Package 'wnl' reference manual

Title:	Minimization Tool for Pharmacokinetic-Pharmacodynamic Data Analysis
Description:	This is a set of minimization tools (maximum likelihood estimation and least square fitting) to solve examples in the Johan Gabrielsson and Dan Weiner's book "Pharmacokinetic and Pharmacodynamic Data Analysis - Concepts and Applications" 5th ed. (ISBN:9198299107). Examples include linear and nonlinear compartmental model, turn-over model, single or multiple dosing bolus/infusion/oral models, allometry, toxicokinetics, reversible metabolism, in-vitro/in-vivo extrapolation, enterohepatic circulation, metabolite modeling, Emax model, inhibitory model, tolerance model, oscillating response model, enantiomer interaction model, effect compartment model, drug-drug interaction model, receptor occupancy model, and rebound phenomena model.
Authors:	Kyun-Seop Bae [aut]
Maintainer:	Kyun-Seop Bae <[email protected]>
License:	GPL-3
Version:	0.8.1
Built:	2024-10-30 06:49:17 UTC
Source:	CRAN

Minimization Tool for Pharmacokinetic-Pharmacodynamic Data Analysis

Description

This is a minimization tool to solve the examples in the book Gabrielsson J, Weiner D. 'Pharmacokinetic and Pharmacodynamic Data Analysis - Concepts and Applications' 5th ed. 2016. (ISBN:9198299107).

Details

This is a set of minimization tools to solve all the examples in the book 'Pharmacokinetic and Pharmacodynamic Data Analysis - Concepts and Applications' 5th ed. 2016.

Author(s)

Kyun-Seop Bae <[email protected]>

References

Gabrielsson J, Weiner D. Pharmacokinetic and Pharmacodynamic Data Analysis - Concepts and Applications. 5th ed. 2016.

Examples

tData = Theoph
colnames(tData) = c("ID", "BWT", "DOSE", "TIME", "DV")

fPK = function(THETA)     # Prediction function
{
  DOSE = 320000           # in microgram
  TIME = e$DATA[,"TIME"]  # use data in e$DATA

  K    = THETA[1]
  Ka   = THETA[2]
  V    = THETA[3]

  Cp   = DOSE/V*Ka/(Ka - K)*(exp(-K*TIME) - exp(-Ka*TIME))
  return(Cp)
}

IDs = unique(tData[,"ID"])
nID = length(IDs)
for (i in 1:nID) {
  Data = tData[tData$ID == IDs[i],]
  Res = nlr(fPK, Data, pNames=c("k", "ka", "V"), IE=c(0.1, 3, 500), 
            SecNames=c("CL", "Thalf", "MRT"), SecForms=c(~V*k, ~log(2)/k, ~1/k))
  print(paste("## ID =", i, "##"))
  print(Res)
}
tData = Theoph
colnames(tData) = c("ID", "BWT", "DOSE", "TIME", "DV")

fPK = function(THETA)     # Prediction function
{
  DOSE = 320000           # in microgram
  TIME = e$DATA[,"TIME"]  # use data in e$DATA

  K    = THETA[1]
  Ka   = THETA[2]
  V    = THETA[3]

  Cp   = DOSE/V*Ka/(Ka - K)*(exp(-K*TIME) - exp(-Ka*TIME))
  return(Cp)
}

IDs = unique(tData[,"ID"])
nID = length(IDs)
for (i in 1:nID) {
  Data = tData[tData$ID == IDs[i],]
  Res = nlr(fPK, Data, pNames=c("k", "ka", "V"), IE=c(0.1, 3, 500), 
            SecNames=c("CL", "Thalf", "MRT"), SecForms=c(~V*k, ~log(2)/k, ~1/k))
  print(paste("## ID =", i, "##"))
  print(Res)
}

Compare model with Chi-square test

Description

It performs chi-square test for two models comparison.

Usage

cmpChi(r1, r2)
cmpChi(r1, r2)

Arguments

`r1`	A result from `nlr`
`r2`	Another result from `nlr`

Details

One model should include the other model.

