Dear NMusers,
I'm using ADVAN2 to model the PK of a drug. To best fit the profile, the
model includes ALAG1 and D1. For the next step, the ADVAN2 needs to be
translated into differential equation to include a PD compartment. How
should I write the differential equation for ALAG1 and D1? As you can
see, there is Ka in the ADVAN2 model. I'm not very clear what's the
meaning of D1 and KA when both are modeled. Any hint or previous link
would be appreciated. Thanks in advance!
$SUBROUTINES ADVAN2
$PK
KASC=THETA(4)
VSC=THETA(5)
CLSC=THETA(6)
LGSC=THETA(8)
MU_4=KASC
MU_5=VSC
MU_6=CLSC
MU_8=THETA(11)
SD=THETA(9)
SIG=SD
KA=EXP(MU_4+ETA(4))
V=EXP(MU_5+ETA(5))
CL=EXP(MU_6+ETA(6))
K=CL/V
S2=V/1000; DOSE IN 1000 U, CONC in U, VOLUME IN mL
ALAG1=LGSC*EXP(ETA(10))
D1=EXP(MU_8+ETA(8))
Final parameter estimates:
$THETA
12 ;THETA5
8.89 ;THETA6
0.0015;THETA8
0.263 ; THETA9
2.87; THETA11
Best regards,
Shelley
========================================
Xiao Hu (Shelley), Ph.D.
Scientist,
Development Pharmacokinetics & Disposition
Biogen Idec, Inc.
14 Cambridge Center
Cambridge, MA 02142
Translate ALAG1 and D1 in ADVAN2 to differential equations
Shelley,
You would use ADVAN6, ADVAN8, or ADVAN13, and code the differential equations
explicitly in the $DES block. See the included CONTROL7 in the NONMEM examples.
Also note, you have an interesting error structure. Usually I have lognormal
errors, that is
KA = THETA(x)*EXP(ETA(x))
You have mu-referenced your variables. When I do this, the following code is
produced:
MU_x = LOG(THETA(x))
KA = EXP(MU_x+ETA(x))
You have instead:
MU_x = THETA(x)
KA = EXP(MU_x+ETA(x))
This means your KA, (which I will call KAs), is equivalent to my KA by the
following transformation:
KAs = LOG(KA)
Is this what you mean?
Matt.
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Xiao Hu
Sent: Tuesday, August 10, 2010 10:50 AM
To: nmusers
Subject: [NMusers] Translate ALAG1 and D1 in ADVAN2 to differential equations
Dear NMusers,
I'm using ADVAN2 to model the PK of a drug. To best fit the profile, the model
includes ALAG1 and D1. For the next step, the ADVAN2 needs to be translated
into differential equation to include a PD compartment. How should I write the
differential equation for ALAG1 and D1? As you can see, there is Ka in the
ADVAN2 model. I'm not very clear what's the meaning of D1 and KA when both are
modeled. Any hint or previous link would be appreciated. Thanks in advance!
$SUBROUTINES ADVAN2
$PK
KASC=THETA(4)
VSC=THETA(5)
CLSC=THETA(6)
LGSC=THETA(8)
MU_4=KASC
MU_5=VSC
MU_6=CLSC
MU_8=THETA(11)
SD=THETA(9)
SIG=SD
KA=EXP(MU_4+ETA(4))
V=EXP(MU_5+ETA(5))
CL=EXP(MU_6+ETA(6))
K=CL/V
S2=V/1000; DOSE IN 1000 U, CONC in U, VOLUME IN mL
ALAG1=LGSC*EXP(ETA(10))
D1=EXP(MU_8+ETA(8))
Final parameter estimates:
$THETA
12 ;THETA5
8.89 ;THETA6
0.0015;THETA8
0.263 ; THETA9
2.87; THETA11
Best regards,
Shelley
========================================
Xiao Hu (Shelley), Ph.D.
Scientist,
Development Pharmacokinetics & Disposition
Biogen Idec, Inc.
14 Cambridge Center
Cambridge, MA 02142
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Thank you.
Xiao Hu,
Part 1)
NONMEM handles the input of all doses automatically via the dataset structure. Therefore, generally there is no need to initialize compartments or to code infusion rates in the $DES block. An exception to this rule is when you are dosing or modeling endogenous substances. Assuming your drug is not an endogenous substance, the differential equations for ADVAN2 with ALAG1 and D1 are shown below (using ADVAN6).
Part 2)
"I'm not very clear what's the meaning of D1 and KA when both are modeled."
