########################################
### Pharmacokinetics of Theophylline ###
########################################
data(Theoph)
TheophODE <- Theoph
TheophODE$Dose[TheophODE$Time!=0] <- 0
TheophODE$Cmt <- rep(1,dim(TheophODE)[1])
OneComp <- list(DiffEq=list(
dy1dt = ~ -ka*y1 ,
dy2dt = ~ ka*y1-ke*y2),
ObsEq=list(
c1 = ~ 0,
c2 = ~ y2/CL*ke),
Parms=c("ka","ke","CL"),
States=c("y1","y2"),
Init=list(0,0))
TheophModel <- nlmeODE(OneComp,TheophODE)
Theoph.nlme <- nlme(conc ~ TheophModel(ka,ke,CL,Time,Subject),
data = TheophODE, fixed=ka+ke+CL~1, random = pdDiag(ka+CL~1),
start=c(ka=0.5,ke=-2.5,CL=-3.2),
control=list(returnObject=TRUE,msVerbose=TRUE,tolerance=1e-1,pnlsTol=1e-1,msTol=1e-1),
verbose=TRUE)
plot(augPred(Theoph.nlme,level=0:1))
#########################################
### Pharmacokinetics of Indomethacine ###
#########################################
data(Indometh)
TwoComp <- list(DiffEq=list(
dy1dt = ~ -(k12+k10)*y1+k21*y2 ,
dy2dt = ~ -k21*y2 + k12*y1),
ObsEq=list(
c1 = ~ y1,
c2 = ~ 0),
States=c("y1","y2"),
Parms=c("k12","k21","k10","start"),
Init=list("start",0))
IndomethModel <- nlmeODE(TwoComp,Indometh)
Indometh.nlme <- nlme(conc ~ IndomethModel(k12,k21,k10,start,time,Subject),
data = Indometh, fixed=k12+k21+k10+start~1, random = pdDiag(start+k12+k10~1),
start=c(k12=-0.05,k21=-0.15,k10=-0.10,start=0.70),
control=list(msVerbose=TRUE,tolerance=1e-1,pnlsTol=1e-1,msTol=1e-1),
verbose=TRUE)
plot(augPred(Indometh.nlme,level=0:1))
#################################################################
### Absorption model with estimation of time/rate of infusion ###
#################################################################
OneCompAbs <- list(DiffEq=list(
dA1dt = ~ -ka*A1,
dA2dt = ~ ka*A1 - CL/V1*A2),
ObsEq=list(
SC= ~0,
C = ~ A2/V1),
States=c("A1","A2"),
Parms=c("ka","CL","V1","F1"),
Init=list(0,0))
ID <- rep(seq(1:18),each=11)
Time <- rep(seq(0,100,by=10),18)
Dose <- c(rep(c(100,0,0,100,0,0,0,0,0,0,0),6),rep(c(100,0,0,0,0,0,0,100,0,0,0),6),rep(c(100,0,0,0,0,0,0,0,0,0,0),6))
Rate <- c(rep(rep(0,11),6),rep(c(5,rep(0,10)),6),rep(rep(0,11),6))
Cmt <- c(rep(1,6*11),rep(c(2,0,0,0,0,0,0,1,0,0,0),6),rep(2,6*11))
Conc <- rep(0,18*11)
Data <- as.data.frame(list(ID=ID,Time=Time,Dose=Dose,Rate=Rate,Cmt=Cmt,Conc=Conc))
SimData <- groupedData( Conc ~ Time | ID,
data = Data,
labels = list( x = "Time", y = "Concentration"))
OneCompAbsModel <- nlmeODE(OneCompAbs,SimData)
kaSim <- rep(log(rep(0.05,18))+0.3*rnorm(18),each=11)
CLSim <- rep(log(rep(0.5,18))+0.2*rnorm(18),each=11)
V1Sim <- rep(log(rep(10,18))+0.1*rnorm(18),each=11)
F1Sim <- rep(log(0.8),18*11)
SimData$Sim <- OneCompAbsModel(kaSim,CLSim,V1Sim,F1Sim,SimData$Time,SimData$ID)
SimData$Conc <- SimData$Sim + 0.3*rnorm(dim(SimData)[1])
Data <- groupedData( Conc ~ Time | ID,
data = SimData,
labels = list( x = "Time", y = "Concentration"))
plot(Data,aspect=1/1)
#Estimation of model parameters
OneCompAbsModel <- nlmeODE(OneCompAbs,Data)
fit1 <- nlme(Conc ~ OneCompAbsModel(ka,CL,V1,F1,Time,ID),
data = Data, fixed=ka+CL+V1+F1~1, random = pdDiag(ka+CL+V1~1),
start=c(ka=log(0.05),CL=log(0.5),V1=log(10.0),F1=log(0.8)),
control=list(msVerbose=TRUE,tolerance=1e-3,pnlsTol=1e-1,msTol=1e-3),
verbose=TRUE)
plot(augPred(fit1,level=0:1,length.out=300),aspect=1/1)
#Estimation of rate of infusion
Data$Rate[Data$Rate==5] <- -1
OneCompAbs <- list(DiffEq=list(
dA1dt = ~ -ka*A1,
dA2dt = ~ ka*A1 - CL/V1*A2),
ObsEq=list(
SC= ~0,
C = ~ A2/V1),
States=c("A1","A2"),
