Hi Shankar,
We published an autoinduction model a few years back (Gordi et al., Br J Clin
Pharmacol. 2005;59(2):189-98). The original paper was based on saliva samples
but the model worked well using plasma data (Asimus and Gordi, Br J Clin
Pharmacol. 2007;63(6):758-62). We also used it to describe the PK of the
compound in a PK/PD model successfully (Gordi et al., Br J Clin Pharmacol.
2005;60(6):594-604). The basic principal is similar to most other models, i.e.,
an indirect response model describes the enzyme compartment and the effect of
the drug on production rate of the enzymes. One major difference is that we
introduced a liver compartment into the system. In all other models I have
seen, plasma concentrations drive the induction effect. This means that as time
passes by, and drug concentrations in plasma decrease due to induction, you
have less and less induction. Having the liver compartment, we allow drug
concentrations (practically amounts, see the control stream below) in the liver
upon absorption to induce the enzyme. This means that subsequent doses of the
drug will have the same inducing effect, which should be closer to the reality.
I am showing a part of the control stream below. In our paper we estimated
interoccasional variability and I'll be more than happy to help you with
implementing that, if you want to. A couple of notes to make the coding easier
to follow: this is based on salivary data, where concentrations reflected the
free fraction of those in plasma (fu=14%), hence the S3 adjustment. The model
also includes a precursor compartment to capture the induction lag time.
Depending on your data, you may want to test a model without it. Finally, the
model includes a nonlinearity in the intrinsic clearance and extraction ratio
(and thereby bioavailability) of the drug, which was known for this particular
compound. You should obviously test a simpler model.
Let me know if you have any questions.
Toufigh
$SUBROUTINE ADVAN6 TRANS1 TOL=5
$MODEL NCOMP=5
COMP=(GUT DEFDOSE)
COMP=LIVER
COMP=(SALIVA DEFOBS)
COMP=ENZPOOL
COMP=PREC
$PK
....
TEN = THETA(1)
KEN = 0.693/TEN
SIND = THETA(2) ;slope for enzyme induction
CLINT = THETA(3)*EXP(ETA(1))
BFL = 0.63*WT ;l/h for 55kg
VS = THETA(4)*EXP(ETA(2))
.....
ALAG1 = THETA(5)
KA = THETA(6)
FU = 0.14
KM = THETA(7)
VL = 1
TPEN = THETA(8)
KPEN = 1/TPEN
S3 = VS/FU
BASENZ= 1
BASEPR= KEN/KPEN
F4 = BASENZ
F5 = BASEPR
$DES
BOX = CLINT*A(4)*KM/(A(2)+KM)
E = FU*BOX/(BFL+FU*BOX) ;extraction ratio
BAV = 1-E ; bioavailability
CLH = BFL*E
DADT(1) = -KA*A(1)
KS0 = BFL/VS
DADT(2) = KA*A(1)-BFL*BAV*A(2)/VL+KS0*A(3)-BFL*E*A(2)/VL
DADT(3) = BFL*BAV*A(2)/VL-KS0*A(3)
DADT(4) = KPEN*A(5)-KEN*A(4)
DADT(5) = KEN*(1+SIND*A(2))-KPEN*A(5)
Toufigh
Toufigh Gordi, PhD
President, PK/PD and Clinical Pharmacology Services
Rosa & Co. LLC: www.rosaandco.com
E-mail: [email protected]
Tel.: 408-480-7314
Fax: 408-370-9810
The information contained in this e-mail message, e-mail message sequence,
and/or any enclosures is confidential, and it may be privileged and protected
from unauthorized use and/or disclosure. If you are not the intended recipient,
any use, dissemination, distribution, or copying is strictly prohibited. If you
received this e-mail in error, PLEASE NOTIFY THE SENDER immediately and destroy
this message, any enclosures, and any copies of the message and/or the
enclosures. Thank you.