Based upon the ADVAN that you are using, NONMEM is putting the dose into the depot compartment as a constant rate infusion with a duration of D1 (hours, days, etc.). It starts the infusion into the depot compartment at time=ALAG1 (hours,days, etc.) after each dose. The dose is then transferred from the depot compartment to the central compartment using a first-order process (Ka 1/hr or 1/day, etc.)
I hope this information helps,
Luann Phillips
---------------------------------------------
Example Code:
$SUBROUTINES ADVAN6 TOL=5
$MODEL
COMP=(DEPOT,DEFDOSE)
COMP=(CENTRAL,DEFOBS)
COMP=(PD1)
etc.
$PK
KASC=THETA(4)
VSC=THETA(5)
CLSC=THETA(6)
LGSC=THETA(8)
MU_4=KASC
MU_5=VSC
MU_6=CLSC
MU_8=THETA(11)
SD=THETA(9)
SIG=SD
KA=EXP(MU_4+ETA(4))
V=EXP(MU_5+ETA(5))
CL=EXP(MU_6+ETA(6))
K=CL/V
S2=V/1000; DOSE IN 1000 U, CONC in U, VOLUME IN mL
ALAG1=LGSC*EXP(ETA(10))
D1=EXP(MU_8+ETA(8))
$DES
DADT(1) = -KA*A(1)
DADT(2) = KA*A(1) - K*A(2)
DADT(3) = equations for PD cmt 1
etc.
--------------------------------------------------
Xiao Hu wrote:
> Dear NMusers,
>
> I'm using ADVAN2 to model the PK of a drug. To best fit the profile, the model includes ALAG1 and D1. For the next step, the ADVAN2 needs to be translated into differential equation to include a PD compartment. How should I write the differential equation for ALAG1 and D1? As you can see, there is Ka in the ADVAN2 model. I'm not very clear what's the meaning of D1 and KA when both are modeled. Any hint or previous link would be appreciated. Thanks in advance!
>
> $SUBROUTINES ADVAN2
>
> $PK
>
> KASC=THETA(4)
> VSC=THETA(5)
> CLSC=THETA(6)
> LGSC=THETA(8)
>
> MU_4=KASC
> MU_5=VSC
> MU_6=CLSC
> MU_8=THETA(11)
>
> SD=THETA(9)
>
> SIG=SD
>
> KA=EXP(MU_4+ETA(4))
> V=EXP(MU_5+ETA(5))
> CL=EXP(MU_6+ETA(6))
> K=CL/V
> S2=V/1000; DOSE IN 1000 U, CONC in U, VOLUME IN mL
> ALAG1=LGSC*EXP(ETA(10))
> D1=EXP(MU_8+ETA(8))
>
> Final parameter estimates:
>
> $THETA
> 12 ;THETA5
> 8.89 ;THETA6
> 0.0015;THETA8
>
> 0.263 ; THETA9 2.87; THETA11
>
> Best regards,
> Shelley
>
> ========================================
> Xiao Hu (Shelley), Ph.D.
> Scientist,
> Development Pharmacokinetics & Disposition
> Biogen Idec, Inc.
> 14 Cambridge Center
> Cambridge, MA 02142
Xiao,
Try running a SIMONLY simulation first. If you are using an additive or additive + constant CV error model, simulation will sometimes generate negative or very tiny DV values. If this is the case, it will cause problems with fitting the model to the simulated data.
Luann
Xiao Hu wrote:
> Dear Luann, Andreas and others,
>
> Both parts are very clear to me now. Thank you very much!
>
> My problem was, when I tried to simulate the differential equation model with parameters from ADVAN2, it did not work. The error message is listed below. This was not an issue during the model switch when D1 was not included in ADVAN2. I then tried to derive the parameters from the differential equation model directly. But there were >10 error messages like below issued. Do you have any insight why this happens?
>
> 0PRED EXIT CODE = 1
>
> 0INDIVIDUAL NO. 1 ID= 2.00100000000000E+03 (WITHIN-INDIVIDUAL) DATA REC NO. 18
>
> THETA=
>
> 4.19E+00 1.22E+01 9.10E+00 1.07E+01 1.20E+01 8.89E+00 0.00E+00 1.50E-03 2.63E-01 2.28E+00
>
> 2.87E+00
>
> NUMERICAL DIFFICULTIES WITH INTEGRATION ROUTINE. MAXIMUM NO. OF EVALUATIONS OF DIFFERENTIAL EQUATIONS, 1000000, EXCEEDED.
>
> Best regards,
> Shelley
>
> ========================================
> Xiao Hu (Shelley), Ph.D.
