nlmeODE (version 0.2-1)

PKPDtol: Simulated turnover PK/PD model with tolerance

Description

Simulated data of an intraveneous bolus dose PK study with administration to twelve subjects and PK and PD plasma concentration measurements at twelve time points pr. subject. The PK/PD is modelled simultaneously using a one-compartment PK model with IV bolus and a turnover PD model with tolerance build-up.

Usage

data(PKPDtol)

Examples

data(PKPDtol)

#Fixed parameters
PKPDtol$Emax <-  rep(log(1),dim(PKPDtol)[1])

ToleranceModel <- list(
              DiffEq = list( 
                dy1dt = ~ -ke*y1,
                dy2dt = ~ Kin * (1-Emax*(y1/Vd)**gamma/(EC50**gamma+(y1/Vd)**gamma)) - Kout * y2 * (1+y3),
                dy3dt = ~ Ktol * (y2-y3)),
              ObsEq  = list(  
                c1 = ~ y1/Vd,
                c2 = ~ y2,
                c3 = ~ 0),        
              States=c("y1","y2","y3"), 
              Parms=c("ke","Vd","Kin","Kout","Emax","EC50","gamma","Ktol"),
              LogParms=TRUE,             
              Init=list(0,"-0.5+(0.25+Kin/Kout)**0.5","-0.5+(0.25+Kin/Kout)**0.5"), 
              JAC=FALSE,           
              SEQ=FALSE)

TolPKPDModel <- nlmeODE(ToleranceModel,PKPDtol)

PKPDtol.nlme <- nlme(Conc ~ TolPKPDModel(ke,Vd,Kin,Kout,Emax,EC50,gamma,Ktol,Time,Subject,Type),
        data = PKPDtol, fixed=ke+Vd+Kin+Kout+EC50+gamma+Ktol~1, random = pdDiag(ke+Vd+EC50~1),
        groups=~Subject,
        weights=varIdent(form=~1|Type),
        start=c(ke=log(0.05),Vd=log(10),Kin=log(10),Kout=log(0.1),EC50=log(5),gamma=log(3),Ktol=log(0.01)),
        control=list(msVerbose=TRUE,tolerance=1e-3,pnlsTol=1e-1,msTol=1e-3,msMaxIter=20,pnlsMaxIter=20))

#Plot results
ni <- 100

TimeSim <- seq(from=0,to=24,length=ni)
TimeSim <- rep(rep(TimeSim,each=2),12)

SubjectSim <- rep(1:12,each=2*ni)
TypeSim <- rep(rep(c(1,2),ni),12)

IndCoef <- coef(PKPDtol.nlme)
IpredSim <- TolPKPDModel(  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(rep(log(1),12),each=2*ni),
                rep(IndCoef[,5],each=2*ni),
                rep(IndCoef[,6],each=2*ni),
                rep(rep(log(0.01),12),each=2*ni),
                TimeSim,SubjectSim,TypeSim)

PopCoef <- fixef(PKPDtol.nlme)
PredSim <- TolPKPDModel(  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(log(1),12),each=2*ni),
                rep(rep(PopCoef[5],12),each=2*ni),
                rep(rep(PopCoef[6],12),each=2*ni),
                rep(rep(log(0.01),12),each=2*ni),
                TimeSim,SubjectSim,TypeSim)

plotTol <- as.data.frame(rbind(cbind(TimeSim,SubjectSim,PredSim,TypeSim,rep("Pred",2400)),
                          cbind(TimeSim,SubjectSim,IpredSim,TypeSim,rep("Ipred",2400)),
                          cbind(PKPDtol$Time,PKPDtol$Subject,PKPDtol$Conc,PKPDtol$Type,rep("Obs",288))
                         ))
names(plotTol) <- c("Time","Subject","Conc","Type","Flag")

plotTol$Subject <- as.factor(as.numeric(as.character(plotTol$Subject)))
plotTol$Type <- as.factor(plotTol$Type)
plotTol$Flag <- as.factor(plotTol$Flag)
plotTol$Conc <- as.numeric(as.character(plotTol$Conc))
plotTol$Time <- as.numeric(as.character(plotTol$Time))

plotTolPK <- subset(plotTol,Type==1)
plotTolPD <- subset(plotTol,Type==2)

trellis.device(width=7, height=6.5,bg="transparent")
sb <- trellis.par.get("strip.background")
sb$col <- c(16,11,9,13,10,15,14) 
trellis.par.set("strip.background",sb)
par(oma=c(0,1,1,0),mgp=c(3,1,.3))
xyplot (Conc~Time | Subject, data=plotTolPK, 
                       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))


trellis.device(width=7, height=6.5,bg="transparent")
sb <- trellis.par.get("strip.background")
sb$col <- c(16,11,9,13,10,15,14)
trellis.par.set("strip.background",sb)
par(oma=c(0,1,1,0),mgp=c(3,1,.3))
xyplot (Conc~Time | Subject, data=plotTolPD, 
                       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,...)},
                       par.strip.text=list(cex=1.0))