Value

Returns a p-value from pchisq

Author(s)

Kyun-Seop Bae <[email protected]>

One compartment model - analytical

Description

It calculates using one compartment model.

Usage

Comp1(Ke, Ka=0, DH)
Comp1(Ke, Ka=0, DH)

Arguments

`Ke`	Elimination rate constant
`Ka`	Absorption rate constant
`DH`	Expanded dosing history table

Details

First compartment is the gut compartment for oral dosing. IV bolus and infusion dosing should be done at the second compartment.

Value

This returns a table with the gut and the central compartment columns

Author(s)

Kyun-Seop Bae <[email protected]>

Examples

DAT
DAT2 = ExpandDH(DAT)
X1 = Comp1(Ke=0.1, Ka=1, DAT2)
X1
matplot(DAT2[, "TIME"], X1, type="l")
DAT
DAT2 = ExpandDH(DAT)
X1 = Comp1(Ke=0.1, Ka=1, DAT2)
X1
matplot(DAT2[, "TIME"], X1, type="l")

An Example of Dosing History Table

Description

This is a conventional NONMEM input data format.

Usage

DATDAT

Format

This data frame has 5 columns with 18 time-points for the simulation.

TIME: Time
AMT: Amount given for the compartment of CMT column
RATE: Infusion rate
CMT: Compartment number, 1=gut, 2=central, 3=peripheral, etc.
DV: Currently blank and not used.

Details

To be used at Comp1 or nComp, expand dosing history with ExpandDH function.

Simplest diagnostic plot for minimization result

Description

It performs a simple diagnostic plot from the result of nlr.

Usage

dx(r)
dx(r)

Arguments

`r`	a result from `nlr` or `wnl5`

Details

This plots 'Observation vs. Prediction' and 'Normalized Redisual vs. Prediction' only. Normalized residual are meant to be distributed as standard normal distribution, N(0, 1).

Value

This just draws a plot.

Author(s)

Kyun-Seop Bae <[email protected]>

Environment's Objects

Description

Get an environment's visible objects as a list.

Usage

  EnvObj(envir = e)
EnvObj(envir = e)

Arguments

envir

environment to get its content

Details

All the visible objects in the environment including functions and data will be returned.

Value

All visible objects as a list

Author(s)

Kyun-Seop Bae <[email protected]>

Expand Dosing History Table

Description

It expands dosing history table.

Usage

ExpandDH(DH, Fo = 1)
ExpandDH(DH, Fo = 1)

Arguments

`DH`	Dosing history table of NONMEM type
`Fo`	Bioavailability of the first (gut) compartment

Details

It expands dosing history table of conventional NONMEM data format. It calculate bioavailable amount, then add time points of non-differentiable, e.g. stopping points of infusion.

Value

Returns expanded dosing history table.

Author(s)

Kyun-Seop Bae <[email protected]>

Examples

DAT
ExpandDH(DAT) # One observation point is increased at the time of 27.
DAT
ExpandDH(DAT) # One observation point is increased at the time of 27.

Hougaard Measure of Skewness

Description

Hougaard measure of skewness with nonlinear regression

Usage

  hSkew(rx)
hSkew(rx)

Arguments

`rx`	a result of nls function

Details

Hougaard measure of skewness can be used to check if the parameters of nonlinear regression behavior in linear fashion, i.e. symmetric confidence interval. Be cautious on the variable name conflict. All the variables in the nonlinear function should be able to be accessed by the function.

Value

Hougaard estimate of skewness for each parameter

`(0`, `0.1]`	The estimate is very close-to-linear in behavior.
`(0.1`, `0.25]`	The estimate is reasonably close-to-linear in behavior.
`(0.25`, `1]`	The skweness is apparent.
`>1`	The estimate is considerably nonlinear in behavior.

Author(s)

Kyun-Seop Bae [email protected]

References

EL-Shehawy SA. On Calculating the Hougaard Measure of Skewness in a Nonlinear Regression Model with Two Parameters. J Math & Stat. 2009;5(4):360-364.

