biexp: Two-phase half-life estimation by biexponential model
In PK: Basic Non-Compartmental Pharmacokinetics
biexp R Documentation
Two-phase half-life estimation by biexponential model
Description
Estimation of initial and terminal half-life by fitting a biexponential model.
Usage
biexp(conc, time, log.scale=FALSE, tol=1E-9, maxit=500)
Arguments
conc
Levels of concentrations as a vector.
time
Time points of concentration assessment as a vector. One time point for each concentration measured needs to be specified.
log.scale
Logical value indicating whether fitting is performed on the observed or log-scale (default=FALSE).
tol
Relative error tolerance (default=1E-9).
maxit
Maximum number of iterations (default=500).
Details
Estimation of initial and terminal half-life using the biexponential y=a1*exp(-b1*x)+a2*exp(-b2*x) model with a parameterization to ensure b1 > b2 > 0 fitted by the least squares criteria with function optim of package base with method "Nelder-Mead". Curve peeling (Foss, 1969) is used get start values for nonlinear model fitting. When no adequate starting values are
determined by curve peeling, a single exponential model is fitted with starting values obtained from an OLS regression on log transformed values with a parameterization to ensure a slope > 0.
Fitting on the log-scale is based on the transform-both-sides approach described for example in chapter 4 of Bonate (2006) which is useful for some error distributions. An additional discussion regarding weighting schemes can be found in Gabrielsson and Weiner (2000, pages 368-374).
Value
A list of S3 class "halflife" containing the following components:
parms
half-life and model estimates.
time
time points of concentration assessments.
conc
levels of concentrations.
method
"biexp".
Note
Records including missing values and values below or equal to zero are omitted.
Author(s)
Martin J. Wolfsegger and Thomas Jaki
References
Bonate P. L. (2006). Pharmacokinetic-Pharmacodynamic Modeling and Simulation. Springer, New York.
Gabrielsson J. and Weiner D. (2000). Pharmacokinetic and Pharmacodynamic Data Analysis: Concepts and Applications. 4th Edition. Swedish Pharmaceutical Press, Stockholm.
Foss S. D. (1969). A Method for Obtaining Initial Estimates of the Parameters in Exponential Curve Fitting. Biometrics, 25:580-584.
Pinheiro J. C. and Bates D. M. (2000). Mixed-Effects Models in S and S-PLUS. Springer, New York.
Wolfsegger M. J. and Jaki T. (2009). Non-compartmental Estimation of Pharmacokinetic Parameters in Serial Sampling Designs. Journal of Pharmacokinetics and Pharmacodynamics, 36(5):479-494.
See Also
lee
Examples
#### example from Pinheiro J.C. and Bates D.M. (2000, page 279)
#### dataset Indometh of package datasets
require(datasets)
data <- subset(Indometh, Subject==2)
time <- data$time
conc <- data$conc
## fitting on observed and log-scale
res.obs <- biexp(conc=conc, time=time, log.scale=FALSE)
res.log <- biexp(conc=conc, time=time, log.scale=TRUE)
print(res.obs$parms)
print(res.log$parms)
plot(res.obs, ylim=c(0,5), xlim=c(0, max(time)), las=1)
plot(res.log, ylim=c(0,5), xlim=c(0, max(time)), las=1, add=TRUE, lty=2)
legend(x=0, y=5, lty=c(1,2), legend=c("fitted on observed scale", "fitted on log-scale"))
## get residuals using function nls with tol=Inf
parms.obs <- list(a1=res.obs$parms[3,1], b1=res.obs$parms[2,1], a2=res.obs$parms[3,2],