On Mar 28, 2011, at 6:52 AM, Shankar Lanke wrote:
> Dear All,
>
> I am working on a Pop PK data where the patients are treated with HIV drug.
> An autoinduction is involved with prolonged administration of the drug. An
> increased CL is expected from day 1 to day 14.
> We have intense data on day 1 and day 14 with sparse data between. Since a
> lag period is involved for the induction I used the equation CL = CLinduced
> -(CLinduced - CLpre)*exp(-kout*(t-Tlag)) described by Johan Gabrielsson as
> more appropriate.
>
> Also when I included a lag period for absorption in my earlier model my fits
> are better and OBF decreased by 200.
>
> However the final model with or without lag time for absorption + auto
> induction model is either terminated or covariance step is being aborted.
> I changed the initial estimates several times but still no luck. Though the
> Auto induction model aborts the fits are better than the lag time model
> however the estimates for Vd are 4 fold less than the expected.
>
> I appreciate your input and suggestions. Here is my code.
>
> $SUBROUTINES ADVAN13 TRANS1 TOL=5 ;(I used ADVAN6 too)
> $MODEL
> NPAR=9 NCOMP=4
> COMP=(DEPOT,DEFDOSE)
> COMP=(LAG)
> COMP=(OBSV,DEFOBS)
> COMP=(PERIP)
> $PK
> CLP=THETA(1)
> CLI=THETA(6)
> KOUT=THETA(7)
> TLAG=THETA(8)*EXP(ETA(6))
>
> TVCL=CLI-(CLI-CLP)*EXP(-KOUT*(TIME-TLAG))
> CL=TVCL*EXP(ETA(1))
> TVV2=THETA(2)
> V2=TVV2*EXP(ETA(2))
> TVQ=THETA(3)
> Q=TVQ*EXP(ETA(3))
> TVV3=THETA(4)
> V3=TVV3*EXP(ETA(4))
> TVKA=THETA(5)
> KA=TVKA*EXP(ETA(5))
> TVALAG1=THETA(9)
> ALAG1=TVALAG1*EXP(ETA(7))
> S3=V2
> $DES
> K=CL/V2
> K23=Q/V2
> K32=Q/V3
> DADT(1)=-KA*A(1)
> DADT(2)=KA*A(1)-A(2)/ALAG1
> DADT(3)=A(2)/ALAG1-K23*A(3)-K*A(3)+K32*A(4)
> DADT(4)=K23*A(3)-K32*A(4)
> $ERROR
> DEL=0
> IF (F.LE.0.0001) DEL=1
> IPRE=F
> W1= 1
> W2= F
> IRES= DV-IPRE
> IWRE=IRES/(W1+W2)
> Y = F + W1*ERR(1) + W2*ERR(2)
> DV2=ABS(V2-TVV2)
> $EST METHOD=1 INTERACTION PRINT=5 MAX=9999 SIG=3 MSFO=JLM.MSF
> $THETA
> (0, 6);[CLP]
> (0, 90);[V2]
> (0, 19);[Q]
> (0, 200);[V3]
> (0, 0.16);[KA]
> (0, 8);[CLI]
> (0, 0.001);[KOUT]
> (0, 250);[TLAG]
> (0, 0.3);[ALAG1]
> $OMEGA
> 0.23 ;[CL] omega(1,1)
> 0.18;[V2] omega(2,2)
> 0 FIXED ;[Q] omega(3,3)
> 0.42;[V3] omega(4,4)
> 0.19;[KA] omega(5,5)
> 0.09;[TLAG for Ka]
> 0.1;[ALAG1 for CLI]
> $SIGMA
> 0.06 ;[P] sigma(1,1)
> 0.09 ;[A] sigma(2,2)
> $COV MATRIX=S
>
>
> Regards,
> Shankar Lanke Ph.D.
> University at Buffalo
> Office # 716-645-4853
> Fax # 716-645-2886
> Cell # 678-232-3567
>