Examples

  r1 = nls(density ~ b1*conc/(b2 + conc), DNase[DNase$Run == 1, ], start=list(b1=3, b2=5))
  hSkew(r1)
r1 = nls(density ~ b1*conc/(b2 + conc), DNase[DNase$Run == 1, ], start=list(b1=3, b2=5))
  hSkew(r1)

Get Amounts of Each Compartments using Lambdas and Coefficients of Multi-compartment Model

Description

It calculates using multi-compartment model.

Usage

nComp(Sol, Ka=0, DH)
nComp(Sol, Ka=0, DH)

Arguments

`Sol`	Solution list of lambdas and coefficients
`Ka`	Absorption rate constant
`DH`	Expanded dosing history table

Details

First compartment is the gut compartment for oral dosing. IV bolus and infusion dosing should be done at the second compartment. If a bolus dose was given at time T, it is reflected at times of larger than T. This is more close to real observation. ADAPT does like this, but NONMEM does not.

Value

This returns a table with the gut and the other compartment columns

Author(s)

Kyun-Seop Bae <[email protected]>

Examples

DAT
DAT2 = ExpandDH(DAT)
Sol = SolComp2(K10=0.1, K12=3, K21=1)
X2 = nComp(Sol, Ka=1, DAT2)
X2
matplot(DAT2[, "TIME"], X2, type="l")
DAT
DAT2 = ExpandDH(DAT)
Sol = SolComp2(K10=0.1, K12=3, K21=1)
X2 = nComp(Sol, Ka=1, DAT2)
X2
matplot(DAT2[, "TIME"], X2, type="l")

Nonlinear Regression in R

Description

It performs nonlinear regression usually for pharmacokinetic and pharmacodynamic models.

Usage

nlr(Fx, Data, pNames, IE, LB, UB, Error="A", ObjFx=ObjDef, SecNames, SecForms, 
    Method="L-BFGS-B", Sx, conf.level=0.95, k, fix=0)
nlr(Fx, Data, pNames, IE, LB, UB, Error="A", ObjFx=ObjDef, SecNames, SecForms, 
    Method="L-BFGS-B", Sx, conf.level=0.95, k, fix=0)

Arguments

`Fx`	Function for structural model. It should return a vector of the same length to observations.
`Data`	Data table which will be used in Fx. Fx should access this with `e$DATA`.
`pNames`	Parameter names in the order of Fx arguments
`IE`	Initial estimates of parameters
`LB`	Lower bound for `optim` function. The default value is 0.
`UB`	Upper bound for `optim` function. The default value is 1e+06.
`Error`	Error model. One of `"A"` for additive error, `"POIS"` for Poisson error, `"P"` for proportional error, `"C"` for combined error model, `"S"` for general error model. With Error="S", `Sx` should be provieded.
`ObjFx`	Objective function to be minimized. The default is maximum likelihood estimation function(-2 log likelihood).
`SecNames`	Names of secondary parameter estimates
`SecForms`	Formula to calculate the secondary parameter estimates
`Method`	`"L-BFGS-B"` is default. See `optim` for more detail.
`Sx`	Scale function. This is usually the inverse of weight. It should return the same length(nrow) of Y. When Error="S", Scale function should be provided as `Sx`.
`conf.level`	Confidence level for confidence interval
`k`	1/k likelihood interval(LI) will be provided. Currently recommended value is exp(qf(1 - alpha, 1, nRec-nPara)/2) + 1.
`fix`	indices of parameters to fix

Details

This uses scaled transformed parameters and environment e internally.

Value

`Est`	Point estimate(PE) with standard error(SE) and relative standard error(RSE)
`LI`	1/k likelihood interval, at which likelihood drops to 1/k of maximum likelihood. This reflects asymmetry better than confidence interval. This is estimated likelihood interval, not profile likelihood interval.
`Skewness`	Hougaard's skewness measure. This is printed only with additive error model. See also `hSkew`
`Cov`	Variance-covariance matrix of the objective function at the value of point estimates
`run$m`	Count of positive residuals
`run$n`	Count of negative residuals
`run$run`	Count of runs of residuals
`run$p.value`	P value of run test with excluding zero points
`Objective Function Value`	Minimum value of the objective function
`-2LL`	-2 times log likelihood
`AIC`	Akaike Information Criterion
`AICc`	Corrected Akaike Information Criterion
`BIC`	Schwarz Bayesian Information Criterion
`Convergence`	Convergence code from `optim`
`Message`	Message from `optim`.
`Prediction`	Fitted(predicted) values
`Residuals`	Residuals
`Scale`	Scales with Error="S". Variances for each points are scale vector multiplied by `ScaleErrVar` in `Est`.
`Elapsed Time`	Consumed time by minimization