b2=res.obs$parms[2,2])
parms.log <- list(a1=res.log$parms[3,1], b1=res.log$parms[2,1], a2=res.log$parms[3,2],
b2=res.log$parms[2,2])
mod.obs <- nls(conc ~ a1*exp(-b1*time) + a2*exp(-b2*time), start=parms.obs,
control=nls.control(tol=Inf))
mod.log <- nls(conc ~ a1*exp(-b1*time) + a2*exp(-b2*time), start=parms.log,
control=nls.control(tol=Inf))
## identical estimates to mod.log but different SEs
summary(nls(log(conc)~log(a1*exp(-b1*time) + a2*exp(-b2*time)), start=parms.log,
control=nls.control(tol=Inf)))
## different approach using weighted least squares (WLS) in nls
mod.ols <- nls(conc ~ a1*exp(-b1*time) + a2*exp(-b2*time), start=parms.obs)
mod.wls1 <- nls(conc ~ a1*exp(-b1*time) + a2*exp(-b2*time), start=parms.obs,
weight=1/predict(mod.ols)^1)
mod.wls2 <- nls(conc ~ a1*exp(-b1*time) + a2*exp(-b2*time), start=parms.obs,
weight=1/predict(mod.ols)^2)
split.screen(c(2,2))
screen(1)
plot(ylim=c(-0.35,0.35), y=resid(mod.obs), x=predict(mod.obs), las=1,
main='Fitted using biexp on observed scale', xlab='Predicted', ylab='Residual')
abline(h=0)
screen(2)
plot(ylim=c(-0.35,0.35), y=resid(mod.log), x=predict(mod.log), las=1,
main='Fitted using biexp on log-scale', xlab='Predicted', ylab='Residual')
abline(h=0)
screen(3)
plot(ylim=c(-0.35,0.35), y=resid(mod.wls1), x=predict(mod.wls1), las=1,
main='Fitted using nls with weights 1/predict(mod.ols)^1', xlab='Predicted', ylab='Residual')
abline(h=0)
screen(4)
plot(ylim=c(-0.35,0.35), y=resid(mod.wls2), x=predict(mod.wls2), las=1,
main='Fitted using nls with weights 1/predict(mod.ols)^2', xlab='Predicted', ylab='Residual')
abline(h=0)
close.screen(all.screens=TRUE)
#### example for a serial sampling data design from Wolfsegger and Jaki (2009)
conc <- c(2.01, 2.85, 2.43, 0.85, 1.00, 0.91, 0.46, 0.35, 0.63, 0.39, 0.32,
0.45, 0.11, 0.18, 0.19, 0.08, 0.09, 0.06)
time <- c(rep(5/60,3), rep(3,3), rep(6,3), rep(9,3), rep(16,3), rep(24,3))
res.biexp1 <- biexp(conc=conc, time=time, log=TRUE)
res.biexp2 <- biexp(conc=conc, time=time, log=FALSE)
print(res.biexp1$parms)
print(res.biexp2$parms)
split.screen(c(1,2))
screen(1)
plot(x=c(0,25), y=c(0,3), type='n', las=1,
ylab='Plasma concentration (IU/mL)', xlab='Time (hours)')
points(x=time, y=conc, pch=21)
plot(res.biexp1, pch=NA, add=TRUE, lty=1)
plot(res.biexp2, pch=NA, add=TRUE, lty=2)
legend(x=25, y=3, xjust=1, col=c('black', 'black'), lty=c(1,2),
title='Nonlinear fitting with function biexp:',
legend=c('option: log=TRUE', 'option: log=FALSE'))
close.screen(1)
screen(2)
plot(x=c(0,25), y=c(0.01, 10), type='n', log='y', yaxt='n',
ylab='Plasma concentration (IU/mL)', xlab='Time (hours)')
axis(side=2, at=c(0.01, 0.1, 1, 10), labels=c('0.01', '0.1', '1', '10'), las=1)
axis(side=2, at=seq(2,9,1), tcl=-0.25, labels=FALSE)
axis(side=2, at=seq(0.2,0.9,0.1), tcl=-0.25, labels=FALSE)
axis(side=2, at=seq(0.02,0.09,0.01), tcl=-0.25, labels=FALSE)
points(x=time, y=conc, pch=21)
plot(res.biexp1, pch=NA, add=TRUE, lty=1)
plot(res.biexp2, pch=NA, add=TRUE, lty=2)
legend(x=25, y=10, xjust=1, col=c('black', 'black'), lty=c(1,2),
title='Nonlinear fitting with function biexp:',
legend=c('option: log=TRUE', 'option: log=FALSE'))
close.screen(all.screens=TRUE)
#### example from Gabrielsson and Weiner (2000, page 743)
#### endogenous concentration is assumed to be constant over time
dose <- 36630
time <- c(-1, 0.167E-01, 0.1167, 0.1670, 0.25, 0.583, 0.8330, 1.083, 1.583, 2.083, 4.083, 8.083,