> Scientist,
> Development Pharmacokinetics & Disposition
> Biogen Idec, Inc.
> 14 Cambridge Center
> Cambridge, MA 02142
>
> *Luann Phillips <[email protected]>*
>
> 10-Aug-2010 01:29 PM
>
> Message Size: *6.6 KB*
>
> To
> Xiao Hu <[email protected]>
> cc
> nmusers <[email protected]>
> Subject
> Re: [NMusers] Translate ALAG1 and D1 in ADVAN2 to differential equations
>
> Xiao Hu,
>
> Part 1)
> NONMEM handles the input of all doses automatically via the dataset
> structure. Therefore, generally there is no need to initialize
> compartments or to code infusion rates in the $DES block. An exception
> to this rule is when you are dosing or modeling endogenous substances.
> Assuming your drug is not an endogenous substance, the differential
> equations for ADVAN2 with ALAG1 and D1 are shown below (using ADVAN6).
>
> Part 2)
> "I'm not very clear what's the meaning of D1 and KA when both are modeled."
>
> Based upon the ADVAN that you are using, NONMEM is putting the dose into
> the depot compartment as a constant rate infusion with a duration of D1
> (hours, days, etc.). It starts the infusion into the depot compartment
> at time=ALAG1 (hours,days, etc.) after each dose. The dose is then
> transferred from the depot compartment to the central compartment using
> a first-order process (Ka 1/hr or 1/day, etc.)
>
> I hope this information helps,
>
> Luann Phillips
>
> ---------------------------------------------
>
> Example Code:
>
> $SUBROUTINES ADVAN6 TOL=5
>
> $MODEL
> COMP=(DEPOT,DEFDOSE)
> COMP=(CENTRAL,DEFOBS)
> COMP=(PD1)
> etc.
>
> $PK
>
> KASC=THETA(4)
> VSC=THETA(5)
> CLSC=THETA(6)
> LGSC=THETA(8)
>
> MU_4=KASC
> MU_5=VSC
> MU_6=CLSC
> MU_8=THETA(11)
>
> SD=THETA(9)
> SIG=SD
>
> KA=EXP(MU_4+ETA(4))
> V=EXP(MU_5+ETA(5))
> CL=EXP(MU_6+ETA(6))
> K=CL/V
> S2=V/1000; DOSE IN 1000 U, CONC in U, VOLUME IN mL
> ALAG1=LGSC*EXP(ETA(10))
> D1=EXP(MU_8+ETA(8))
>
> $DES
>
> DADT(1) = -KA*A(1)
> DADT(2) = KA*A(1) - K*A(2)
> DADT(3) = equations for PD cmt 1
>
> etc.
>
> --------------------------------------------------
>
> Xiao Hu wrote:
> >
> > Dear NMusers,
> >
> > I'm using ADVAN2 to model the PK of a drug. To best fit the profile,
> > the model includes ALAG1 and D1. For the next step, the ADVAN2 needs to
> > be translated into differential equation to include a PD compartment.
> > How should I write the differential equation for ALAG1 and D1? As you
> > can see, there is Ka in the ADVAN2 model. I'm not very clear what's the
> > meaning of D1 and KA when both are modeled. Any hint or previous link
> > would be appreciated. Thanks in advance!
> >
> > $SUBROUTINES ADVAN2
>
> > $PK >
>
> > KASC=THETA(4)
> > VSC=THETA(5)
> > CLSC=THETA(6)
> > LGSC=THETA(8)
> >
> > MU_4=KASC
> > MU_5=VSC
> > MU_6=CLSC
> > MU_8=THETA(11)
>
> > > SD=THETA(9)
>
> > SIG=SD
> >
> > KA=EXP(MU_4+ETA(4))
> > V=EXP(MU_5+ETA(5))
> > CL=EXP(MU_6+ETA(6))
> > K=CL/V
> > S2=V/1000; DOSE IN 1000 U, CONC in U, VOLUME IN mL
> > ALAG1=LGSC*EXP(ETA(10))
> > D1=EXP(MU_8+ETA(8))
> >
> > Final parameter estimates:
> >
> > $THETA
> > 12 ;THETA5
> > 8.89 ;THETA6
> > 0.0015;THETA8
>
> > 0.263 ; THETA9 > 2.87; THETA11
>
> >
> > Best regards,
> > Shelley
> >
> > ========================================
> > Xiao Hu (Shelley), Ph.D.
> > Scientist,
> > Development Pharmacokinetics & Disposition
> > Biogen Idec, Inc.
> > 14 Cambridge Center
> > Cambridge, MA 02142