群体药动学药效学模型
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群体药动学药效学模型
一、药效学模型简介
明确药物暴露、药效和时间之间的关系。
基于经验 的药动学-药效学研究涵盖了直接影响机制、作用室理论以及反转机制。
机制性模型
二、常用的药动学药效学模型
直接效应模型
可描述大多数药动学和药效学之间的关系。表达式如下：
药物和效应也可以为线性关系：
E=E0+slope*C
slope为斜率
1. ADVAN模块
$PROBLEM synchronous pd, pkpd_advan, direct Emax
$INPUT ID TIME DV AMT MDV EVID DVID WT
$DATA 8-1.csv IGNORE=#
$SUBROUTINES ADVAN2 TRANS2 ; 1cmt oral
$PK
;--------------pk prameters------------
KA = THETA(1)
CL = THETA(2) * EXP(ETA(1)) * (WT/60)**(THETA(8))
V = THETA(3) * EXP(ETA(2)) * (WT/60)
;---------------pd parameters------------------------
EMAX = THETA(4) * EXP(ETA(3))
EC50 = THETA(5)
EBSL = THETA(6)
HILL = THETA(7)
$ERROR
CP = A(2)/V ; drug concentration of central compartment
EFF = EBSL + EMAX*CP**HILL/(EC50**HILL+CP**HILL) ; drug effect
FLAG = 1
IF(DVID .EQ. 3 ) FLAG = 0
Y = FLAG*(CP*(1+EPS(1))+EPS(2)) + (1-FLAG)*(EFF*(1+EPS(3)))
IPRED = FLAG*CP + (1-FLAG)*EFF
IRES = DV - IPRED
DEL = 0
IF (DV .EQ. 0) DEL = 1
IWRES = (1-DEL) * IRES/(DV + DEL)
$THETA
(0,1) ;KA
(0,0.5) ;CL
(0,10) ;V
(0,100) ;EMAX
(0,12) ;EC50
(0,1) ;EBSL
(0,1) ;Hill
(0,1) ;WT_CL
$OMEGA
(0.1) ; IIV CL
(0.1) ; IIV V
(0.1) ; IIV EMAX
$SIGMA
(0.1) ; EPS1_prop pk
(0.1) ; EPS2_add pk
(0.1) ; EPS3_prop pd
$EST METHOD=1 INTER MAXEVAL=9999 NOABORT SIG=3 PRINT=5
$COV PRINT=E
; Xpose
$TABLE ID TIME DV AMT DVID MDV EVID DVID WT KA CL V EMAX EC50 EBSL HILL ETA1 ETA2 ETA3 CP EFF
PRED IPRED RES IRES IWRES CWRES ONEHEADER NOPRINT FILE=run8-1.fit
$TABLE ID TIME DV AMT DVID MDV EVID PRED IPRED RES IRES IWRES CWRES ONEHEADER NOPRINT FILE=sdtab8-12. PRED模块
- 每个受试者仅有单个观测值
;; 2. Description: pkpd_pred, linear
$PROBLEM pkpd_pred, linear
$INPUT ID=DROP DQTC=DV CMAX
$DATA 8-2.csv IGNORE=#
$PRED
A = THETA(1) ;slope
B = THETA(2) ;intercepter
EFF = A * CMAX +B ;linear pd
Y = EFF + ETA(1) ;加和型 个体间+个体内总变异
$THETA
(0,0.08) ; slope
(0,0.3) ; intercepter
$OMEGA
(0.1) ; inter-&intra-individual
$EST METHOD=0 MAXEVAL=9999 NOABORT SIG=3 PRINT=5
$COV PRINT=E
$TABLE DV CMAX EFF FILE=run8-2.fit- 每个受试者有多个观测值
;; 2. Description: pkpd_pred, Emax
$PROBLEM synchronous pd, pkpd_pred, Emax
$INPUT ID TIME DV CON
$DATA 8-3.csv IGNORE=#
$PRED