12, 23.5, 24.25, 26.75, 32)
conc <- c(20.34, 3683, 884.7, 481.1, 215.6, 114, 95.8, 87.89, 60.19, 60.17, 34.89, 20.99, 20.54,
19.28, 18.18, 19.39, 22.72)
data <- data.frame(conc,time)
## get starting values using function biexp using naive adjustment for endogenous concentration
## by subtraction of pre-value
data$concadj <- data$conc - data$conc[1]
data$concadj[min(which(data$concadj<0)):nrow(data)] <- NA
res.biexp <- biexp(conc=data$concadj[-1], time=data$time[-1])$parms
start <- list(a1=res.biexp[3,1], k1=res.biexp[2,1], a2=res.biexp[3,2], k2=res.biexp[2,2])
## specify indicator variable enabling inclusion of pre-dose concentration for fitting
data$i1 <- ifelse(data$time <0, 1, 0)
data$i2 <- ifelse(data$time <0, 0, 1)
## assuming constant absolute error: ordinary least squares
mod.ols <- nls(conc ~ i1*base + i2*(base + a1*exp(-k1*time) + a2*exp(-k2*time)),
start=c(base=20.34, start), data=data, trace=TRUE)
## assuming constant relative error (i.e. proportional error - weight of 2): weighted least
## squares
mod.wls <- nls(conc ~ i1*base + i2*(base + a1*exp(-k1*time) + a2*exp(-k2*time)),
start=c(base=20.34, start), data=data, weight=1/predict(mod.ols)^2, trace=TRUE)
## assuming constant relative error (i.e. proportional error - weight of 2): iteratively
## re-weighted least squares
mod.irwls <- mod.wls
for(i in 1:10){
print(as.vector(coef(mod.irwls)))
mod.irwls <- nls(conc ~ i1*base + i2*(base + a1*exp(-k1*time) + a2*exp(-k2*time)),
start=c(base=20.34, start), data=data, weight=1/predict(mod.irwls)^2)
}
summary(mod.ols)
summary(mod.wls)
summary(mod.irwls)
newdata <- data.frame(time=seq(0,32,0.01))
newdata$i1 <- ifelse(newdata$time <0, 1, 0)
newdata$i2 <- ifelse(newdata$time <0, 0, 1)
plot(conc ~ time, data=data, ylim=c(10,1E4), log='y', yaxt='n',
xlab='Time (hours)', ylab='Log of concentration (pmol/L)')
axis(side=2, at=c(10, 100, 1000, 10000), las=1)
axis(side=2, at=seq(1E1,1E2,1E1), tcl=-0.25, labels=FALSE)
axis(side=2, at=seq(1E2,1E3,1E2), tcl=-0.25, labels=FALSE)
axis(side=2, at=seq(1E3,1E4,1E3), tcl=-0.25, labels=FALSE)
points(x=newdata$time, y=predict(mod.irwls, newdata), type='l')
## get total clearance (cls), inter-compartmental distribution (cld), and volume of distributions
## from macro constant parametrization according to Gabrielsson and Weiner (2000)
parm <- coef(mod.wls)[-1]
## get micro constants
k21 <- as.double((parm[1]*parm[4]+parm[3]*parm[2])/(parm[1]+parm[3]))
k10 <- as.double(parm[2]*parm[4] / k21)
k12 <- as.double(parm[2]+parm[4] - k21 - k10)
## get cls, cld, vc, and vt
cls <- as.double(dose / (parm[1]/parm[2] + parm[3]/parm[4]))
vc <- as.double(dose / (parm[1] + parm[2]))
cld <- k12*vc
vt <- cld / k21
print(c(cls, cld, vc, vt))
## turnover model to account for endogenous baseline according to Gabrielsson and Weiner
## using a biexponential (i.e. two-compartment) model parametrized in terms of clearance
## Not run: require(rgenoud)
require(deSolve)
k <- 2 # assuming proportional error - weighting in function objfun
tinf <- 1/60 # duration of bolus in hours
data <- subset(data, time>0)
defun <- function(time, y, parms) {
rte1 <- ifelse(time <= tinf, dose/tinf, 0)
dCptdt1 <- (rte1 + parms["synt"] - parms["cls"]*y[1] - parms["cld"]*y[1] +
parms["cld"]*y[2]) / parms["vc"]
dCptdt2 <- (parms["cld"]*y[1] - parms["cld"]*y[2])/parms["vt"]
list(c(dCptdt1, dCptdt2))
}