Parms=c("ka","CL","V1","F1","Rate"),
Init=list(0,0))
OneCompAbsModel <- nlmeODE(OneCompAbs,Data)
fit2 <- nlme(Conc ~ OneCompAbsModel(ka,CL,V1,F1,Rate,Time,ID),
data = Data, fixed=ka+CL+V1+F1+Rate~1, random = pdDiag(ka+CL+V1~1),
start=c(ka=log(0.05),CL=log(0.5),V1=log(10.0),F1=log(0.8),Rate=log(5)),
control=list(msVerbose=TRUE,tolerance=1e-3,pnlsTol=1e-1,msTol=1e-3),
verbose=TRUE)
plot(augPred(fit2,level=0:1,length.out=300),aspect=1/1)
#Estimation of length of infusion
Data$Rate[Data$Rate==-1] <- -2
OneCompAbs <- list(DiffEq=list(
dA1dt = ~ -ka*A1,
dA2dt = ~ ka*A1 - CL/V1*A2),
ObsEq=list(
SC= ~0,
C = ~ A2/V1),
States=c("A1","A2"),
Parms=c("ka","CL","V1","F1","Tcrit"),
Init=list(0,0))
OneCompAbsModel <- nlmeODE(OneCompAbs,Data)
fit3 <- nlme(Conc ~ OneCompAbsModel(ka,CL,V1,F1,Tcrit,Time,ID),
data = Data, fixed=ka+CL+V1+F1+Tcrit~1, random = pdDiag(ka+CL+V1~1),
start=c(ka=log(0.05),CL=log(0.5),V1=log(10.0),F1=log(0.8),Tcrit=log(20)),
control=list(msVerbose=TRUE,tolerance=1e-3,pnlsTol=1e-1,msTol=1e-3),
verbose=TRUE)
############################################################
### Simulation and simultaneous estimation of PK/PD data ###
############################################################
PoolModel <- list(
DiffEq=list(
dy1dt = ~ -ke*y1,
dy2dt = ~ krel * (1-Emax*(y1/Vd)**gamma/(EC50**gamma+(y1/Vd)**gamma)) * y3 - kout * y2,
dy3dt = ~ Kin - krel * (1-Emax*(y1/Vd)**gamma/(EC50**gamma+(y1/Vd)**gamma))*y3),
ObsEq=list(
PK = ~ y1/Vd,
PD = ~ y2,
Pool = ~ 0),
States=c("y1","y2","y3"),
Parms=c("ke","Vd","Kin","kout","krel","Emax","EC50","gamma"),
Init=list(0,"Kin/kout","Kin/krel"))
ID <- rep(seq(1:12),each=2*12)
Time <- rep(rep(c(0,0.25,0.5,0.75,1,2,4,6,8,10,12,24),each=2),12)
Dose <- rep(c(100,rep(0,23)),12)
Cmt <- rep(rep(c(1,2),12),12)
Type <- rep(rep(c(1,2),12),12)
Conc <- rep(0,2*12*12)
Data <- as.data.frame(list(ID=ID,Time=Time,Dose=Dose,Cmt=Cmt,Type=Type,Conc=Conc))
SimData <- groupedData( Conc ~ Time | ID/Type,
data = Data,
labels = list( x = "Time", y = "Concentration"))
PKPDpoolModel <- nlmeODE(PoolModel,SimData,JAC=FALSE)
keSim <- rep(log(rep(0.05,12))+0.1*rnorm(12),each=2*12)
VdSim <- rep(log(rep(10,12))+0.01*rnorm(12),each=2*12)
EC50Sim <- rep(log(rep(5,12))+0.1*rnorm(12),each=2*12)
KinSim <- rep(log(5),2*12*12)
koutSim <- rep(log(0.5),2*12*12)
krelSim <- rep(log(2),2*12*12)
EmaxSim <- rep(log(1),2*12*12)
gammaSim <- rep(log(3),2*12*12)
SimData$Sim <- PKPDpoolModel(keSim,VdSim,KinSim,koutSim,krelSim,EmaxSim,EC50Sim,gammaSim,SimData$Time,SimData$ID,SimData$Type)
SimData$Conc[SimData$Type==1] <- SimData$Sim[SimData$Type==1] + 0.1*rnorm(length(SimData[SimData$Type==1,1]))
SimData$Conc[SimData$Type==2] <- SimData$Sim[SimData$Type==2] + 0.01*rnorm(length(SimData[SimData$Type==2,1]))
Data <- groupedData( Conc ~ Time | ID/Type,
data = SimData,
labels = list( x = "Time", y = "Concentration"))
plot(Data,display=1,aspect=1/1)
#Fixed parameters
Data$Emax <- rep(log(1),dim(Data)[1])
#Estimation of model parameters
PKPDpoolModel <- nlmeODE(PoolModel,Data,JAC=FALSE)
PKPDpool.nlme <- nlme(Conc ~ PKPDpoolModel(ke,Vd,Kin,kout,krel,Emax,EC50,gamma,Time,ID,Type),
data = Data, fixed=ke+Vd+Kin+kout+krel+EC50+gamma~1, random = pdDiag(ke+Vd+EC50~1),
groups=~ID,
weights=varIdent(form=~1|Type),
start=c(ke=log(0.05),Vd=log(10),Kin=log(5),kout=log(0.5),krel=log(2),EC50=log(5),gamma=log(3)),
control=list(msVerbose=TRUE,tolerance=1e-1,pnlsTol=1e-1,msTol=1e-1,msMaxIter=20,pnlsMaxIter=20),
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