EMAX = THETA(1) * EXP(ETA(1))
EC50 = THETA(2)
EBSL = THETA(3)
HILL = THETA(4) * EXP(ETA(2))
EFF = EBSL + EMAX*(CON**HILL)/(EC50**HILL+CON**HILL)
IPRED = EFF
Y = EFF * (1+EPS(1))
IRES = DV-IPRED
DEL = 0
IF (DV .EQ. 0) DEL = 1
IWRES = (1-DEL) * IRES/(DV + DEL)
$THETA
(0,100) ;EMAX
(0,10) ;EC50
(0,1) ;EBSL
(0,1) ;HILL
$OMEGA
(0.1) ; IIV EMAX
(0.1) ; IIV HILL
$SIGMA
(0.1) ; EPS1_prop
$EST METHOD=1 INTER MAXEVAL=9999 NOABORT SIG=3 PRINT=5
$COV PRINT=E
; Xpose
$TABLE ID TIME DV CON EFF EMAX EC50 EBSL HILL ETA1 ETA2 IPRED PRED RES IRES IWRES CWRES ONEHEADER NOPRINT FILE=run8-3.fit
$TABLE ID TIME DV PRED IPRED RES IRES IWRES CWRES ONEHEADER NOPRINT FILE=sdtab8-3效应室模型
$PROBLEM 2cmt pkpd_Effect compartment ADVAN4
$INPUT ID TIME DV AMT MDV EVID DVID WT
$DATA 8-4.csv IGNORE=#
$SUBROUTINES ADVAN4 TRANS4 ; 1cmt oral + effect compartment
$PK
;---------------pk prameters------------
KA = THETA(1)
CL = THETA(2) * EXP(ETA(1)) * (WT/60)**(THETA(9))
V2 = THETA(3) * EXP(ETA(2)) * (WT/60)
;---------------pd parameters------------------------
EMAX = THETA(4) * EXP(ETA(3))
EC50 = THETA(5) * EXP(ETA(4))
EBSL = THETA(6)
HILL = THETA(7) * EXP(ETA(5))
;----------------effect compartment parameters---------
KE0 = THETA(8)
V3 = V2 * 0.001 ; effect volume,set to very small
Q = KE0 * V3
$ERROR
CP = A(2)/V2 ; drug concentration in central compartment
CE = A(3)/V3 ; drug concentration in effect compartment
EFF = EBSL + EMAX*CE**HILL/(EC50**HILL+CE**HILL) ; drug effect
FLAG = 1
IF(DVID .EQ. 3 ) FLAG = 0
Y = FLAG*(CP*(1+EPS(1))+EPS(2)) + (1-FLAG)*(EFF*(1+EPS(3)))
IPRED = FLAG*CP + (1-FLAG)*EFF
IRES = DV - IPRED
DEL = 0
IF (DV .EQ. 0) DEL = 1
IWRES = (1-DEL) * IRES/(DV + DEL)
$THETA
(0,1) ;KA
(0,0.5) ;CL
(0,10) ;V2
(0,100) ;EMAX
(0,10) ;EC50
(0,1) ;EBSL
(0,1) ;Hill
(0,0.03) ;KE0
(0,1) ;WT_CL
$OMEGA
(0.1) ;IIV CL
(0.1) ;IIV V2
(0.1) ;IIV EMAX
(0.1) ;IIV EC50
(0.1) ;IIV HILL
$SIGMA
(0.1) ; EPS1_prop pk
(0.01) ; EPS2_add pk
(0.1) ; EPS3_prop pd
$EST METHOD=1 INTER MAXEVAL=9999 NOABORT SIG=3 PRINT=5
$COV PRINT=E
; Xpose
$TABLE ID TIME DV AMT DVID MDV EVID WT KA KE0 CL V2 EMAX EC50 EBSL HILL ETA1 ETA2 ETA3 ETA4 CP CE EFF