modfun <- function(time, synt, cls, cld, vc, vt) {
out <- lsoda(y=c(synt/cls, synt/cls), times=c(0, data$time), defun,
parms=c(synt=synt, cls=cls, cld=cld, vc=vc, vt=vt), rtol=1e-5, atol=1e-5)[-1,2]
}
objfun <- function(par) {
out <- modfun(data$time, par[1], par[2], par[3], par[4], par[5])
gift <- which(data$conc != 0 )
sum((data$conc[gift]-out[gift])^2 / data$conc[gift]^k)
}
## grid search to get starting values for Nelder-Mead
## increase values of pop.size and max.generation to get better starting values
## values of 10 are used for illustration purpose only
options(warn = -1) # omit warning when hard maximum limit is hit
gen <- genoud(objfun, nvars=5, max=FALSE, pop.size=10, max.generation=10,
starting.value=c(1500, cls, cld, vc, vt), BFGS=FALSE,
print.level=1, boundary.enforcement=2,
Domains=matrix(c(0,0,0,0,0,1E4,1E3,1E3,1E3,1E3),5,2),
MemoryMatrix=TRUE)
options(warn = 0) # set back to default
opt <- optim(gen$par, objfun, method="Nelder-Mead")
trn.wls <- nls(conc ~ modfun(time, synt, cls, cld, vc, vt), data=data,
start=list(synt=opt$par[1], cls=opt$par[2], cld=opt$par[3], vc=opt$par[4],
vt=opt$par[5]),
trace=TRUE, nls.control(tol=Inf))
summary(trn.wls)
## End(Not run)
PK documentation built on Sept. 12, 2023, 9:06 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
| biexp | R Documentation |
Two-phase half-life estimation by biexponential model
Description
Estimation of initial and terminal half-life by fitting a biexponential model.
Usage
biexp(conc, time, log.scale=FALSE, tol=1E-9, maxit=500)Arguments
conc |
Levels of concentrations as a vector. |
time |
Time points of concentration assessment as a vector. One time point for each concentration measured needs to be specified. |
log.scale |
Logical value indicating whether fitting is performed on the observed or log-scale (default= |
tol |
Relative error tolerance (default= |
maxit |
Maximum number of iterations (default= |
Details
Estimation of initial and terminal half-life using the biexponential y=a1*exp(-b1*x)+a2*exp(-b2*x) model with a parameterization to ensure b1 > b2 > 0 fitted by the least squares criteria with function optim of package base with method "Nelder-Mead". Curve peeling (Foss, 1969) is used get start values for nonlinear model fitting. When no adequate starting values are
determined by curve peeling, a single exponential model is fitted with starting values obtained from an OLS regression on log transformed values with a parameterization to ensure a slope > 0.
Fitting on the log-scale is based on the transform-both-sides approach described for example in chapter 4 of Bonate (2006) which is useful for some error distributions. An additional discussion regarding weighting schemes can be found in Gabrielsson and Weiner (2000, pages 368-374).
Value
A list of S3 class "halflife" containing the following components:
parms |
half-life and model estimates. |
time |
time points of concentration assessments. |
conc |
levels of concentrations. |
method |
"biexp". |
Note
Records including missing values and values below or equal to zero are omitted.
Author(s)
Martin J. Wolfsegger and Thomas Jaki
References
Bonate P. L. (2006). Pharmacokinetic-Pharmacodynamic Modeling and Simulation. Springer, New York.
Gabrielsson J. and Weiner D. (2000). Pharmacokinetic and Pharmacodynamic Data Analysis: Concepts and Applications. 4th Edition. Swedish Pharmaceutical Press, Stockholm.