Author(s)

Kyun-Seop Bae <[email protected]>

Examples

  tData = Theoph
  colnames(tData) = c("ID", "BWT", "DOSE", "TIME", "DV")

  fPK = function(THETA) # Prediction function
  {
    DOSE = 320000 # in microgram
    TIME = e$DATA[, "TIME"] # use data in e$DATA

    K    = THETA[1]
    Ka   = THETA[2]
    V    = THETA[3]

    P  = DOSE/V*Ka/(Ka - K) * (exp(-K*TIME) - exp(-Ka*TIME))
    return(P)
  }

  IDs = unique(tData[,"ID"])
  nID = length(IDs)
  for (i in 1:nID) {
    Data = tData[tData$ID == IDs[i],]
    Res = nlr(fPK, Data, pNames=c("k", "ka", "V"), IE=c(0.1, 3, 500), 
              SecNames=c("CL", "Thalf", "MRT"), SecForms=c(~V*k, ~log(2)/k, ~1/k))
    print(paste("## ID =", i, "##"))
    print(Res)
  }

  # Another example from radioimmunoassay(RIA)
  d1 = data.frame(conc = c(200, 100, 50, 25, 12.5, 6.25, 3.125, 0),
                  DV = c(1.78, 1.5, 1.17, 0.74, 0.51, 0.31, 0.19, 0.04))

  PRED = function(TH) TH[1] + TH[2]*d1$conc^TH[4]/(TH[3]^TH[4] + d1$conc^TH[4])
  Scale = function(TH) 1/(PRED(TH) - (TH[1] + TH[2])/2)^2

  nlr(PRED, d1, pNames=c("R0", "Rmax", "RC50", "Hill"), IE=c(0.1, 3, 50, 1), 
      Error="S", Sx=Scale)
tData = Theoph
  colnames(tData) = c("ID", "BWT", "DOSE", "TIME", "DV")

  fPK = function(THETA) # Prediction function
  {
    DOSE = 320000 # in microgram
    TIME = e$DATA[, "TIME"] # use data in e$DATA

    K    = THETA[1]
    Ka   = THETA[2]
    V    = THETA[3]

    P  = DOSE/V*Ka/(Ka - K) * (exp(-K*TIME) - exp(-Ka*TIME))
    return(P)
  }

  IDs = unique(tData[,"ID"])
  nID = length(IDs)
  for (i in 1:nID) {
    Data = tData[tData$ID == IDs[i],]
    Res = nlr(fPK, Data, pNames=c("k", "ka", "V"), IE=c(0.1, 3, 500), 
              SecNames=c("CL", "Thalf", "MRT"), SecForms=c(~V*k, ~log(2)/k, ~1/k))
    print(paste("## ID =", i, "##"))
    print(Res)
  }

  # Another example from radioimmunoassay(RIA)
  d1 = data.frame(conc = c(200, 100, 50, 25, 12.5, 6.25, 3.125, 0),
                  DV = c(1.78, 1.5, 1.17, 0.74, 0.51, 0.31, 0.19, 0.04))

  PRED = function(TH) TH[1] + TH[2]*d1$conc^TH[4]/(TH[3]^TH[4] + d1$conc^TH[4])
  Scale = function(TH) 1/(PRED(TH) - (TH[1] + TH[2])/2)^2

  nlr(PRED, d1, pNames=c("R0", "Rmax", "RC50", "Hill"), IE=c(0.1, 3, 50, 1), 
      Error="S", Sx=Scale)

Plot Compartment Model Diagram

Description

It plots the diagrom of a comparment model.