PRED IPRED RES IRES IWRES CWRES ONEHEADER NOPRINT NOAPP FILE=run8-4.fit
$TABLE ID TIME DV AMT DVID MDV EVID PRED IPRED RES IRES IWRES CWRES ONEHEADER NOPRINT FILE=sdtab8-4
$TABLE ID TIME MDV DVID KA KE0 CL V2 EMAX EC50 EBSL HILL ETA1 ETA2 ETA3 ETA4 ONEHEADER NOPRINT FILE=patab8-4
$TABLE ID TIME MDV DVID WT ONEHEADER NOPRINT FILE=cotab8-4自定义模型
;; 2. Description: pkpd_advan6, Effect compartment
$PROBLEM 2cmt pkpd_Effect compartment
$INPUT ID TIME DV AMT CMT MDV EVID DVID WT
$DATA 8-5.csv IGNORE=#
$SUBROUTINES ADVAN6 TOL=6 ; 1cmt oral + effect compartment
$MODEL
COMP=(DEPO,DEFDOSE)
COMP=(CENTRAL,DEFOBS)
COMP=(EFF)
$PK
;---------------pk prameters------------
KA = THETA(1)
CL = THETA(2) * EXP(ETA(1)) * (WT/60)**(THETA(9))
V2 = THETA(3) * EXP(ETA(2)) * (WT/60)
K20 = CL/V2
;--------------pd prameters------------
EMAX = THETA(4) * EXP(ETA(3))
EC50 = THETA(5) * EXP(ETA(4))
EBSL = THETA(6)
HILL = THETA(7) * EXP(ETA(5))
;----------------effect compartment parameters---------
KE0 = THETA(8)
$DES
DADT(1) = -KA * A(1)
DADT(2) = KA * A(1) - K20 * A(2)
DADT(3) = KE0* (A(2)/V2-A(3)) ; A(3) was defined as drug concentration in effect compartment
$ERROR
CE = A(3) ; drug concentration in effect compartment
CP = A(2)/V2 ; drug concentration in central compartment
EFF = EBSL + EMAX*CE**HILL/(EC50**HILL+CE**HILL) ; drug effect
FLAG = 1
IF(CMT .EQ. 3 ) FLAG = 0
Y = FLAG*(CP*(1+EPS(1))+EPS(2)) + (1-FLAG)*(EFF*(1+EPS(3)))
IPRED = FLAG*CP + (1-FLAG)*EFF
IRES = DV - IPRED
DEL = 0
IF (DV .EQ. 0) DEL = 1
IWRES = (1-DEL) * IRES/(DV + DEL)
$THETA
(0,1) ;KA
(0,0.5) ;CL
(0,10) ;V2
(0,100) ;EMAX
(0,10) ;EC50
(0,1) ;EBSL
(0,1) ;Hill
(0,0.03) ;KE0
(0,1) ;WT_CL
$OMEGA
(0.1) ;IIV CL
(0.1) ;IIV V2
(0.1) ;IIV EMAX
(0.1) ;IIV EC50
(0.1) ;IIV HILL
$SIGMA
(0.1) ; EPS1_prop pk
(0.01) ; EPS2_add pk
(0.1) ; EPS3_prop pd
$EST METHOD=1 INTER MAXEVAL=9999 NOABORT SIG=3 PRINT=5
$COV PRINT=E
; Xpose
$TABLE ID TIME DV AMT CMT MDV EVID DVID WT KA KE0 CL V2 EMAX EC50 EBSL HILL ETA1 ETA2 ETA3 ETA4 ETA5 CP CE EFF
PRED IPRED RES IRES IWRES CWRES ONEHEADER NOPRINT FILE=run8-5.fit
$TABLE ID TIME DV AMT CMT MDV PRED IPRED RES IRES IWRES CWRES ONEHEADER NOPRINT FILE=sdtab8-5