Foss S. D. (1969). A Method for Obtaining Initial Estimates of the Parameters in Exponential Curve Fitting. Biometrics, 25:580-584.
Pinheiro J. C. and Bates D. M. (2000). Mixed-Effects Models in S and S-PLUS. Springer, New York.
Wolfsegger M. J. and Jaki T. (2009). Non-compartmental Estimation of Pharmacokinetic Parameters in Serial Sampling Designs. Journal of Pharmacokinetics and Pharmacodynamics, 36(5):479-494.
See Also
lee
Examples
#### example from Pinheiro J.C. and Bates D.M. (2000, page 279)
#### dataset Indometh of package datasets
require(datasets)
data <- subset(Indometh, Subject==2)
time <- data$time
conc <- data$conc
## fitting on observed and log-scale
res.obs <- biexp(conc=conc, time=time, log.scale=FALSE)
res.log <- biexp(conc=conc, time=time, log.scale=TRUE)
print(res.obs$parms)
print(res.log$parms)
plot(res.obs, ylim=c(0,5), xlim=c(0, max(time)), las=1)
plot(res.log, ylim=c(0,5), xlim=c(0, max(time)), las=1, add=TRUE, lty=2)
legend(x=0, y=5, lty=c(1,2), legend=c("fitted on observed scale", "fitted on log-scale"))
## get residuals using function nls with tol=Inf
parms.obs <- list(a1=res.obs$parms[3,1], b1=res.obs$parms[2,1], a2=res.obs$parms[3,2],
b2=res.obs$parms[2,2])
parms.log <- list(a1=res.log$parms[3,1], b1=res.log$parms[2,1], a2=res.log$parms[3,2],
b2=res.log$parms[2,2])
mod.obs <- nls(conc ~ a1*exp(-b1*time) + a2*exp(-b2*time), start=parms.obs,
control=nls.control(tol=Inf))
mod.log <- nls(conc ~ a1*exp(-b1*time) + a2*exp(-b2*time), start=parms.log,
control=nls.control(tol=Inf))
## identical estimates to mod.log but different SEs
summary(nls(log(conc)~log(a1*exp(-b1*time) + a2*exp(-b2*time)), start=parms.log,
control=nls.control(tol=Inf)))
## different approach using weighted least squares (WLS) in nls
mod.ols <- nls(conc ~ a1*exp(-b1*time) + a2*exp(-b2*time), start=parms.obs)
mod.wls1 <- nls(conc ~ a1*exp(-b1*time) + a2*exp(-b2*time), start=parms.obs,
weight=1/predict(mod.ols)^1)
mod.wls2 <- nls(conc ~ a1*exp(-b1*time) + a2*exp(-b2*time), start=parms.obs,
weight=1/predict(mod.ols)^2)
split.screen(c(2,2))
screen(1)
plot(ylim=c(-0.35,0.35), y=resid(mod.obs), x=predict(mod.obs), las=1,
main='Fitted using biexp on observed scale', xlab='Predicted', ylab='Residual')
abline(h=0)
screen(2)
plot(ylim=c(-0.35,0.35), y=resid(mod.log), x=predict(mod.log), las=1,
main='Fitted using biexp on log-scale', xlab='Predicted', ylab='Residual')
abline(h=0)
screen(3)
plot(ylim=c(-0.35,0.35), y=resid(mod.wls1), x=predict(mod.wls1), las=1,
main='Fitted using nls with weights 1/predict(mod.ols)^1', xlab='Predicted', ylab='Residual')
abline(h=0)
screen(4)
plot(ylim=c(-0.35,0.35), y=resid(mod.wls2), x=predict(mod.wls2), las=1,
main='Fitted using nls with weights 1/predict(mod.ols)^2', xlab='Predicted', ylab='Residual')
abline(h=0)
close.screen(all.screens=TRUE)
#### example for a serial sampling data design from Wolfsegger and Jaki (2009)
conc <- c(2.01, 2.85, 2.43, 0.85, 1.00, 0.91, 0.46, 0.35, 0.63, 0.39, 0.32,
0.45, 0.11, 0.18, 0.19, 0.08, 0.09, 0.06)
time <- c(rep(5/60,3), rep(3,3), rep(6,3), rep(9,3), rep(16,3), rep(24,3))