Usage

pComp(dComp, dRate, Shape="rect", Col=NA, Bx=0.3, By=0.2, Cex=1.0, Lwd=3, 
      Radius=0.3, thIn=pi/2, thOut=pi/2, ...)
pComp(dComp, dRate, Shape="rect", Col=NA, Bx=0.3, By=0.2, Cex=1.0, Lwd=3, 
      Radius=0.3, thIn=pi/2, thOut=pi/2, ...)

Arguments

`dComp`	data.frame for a compartment model. See the example.
`dRate`	data.frame for rate information. See the example.
`Shape`	rectangle or cricle
`Col`	filling color
`Bx`	half width of compartment box
`By`	half height of compartment box
`Cex`	character expansion
`Lwd`	line width
`Radius`	radius of compartment circle
`thIn`	Input angle in radian
`thOut`	Output angle in radian
`...`	arguments to be passed to `plot` function

Details

Flow direction is from the top to bottom.

Value

It plots.

Author(s)

Kyun-Seop Bae <[email protected]>

Examples

dA = data.frame(No = c(1, 2, 3, 4), Name=c("Gut Depot", "Skin Depot", "Central", "Peripheral"), 
                Level=c(1, 1, 2, 2), xPos=c(-0.5, 0.5, 0, 1))
dB = data.frame(From = c(1, 2, 3, 4, 3, 0, 0), To=c(3, 3, 4, 3, 5, 1, 2), 
                Name=c("KA", "KA2", "K12", "K21", "CL", "F1", "F2"))

pComp(dA, dB)
#par(oma=c(0, 0, 0, 0), mar=c(0, 0, 1, 0)) # If need, adjust margin before calling
pComp(dA, dB, "circ", main="Compartmental Model Diagram")

pComp(dA, dB, "circ", main="Compartmental Model Diagram", Col="#DDEEFF", asp=1)
dA = data.frame(No = c(1, 2, 3, 4), Name=c("Gut Depot", "Skin Depot", "Central", "Peripheral"), 
                Level=c(1, 1, 2, 2), xPos=c(-0.5, 0.5, 0, 1))
dB = data.frame(From = c(1, 2, 3, 4, 3, 0, 0), To=c(3, 3, 4, 3, 5, 1, 2), 
                Name=c("KA", "KA2", "K12", "K21", "CL", "F1", "F2"))

pComp(dA, dB)
#par(oma=c(0, 0, 0, 0), mar=c(0, 0, 1, 0)) # If need, adjust margin before calling
pComp(dA, dB, "circ", main="Compartmental Model Diagram")

pComp(dA, dB, "circ", main="Compartmental Model Diagram", Col="#DDEEFF", asp=1)

Plot Likelihood or Objective Fnnction Value Profile

Description

It plots estimated likelihood profile. This is not profile likelihood profile.

Usage

  pProf(Bag = e, Title = "", ...)
pProf(Bag = e, Title = "", ...)

Arguments

`Bag`	an environment or an object containing the objects of resultant environment e after nlr()
`Title`	title for the plot
`...`	arguments to pass to the plot function

Details

This plots likelihood profile from the result of nlr() function. Bag should contain the results of nlr().

Value

No values but a plot.

Author(s)

Kyun-Seop Bae <[email protected]>

Get Secondary Parameter Estimates

Description

Get standard error and relative standard error (cv) of the secondary parameter estimate

Usage

Secondary(Formula, PE, COV)
Secondary(Formula, PE, COV)

Arguments

`Formula`	Formula to calculate the secondary parameter estimate
`PE`	Point estimates of primary parameters with names
`COV`	Variance-covariance matrix of primary estimates

Details

Variables within Formula should exist in the names of PE vector.

Value

This returns point estimate, standard error, relative standard error of the secondary parameter estimate.