$TABLE ID TIME MDV CMT KA KE0 CL V2 EMAX EC50 EBSL HILL ETA1 ETA2 ETA3 ETA4 ETA5 ONEHEADER NOPRINT FILE=patab8-5
$TABLE ID TIME MDV CMT WT ONEHEADER NOPRINT FILE=cotab8-5翻转模型
;; 2. Description: pkpd_advan6, Turn over
$PROBLEM pkpd Turn over
$INPUT ID TIME DV AMT CMT MDV EVID DVID WT
$DATA 8-6.csv IGNORE=#
$SUBROUTINES ADVAN6 TOL=6 ; 1cmt oral + turn over compartment
$MODEL
COMP=(DEPO,DEFDOSE)
COMP=(CENTRAL,DEFOBS)
COMP=(TURNOVER)
$PK
;--------------pk prameters------------
KA = THETA(1)
CL = THETA(2) * EXP(ETA(1)) * (WT/60)**(THETA(9))
V2 = THETA(3) * EXP(ETA(2)) * (WT/60)
K20 = CL/V2
S2 = V2
;--------------pd prameters------------
EMAX = THETA(4) * EXP(ETA(3))
EC50 = THETA(5) * EXP(ETA(4))
EBSL = THETA(6)
HILL = THETA(7)
;--------------turn over prameters------------
A_0(3) = EBSL
KOUT = THETA(8) * EXP(ETA(5))
KIN = KOUT * EBSL
$DES
CP = A(2)/V2 ; drug concentration in central compartment
EFF = 1 + EMAX*CP**HILL/(EC50**HILL+CP**HILL) ; drug effect
DADT(1) = -KA * A(1)
DADT(2) = KA * A(1) - K20 * A(2)
DADT(3) = KIN* EFF - KOUT * A(3)
$ERROR
IPRED = F
FLAG = 1
IF(CMT .EQ. 3 ) FLAG = 0
Y = FLAG*(F*(1+EPS(1))+EPS(2)) + (1-FLAG)*(F*(1+EPS(3)))
IRES = DV-IPRED
DEL = 0
IF (DV .EQ. 0) DEL = 1
IWRES = (1-DEL) * IRES/(DV + DEL)
$THETA
(0,1) ;KA
(0,0.5) ;CL
(0,10) ;V2
(0,100) ;EMAX
(0,10) ;EC50
(0,1) ;EBSL
(0,1) ;Hill
(0,0.05) ;KOUT
(0,1) ;WT_CL
$OMEGA
(0.1) ;IIV CL
(0.1) ;IIV V2
(0.1) ;IIV EMAX
(0.1) ;IIV EC50
(0.1) ;IIV KOUT
$SIGMA
(0.1) ; EPS1_prop pk
(0.01) ; EPS2_add pk
(0.1) ; EPS3_prop pd
$EST METHOD=1 INTER MAXEVAL=9999 NOABORT SIG=3 PRINT=5
$COV PRINT=E
; Xpose
$TABLE ID TIME DV AMT CMT MDV EVID DVID WT KA KOUT CL V2 EMAX EC50 EBSL HILL ETA1 ETA2 ETA3 ETA4 ETA5 CP EFF
PRED IPRED RES IRES IWRES CWRES ONEHEADER NOPRINT NOAPP FILE=run8-6.fit
$TABLE ID TIME DV AMT CMT MDV PRED IPRED RES IRES IWRES CWRES ONEHEADER NOPRINT FILE=sdtab8-6
$TABLE ID TIME MDV CMT KA KOUT CL V2 EMAX EC50 EBSL HILL ETA1 ETA2 ETA3 ETA4 ETA5 ONEHEADER NOPRINT FILE=patab8-6
$TABLE ID TIME MDV CMT WT ONEHEADER NOPRINT FILE=cotab8-6三、药动学药效学模型的其他考虑
药动学参数的输出
输出cmax和tmax定义
$ABBREVIATED COMRES=2模块的选择
药动学药效学模型的拟合顺序
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