res.biexp1 <- biexp(conc=conc, time=time, log=TRUE)
res.biexp2 <- biexp(conc=conc, time=time, log=FALSE)
print(res.biexp1$parms)
print(res.biexp2$parms)
split.screen(c(1,2))
screen(1)
plot(x=c(0,25), y=c(0,3), type='n', las=1,
ylab='Plasma concentration (IU/mL)', xlab='Time (hours)')
points(x=time, y=conc, pch=21)
plot(res.biexp1, pch=NA, add=TRUE, lty=1)
plot(res.biexp2, pch=NA, add=TRUE, lty=2)
legend(x=25, y=3, xjust=1, col=c('black', 'black'), lty=c(1,2),
title='Nonlinear fitting with function biexp:',
legend=c('option: log=TRUE', 'option: log=FALSE'))
close.screen(1)
screen(2)
plot(x=c(0,25), y=c(0.01, 10), type='n', log='y', yaxt='n',
ylab='Plasma concentration (IU/mL)', xlab='Time (hours)')
axis(side=2, at=c(0.01, 0.1, 1, 10), labels=c('0.01', '0.1', '1', '10'), las=1)
axis(side=2, at=seq(2,9,1), tcl=-0.25, labels=FALSE)
axis(side=2, at=seq(0.2,0.9,0.1), tcl=-0.25, labels=FALSE)
axis(side=2, at=seq(0.02,0.09,0.01), tcl=-0.25, labels=FALSE)
points(x=time, y=conc, pch=21)
plot(res.biexp1, pch=NA, add=TRUE, lty=1)
plot(res.biexp2, pch=NA, add=TRUE, lty=2)
legend(x=25, y=10, xjust=1, col=c('black', 'black'), lty=c(1,2),
title='Nonlinear fitting with function biexp:',
legend=c('option: log=TRUE', 'option: log=FALSE'))
close.screen(all.screens=TRUE)
#### example from Gabrielsson and Weiner (2000, page 743)
#### endogenous concentration is assumed to be constant over time
dose <- 36630
time <- c(-1, 0.167E-01, 0.1167, 0.1670, 0.25, 0.583, 0.8330, 1.083, 1.583, 2.083, 4.083, 8.083,
12, 23.5, 24.25, 26.75, 32)
conc <- c(20.34, 3683, 884.7, 481.1, 215.6, 114, 95.8, 87.89, 60.19, 60.17, 34.89, 20.99, 20.54,
19.28, 18.18, 19.39, 22.72)
data <- data.frame(conc,time)
## get starting values using function biexp using naive adjustment for endogenous concentration
## by subtraction of pre-value
data$concadj <- data$conc - data$conc[1]
data$concadj[min(which(data$concadj<0)):nrow(data)] <- NA
res.biexp <- biexp(conc=data$concadj[-1], time=data$time[-1])$parms
start <- list(a1=res.biexp[3,1], k1=res.biexp[2,1], a2=res.biexp[3,2], k2=res.biexp[2,2])
## specify indicator variable enabling inclusion of pre-dose concentration for fitting
data$i1 <- ifelse(data$time <0, 1, 0)
data$i2 <- ifelse(data$time <0, 0, 1)
## assuming constant absolute error: ordinary least squares
mod.ols <- nls(conc ~ i1*base + i2*(base + a1*exp(-k1*time) + a2*exp(-k2*time)),
start=c(base=20.34, start), data=data, trace=TRUE)
## assuming constant relative error (i.e. proportional error - weight of 2): weighted least
## squares
mod.wls <- nls(conc ~ i1*base + i2*(base + a1*exp(-k1*time) + a2*exp(-k2*time)),
start=c(base=20.34, start), data=data, weight=1/predict(mod.ols)^2, trace=TRUE)
## assuming constant relative error (i.e. proportional error - weight of 2): iteratively
## re-weighted least squares
mod.irwls <- mod.wls
for(i in 1:10){
print(as.vector(coef(mod.irwls)))
mod.irwls <- nls(conc ~ i1*base + i2*(base + a1*exp(-k1*time) + a2*exp(-k2*time)),
start=c(base=20.34, start), data=data, weight=1/predict(mod.irwls)^2)
}
