 COMP=(DEPOT) COMP=(CENTRAL,DEFOBS) COMP=(PERIPH)
\$PK
"FIRST
" COMMON /PRCOMG/ IDUM1,IDUM2,IMAX,IDUM4,IDUM5
" INTEGER IDUM1,IDUM2,IMAX,IDUM4,IDUM5
" IMAX=9900000

IF(AMT.GT.0.AND.CMT.EQ.1) PD=AMT
IF(AMT.GT.0) TDOS=TIME

TVCL=THETA(1)
CL=TVCL*EXP(ETA(1))
TVV2=THETA(2)
V2=TVV2*EXP(ETA(2))

TVV3=THETA(3)
V3=TVV3*EXP(ETA(3))
TVQ=THETA(4)
Q=TVQ*EXP(ETA(4))

; Absorption model
;F1=0 delete NONMEMS Dose record
F1=0

TVKA=THETA(5)
KA=TVKA*EXP(ETA(5))

;Mean transit time
TVMTT=THETA(6)
MTT=TVMTT*EXP(ETA(6))

;Number of transit compartments
TVNN=THETA(7)
NN=TVNN*EXP(ETA(7))

;Transit rate constant
KTR=(NN+1)/MTT

;Sterling
L=LOG(2.5066)+(NN+.5)*LOG(NN)-NN

S2=V2/1000

; DOSE : mg
; CONC: ng/ml

\$DES
X=0.00001; Avoid LOG 0
;multiple dose
IF(T.GE.TDOS)THEN ; if current time greater than TDOS

Is this correct? I think GE might be a typo and should be GT?

DADT(1) = EXP(LOG(PD + X) + LOG(KTR +
X)+NN*LOG(KTR*(T-TDOS)+X)-KTR*(T-TDOS)-L)-KA*A(1)

ELSE
; Dose given
DADT(1) = EXP(LOG(PD + X) + LOG(KTR + X)+ NN*LOG(KTR*T + X) - KTR*T - L)-=

KA*A(1)
ENDIF

T.GE.TDOS (see above) might be a typo; otherwise this equation will never
be active?
I try this model with GT, the fit improves, but why is this statement
needed?

Can someone explain this (red) part of the equation, please?
I think if the time is e.g. 24 hours (time of second dose) the value of
the input function will be low, as it should be to simulate the lag time
(I used MTT=1, NN=4, to recalculate it). With further increased time (n=
ext
doses), the value of the input function will be approximately zero (ok).

But without this equation and
IF(AMT.GT.0.AND.CMT.EQ.1) PD=AMT
IF(AMT.GT.0) TDOS=TIME

(T-TDOS) should be zero at each dose event and the value of the input
function at a new dose event is also approximately zero (same as above?)

Any help to enhance my understanding is welcome

\$ERROR

One last question:
For some subjects I got some bizarre estimation values. I think this might =

be because I have sometimes dose events, but no observations (multiple
dose study) prior to the next dose.. Therefore, if I correctly understand
the code, the input value for these dose events will be approximately
zero.

Any suggestions to solve this problem are welcome.

Best regards

Dirk Garmann

SCHWARZ BIOSCIENCES GmbH
A Member of the UCB Group
Alfred-Nobel-Str. 10 - 40789 Monheim - Germany
Tel +49 2173 48 0 - Fax +49 2173 48 1608
Geschaeftsfuehrer: Prof. Dr. Iris Loew-Friedrich, Detlef Thielgen
Amtsgericht Duesseldorf HRB 46849

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Received on Fri Sep 05 2008 - 07:38:28 EDT

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