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$Emax <- rep(log(1),dim(Data)[1])
#Estimation of model parameters
PKPDpoolModel <- nlmeODE(PoolModel,Data,JAC=FALSE)
PKPDpool.nlme <- nlme(Conc ~ PKPDpoolModel(ke,Vd,Kin,kout,krel,Emax,EC50,gamma,Time,ID,Type),
data = Data, fixed=ke+Vd+Kin+kout+krel+EC50+gamma~1, random = pdDiag(ke+Vd+EC50~1),
groups=~ID,
weights=varIdent(form=~1|Type),
start=c(ke=log(0.05),Vd=log(10),Kin=log(5),kout=log(0.5),krel=log(2),EC50=log(5),gamma=log(3)),
control=list(msVerbose=TRUE,tolerance=1e-1,pnlsTol=1e-1,msTol=1e-1,msMaxIter=20,pnlsMaxIter=20),
verbose=TRUE)
#Plot results
ni <- 100
TimeSim <- seq(from=0,to=24,length=ni)
TimeSim <- rep(rep(TimeSim,each=2),12)
IDSim <- rep(1:12,each=2*ni)
TypeSim <- rep(rep(c(1,2),ni),12)
IndCoef <- coef(PKPDpool.nlme)
IpredSim <- PKPDpoolModel( rep(IndCoef[,1],each=2*ni),
rep(IndCoef[,2],each=2*ni),
rep(IndCoef[,3],each=2*ni),
rep(IndCoef[,4],each=2*ni),
rep(IndCoef[,5],each=2*ni),
rep(rep(log(1),12),each=2*ni),
rep(IndCoef[,6],each=2*ni),
rep(IndCoef[,7],each=2*ni),
TimeSim,IDSim,TypeSim)
PopCoef <- fixef(PKPDpool.nlme)
PredSim <- PKPDpoolModel( rep(rep(PopCoef[1],12),each=2*ni),
rep(rep(PopCoef[2],12),each=2*ni),
rep(rep(PopCoef[3],12),each=2*ni),
rep(rep(PopCoef[4],12),each=2*ni),
rep(rep(PopCoef[5],12),each=2*ni),
rep(rep(log(1),12),each=2*ni),
rep(rep(PopCoef[6],12),each=2*ni),
rep(rep(PopCoef[7],12),each=2*ni),
TimeSim,IDSim,TypeSim)
plotPool <- as.data.frame(rbind(cbind(TimeSim,IDSim,PredSim,TypeSim,rep("Pred",2400)),
cbind(TimeSim,IDSim,IpredSim,TypeSim,rep("Ipred",2400)),
cbind(Data$Time,Data$ID,Data$Conc,Data$Type,rep("Obs",288))))
names(plotPool) <- c("Time","ID","Conc","Type","Flag")
plotPool$ID <- as.factor(as.numeric(as.character(plotPool$ID)))
plotPool$Type <- as.factor(plotPool$Type)
plotPool$Flag <- as.factor(plotPool$Flag)
plotPool$Conc <- as.numeric(as.character(plotPool$Conc))
plotPool$Time <- as.numeric(as.character(plotPool$Time))
plotPoolPK <- subset(plotPool,Type==1)
plotPoolPD <- subset(plotPool,Type==2)
require(lattice)
xyplot (Conc~Time | ID, data=plotPoolPK,
layout=c(4,3),
aspect=1/1,
groups=Flag,
grid=TRUE,
xlab="Time since drug administration (hr)",
ylab="PK concentration (ng/mL)",
key=list(x=0.23,y=1.03,corner=c(0,1),transparent=TRUE,
text = list(c("Population", "Individual","Observed")),
lines = list(type=c("l","l","p"), pch=1, col=c(1,1,1), lty=c(1,2,1)),columns=3),
strip = function(...) strip.default(..., strip.names=c(FALSE,TRUE), style=1),
panel = function(x, y, groups,...) {
panel.grid(h=3,v=3,col="lightgray",lwd=0.7,...)
panel.superpose.2(x,y,groups,type=c("l","p","l"), col=c(1,1,1), lty=c(2,1,1),pch=1, lwd=1.4,...)},
par.strip.text=list(cex=1.0))
xyplot (Conc~Time | ID, data=plotPoolPD,
layout=c(4,3),
aspect=1/1,
groups=Flag,
grid=TRUE,
xlab="Time since drug administration (hr)",
ylab="PD concentration (ng/mL)",
key=list(x=0.23,y=1.03,corner=c(0,1),transparent=TRUE,
text = list(c("Population", "Individual","Observed")),
lines = list(type=c("l","l","p"), pch=1, col=c(1,1,1), lty=c(1,2,1)),columns=3),
strip = function(...) strip.default(..., strip.names=c(FALSE,TRUE), style=1),
panel = function(x, y, groups,...) {
panel.grid(h=3,v=3,col="lightgray",lwd=0.7,...)
panel.superpose.2(x,y,groups,type=c("l","p","l"), col=c(1,1,1), lty=c(2,1,1),pch=1, lwd=1.4,...)},
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