summary(mod.ols)
summary(mod.wls)
summary(mod.irwls)
newdata <- data.frame(time=seq(0,32,0.01))
newdata$i1 <- ifelse(newdata$time <0, 1, 0)
newdata$i2 <- ifelse(newdata$time <0, 0, 1)
plot(conc ~ time, data=data, ylim=c(10,1E4), log='y', yaxt='n',
xlab='Time (hours)', ylab='Log of concentration (pmol/L)')
axis(side=2, at=c(10, 100, 1000, 10000), las=1)
axis(side=2, at=seq(1E1,1E2,1E1), tcl=-0.25, labels=FALSE)
axis(side=2, at=seq(1E2,1E3,1E2), tcl=-0.25, labels=FALSE)
axis(side=2, at=seq(1E3,1E4,1E3), tcl=-0.25, labels=FALSE)
points(x=newdata$time, y=predict(mod.irwls, newdata), type='l')
## get total clearance (cls), inter-compartmental distribution (cld), and volume of distributions
## from macro constant parametrization according to Gabrielsson and Weiner (2000)
parm <- coef(mod.wls)[-1]
## get micro constants
k21 <- as.double((parm[1]*parm[4]+parm[3]*parm[2])/(parm[1]+parm[3]))
k10 <- as.double(parm[2]*parm[4] / k21)
k12 <- as.double(parm[2]+parm[4] - k21 - k10)
## get cls, cld, vc, and vt
cls <- as.double(dose / (parm[1]/parm[2] + parm[3]/parm[4]))
vc <- as.double(dose / (parm[1] + parm[2]))
cld <- k12*vc
vt <- cld / k21
print(c(cls, cld, vc, vt))
## turnover model to account for endogenous baseline according to Gabrielsson and Weiner
## using a biexponential (i.e. two-compartment) model parametrized in terms of clearance
## Not run: require(rgenoud)
require(deSolve)
k <- 2 # assuming proportional error - weighting in function objfun
tinf <- 1/60 # duration of bolus in hours
data <- subset(data, time>0)
defun <- function(time, y, parms) {
rte1 <- ifelse(time <= tinf, dose/tinf, 0)
dCptdt1 <- (rte1 + parms["synt"] - parms["cls"]*y[1] - parms["cld"]*y[1] +
parms["cld"]*y[2]) / parms["vc"]
dCptdt2 <- (parms["cld"]*y[1] - parms["cld"]*y[2])/parms["vt"]
list(c(dCptdt1, dCptdt2))
}
modfun <- function(time, synt, cls, cld, vc, vt) {
out <- lsoda(y=c(synt/cls, synt/cls), times=c(0, data$time), defun,
parms=c(synt=synt, cls=cls, cld=cld, vc=vc, vt=vt), rtol=1e-5, atol=1e-5)[-1,2]
}
objfun <- function(par) {
out <- modfun(data$time, par[1], par[2], par[3], par[4], par[5])
gift <- which(data$conc != 0 )
sum((data$conc[gift]-out[gift])^2 / data$conc[gift]^k)
}
## grid search to get starting values for Nelder-Mead
## increase values of pop.size and max.generation to get better starting values
## values of 10 are used for illustration purpose only
options(warn = -1) # omit warning when hard maximum limit is hit
gen <- genoud(objfun, nvars=5, max=FALSE, pop.size=10, max.generation=10,
starting.value=c(1500, cls, cld, vc, vt), BFGS=FALSE,
print.level=1, boundary.enforcement=2,
Domains=matrix(c(0,0,0,0,0,1E4,1E3,1E3,1E3,1E3),5,2),
MemoryMatrix=TRUE)
options(warn = 0) # set back to default
opt <- optim(gen$par, objfun, method="Nelder-Mead")
trn.wls <- nls(conc ~ modfun(time, synt, cls, cld, vc, vt), data=data,
start=list(synt=opt$par[1], cls=opt$par[2], cld=opt$par[3], vc=opt$par[4],
vt=opt$par[5]),
trace=TRUE, nls.control(tol=Inf))
summary(trn.wls)
## End(Not run)
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.