From: Silvy Laporte <laporte_s@univ-st-etienne.fr>

Subject: indirect PK-PD model and lag-time

Date: 23 Sep 1998 11:41:34 -0400

Dear NM users,

We are trying to use ADVAN6 to model an indirect response model for an oral anticoagulant. The PD marker is the Prothrombin time ratio. Using a code as following, the effect is too early modified. We want to include a lag-time for this PD marker to take into account the fact the first effect is measured 10 hours after administration of the drug. Must we use an ALAG parameter and which one ? Or is there another solution?

Any advice would be very appreciated.

Thank you in advance.

Silvy Laporte and Patrick Mismetti.

Thrombosis Research Group St-Etienne FRANCE

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$PROBLEM mod=E8le PKPD PTR ACENOC PK 2 cpt

$DATA tp2.dat

$INPUT ID TIME AMT DV EVID MDV CMT

$SUBROUTINE ADVAN6 TOL=3 ; IV two-CMT

$MODEL

COMP=(CENTRAL,DEFDOSE,DEFOBS)

COMP=PERIPH

COMP=EFFECT

$PK

K=THETA(1)*EXP(ETA(1))

V1 =THETA(2)*EXP(ETA(2))

CL=V1*K

K12=THETA(3)

K21=THETA(4)

Q=K12*V1

V2=Q/K21

S1=V1/1000

KIN=THETA(5)*EXP(ETA(3))

KOUT=KIN

C50=THETA(6)*EXP(ETA(4))

$DES

DADT(1)=-(K12+K)*A(1) ; PK model 1st cpt

DADT(2)= K12*A(1)-K21*A(2) ; PK model 2nd cpt

EFF=C50/(C50+A(1)/S1)

DADT(3)=KIN*EFF-KOUT*A(3) ; PTR model

$ERROR

Y1=F*EXP(ERR(1))+ERR(2)

PTR=THETA(7)*F/(THETA(8)+F)

Y2=PTR*EXP(ERR(3))

BIN=1

IF (CMT.EQ.3) BIN=0

Y=BIN*Y1 + (1-BIN)*Y2

$THETA (0,0.05,10) (1,5,100) ; K and V1

(0.001,0.05,2) (0.001,0.2,5) ; K12 and K21

(0.001,0.02) (0.005,0.1) ; KIN and C50

(100 FIX)

(0.01,0.1)

$OMEGA (0.0271 FIX) (0.0185 FIX)

0.16 0.16

$SIGMA (0.0270 FIX) (57.9 FIX) 0.16

$ESTIMATION PRINT=5 MAXEVAL=3000

$SCATTER PRED VS TIME BY BIN

$SCATTER PRED VS DV UNIT BY BIN

----------------------------------------------------------------------

****

From: alison@c255.ucsf.EDU (ABoeckmann)

Subject: indirect PK-PD model and lag-time

Date: 24 Sep 1998 14:13:17 -0400

PREDPP is not able to model intercompartmental lag. It can only model absorption lag, i.e., it can delay the dose from entering the system.

In Guide VIII, there is an example " PK PD SEQUENTIAL 1 EXAMPLE ". In this example, the PK data is fit first, then the PK parameters are held fixed and the PD data is fit. We say in this example:

If, moreover, an absorption lag (ALAG1) parameter is modeled in $PK with parameters estimated from the PD data only, then this introduces a lag in the dose - Ce relationship. Since this lag was not present in the dose - Cp relationship, it may be interpreted as a lag in the Cp - Ce relationship.

In Sylvie's control stream, ALAG1 could be used in the second run, when the PD data is fit, and would provide the desired lag.

However, the $DES block does not look right:

$DES

DADT(1)=-(K12+K)*A(1) ; PK model 1st cpt

DADT(2)= K12*A(1)-K21*A(2) ; PK model 2nd cpt

EFF=C50/(C50+A(1)/S1)

DADT(3)=KIN*EFF-KOUT*A(3) ; PTR model

I would expect the first DE to include the K21 term, returning drug from periperal to central:

DADT(1)=-(K12+K)*A(1)+K21*A(2) ; PK model 1st cpt

Lewis Sheiner also suggests the following approach, which allows simultaneous fit of PK and PD data:

If you want a lag time, it would be on the compartment into which you put the dose, presumably CENTRAL. This will simply cause all the PK and PD events to be delayed relative to the time of the dose. If you prefer a 'real' lag; that is, more equilibration time between PK (compt 1) and effect, you could use a catenary chain leading to the 'effect' site. That is, interpose say 2 delay (DLY1, DLY2) compartments between CENTRAL and EFFECT, with the transfer rate from CENTRAL to DLY1 equal to that from DLY1 to DLY2. Don't bother with an eta on this rate. You'll have to choose the number of delay compartments arbitrarily since it's much harder to try to estimate how many of these you need. This is equivalent to having an 'Erlang' disposition function for the delay... see papers by Jim Matis in JPB several years ago.

By the way, why do you have an eta on the input rate constant for the bioeffector compartment, rather than on C50; and why no eta on the exit rate for the bioeffector?

Alison Boeckmann

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From: "Hui C. Ko" <koh@compuserve.com>

Subject: indirect PK-PD model and lag-time

Date: 29 Sep 1998 10:31:21 -0400

Dear Silvy and Patrick,

Your NM control;

$DES

DADT(1)=-(K12+K)*A(1) ; PK model 1st cpt

DADT(2)= K12*A(1)-K21*A(2) ; PK model 2nd cpt

EFF=C50/(C50+A(1)/S1)

DADT(3)=KIN*EFF-KOUT*A(3) ; PTR model

needs corrections on;

1. DADT(1) as Alison pointed out,

2. your inhibition function, EFF, should be 1-C50/(C50+A(1)/S1) if you assume Emax is 1.

Hui Ko