PKPD model

PKPD model can be performed either sequentially or simultaneously. Let us first consider simultaneous model in which PD is based on PK plasma concentration through an effect compartment.

PK/PD simultaneous modeled

Consider data item DV be either concentration in the central compartment (CMT=1), or the drug effect dependent on concentration in the effect compartment (CMT=2). The drug effect is modeled using the Emax model. We use ADVAN3 (LSODA ODE solver) to solve the coupled PK/PD equations numerically.

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  $PROB RUN# 702 ADVAN6
  $INPUT C ID AMT TIME DV CMT
  $DATA 006.csv IGNORE=C
  $SUBROUTINE ADVAN13 TRANS=1 TOL=10 ATOL=10
  $MODEL NCOMP=3
    COMP=(GUT)
    COMP=(CENTRAL)
    COMP=(EFFECT)
  $PK
   KA=THETA(1)*EXP(ETA(1))
   KE=THETA(2)*EXP(ETA(2))
   V2=THETA(3)*EXP(ETA(3))
   S2=V2

   KE0=THETA(4)
   EMAX=THETA(5)
   EC50=THETA(6)*EXP(ETA(4))

  $DES
   DADT(1)=-KA*A(1)
   DADT(2)=KA*A(1)-KE*A(2)
   DADT(3)=KE0*(A(2)/V2-A(3))

  $ERROR
  ;TYPE=0 FOR CP (CMT=2), TYPE=1 FOR E (CMT=3)
  CP=A(2)/S2
  CE=A(3)
  TYPE=1
  IF(CMT.EQ.2) TYPE=0
  YC=CP*(1.0+ERR(1)) ;PK residual error model
  EE=EMAX*CE/(EC50+CE)
  YE=EE+ERR(2)     ;PD residual error model
  Y= (1-TYPE)*YC + TYPE*YE
  IPRE=CP
  IF(TYPE.EQ.1) IPRE=EE

  $THETA
  (0,2)       ;[KA]
  (0,0.1)     ;[KE]
  (0,32)      ;[V2]
  (0,0.5)     ;[KE0]
  (0,1.2)     ;[EMAX]
  (0,6.7)     ;[EC50]

  $OMEGA
  0.03 ;[P]
  0.03 ;[P]
  0.03 ;[P]
  0.03 ;[P]

  $SIGMA
  0.01 ;[P]
  0.1  ;[A]

  $ESTIMATION METHOD=1 INTER MAXEVAL=5000 PRINT=5 MSF=702.MSF SIGL=12
  $COV MATRIX=R UNCONDITIONAL PRINT=E
  $TABLE ID TIME YC YE CP CE IPRE TYPE CMT CWRES FILE=702.tab NOPRINT

PK/PD sequentially modeled

Assume a previous PK model run provides individual elimination rate constant and volume of distribution prediction as data item KEIN and V2IN, then we can use them in the Emax PD model sequentially.

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;# ...
$PK
 KA=KIND
 KE=KEIN
 V2=V2IN
 S2=V2
;# LINEAR EFFECT MODEL

 INTR=THETA(1)
 SLOP=THETA(2)*EXP(ETA(1))
 KE0 =THETA(3)

$DES
 DADT(1)=-KA*A(1)
 DADT(2)=KA*A(1)-KE*A(2)
 DADT(3)=KE0*(A(2)/V2-A(3))

$ERROR
 CE=A(3)
 E=INTR+SLOP*CE

Y=E+ERR(1)

CP=A(2)/S2
IPRE=E
$THETA
(0,0.1)     ;# [INTR]
(0.5)       ;# [SLOP]
(0,0.5)     ;# [KE0]

$OMEGA
0.01 ;[P]

$SIGMA
 .01;[A]
;# ...