Author(s)

Kyun-Seop Bae <[email protected]>

Examples

tData = Theoph
colnames(tData) = c("ID", "BWT", "DOSE", "TIME", "DV") # Table requires DV column

fPK = function(THETA) # Prediction function
{
  AMT  = 320000 # in microgram
  TIME = e$DATA[,"TIME"]
  V  = THETA[1]
  K  = THETA[2]
  Ka = THETA[3]
  Cp = AMT/V*Ka/(Ka - K)*(exp(-K*TIME) - exp(-Ka*TIME))
  return(Cp)
}
Data = tData[tData$ID == 1,]
Res = nlr(fPK, Data, pNames=c("V", "K", "Ka"), IE=c(30000, 0.1, 2))
Secondary(~V*K, Res$Est["PE",1:e$nPara], Res$Cov)
tData = Theoph
colnames(tData) = c("ID", "BWT", "DOSE", "TIME", "DV") # Table requires DV column

fPK = function(THETA) # Prediction function
{
  AMT  = 320000 # in microgram
  TIME = e$DATA[,"TIME"]
  V  = THETA[1]
  K  = THETA[2]
  Ka = THETA[3]
  Cp = AMT/V*Ka/(Ka - K)*(exp(-K*TIME) - exp(-Ka*TIME))
  return(Cp)
}
Data = tData[tData$ID == 1,]
Res = nlr(fPK, Data, pNames=c("V", "K", "Ka"), IE=c(30000, 0.1, 2))
Secondary(~V*K, Res$Est["PE",1:e$nPara], Res$Cov)

Get Lambdas and Coefficients of Two-compartment Model

Description

It calculates lambdas and coefficients for two-compartment model from K10, K12, and K21.

Usage

SolComp2(K10, K12, K21)
SolComp2(K10, K12, K21)

Arguments

`K10`	Ke, Elimination rate constant from central compartment
`K12`	Rate constant from the central to the peripheral compartment
`K21`	Rate constant from the peripheral to the central compartment

Details

It calculates lambdas and coefficients of two-compartment model from K10, K12, and K21. Lambdas should have no identical values.

Value

This returns a list of lambdas and coefficients.

Author(s)

Kyun-Seop Bae <[email protected]>

Examples

DAT
DAT2 = ExpandDH(DAT)
Sol = SolComp2(K10=0.1, K12=3, K21=1)
X2 = nComp(Sol, Ka=1, DAT2)
X2
matplot(DAT2[, "TIME"], X2, type="l")
DAT
DAT2 = ExpandDH(DAT)
Sol = SolComp2(K10=0.1, K12=3, K21=1)
X2 = nComp(Sol, Ka=1, DAT2)
X2
matplot(DAT2[, "TIME"], X2, type="l")

Get Lambdas and Coefficients of Three-compartment Model

Description

It calculates lambdas and coefficients for three-compartment model from K10, K12, K21, K13, and K31.

Usage

SolComp3(K10, K12, K21, K13, K31)
SolComp3(K10, K12, K21, K13, K31)

Arguments

`K10`	Ke, Elimination rate constant from central compartment
`K12`	Rate constant from the central to the first peripheral compartment
`K21`	Rate constant from the first peripheral to the central compartment
`K13`	Rate constant from the central to the second peripheral compartment
`K31`	Rate constant from the second peripheral to the central compartment

Details

It calculates lambdas and coefficients of two-compartment model from K10, K12, and K21. Lambdas should have no identical values.

Value

This returns a list of lambdas and coefficients.

Author(s)

Kyun-Seop Bae <[email protected]>

Examples

DAT
DAT2 = ExpandDH(DAT)
Sol = SolComp3(K10=0.1, K12=3, K21=1, K13=2, K31=0.5)
X3 = nComp(Sol, Ka=1, DAT2)
X3
matplot(DAT2[, "TIME"], X3, type="l")
DAT
DAT2 = ExpandDH(DAT)
Sol = SolComp3(K10=0.1, K12=3, K21=1, K13=2, K31=0.5)
X3 = nComp(Sol, Ka=1, DAT2)
X3
matplot(DAT2[, "TIME"], X3, type="l")

Old type WinNonlin - Least Square not MLE

Description

It performs old type Winnonlin regression.

Usage

wnl5(Fx, Data, pNames, IE, LB, UB, Error="A", ObjFx=ObjLS)
wnl5(Fx, Data, pNames, IE, LB, UB, Error="A", ObjFx=ObjLS)

Arguments

`Fx`	Function for structural model. It should return a vector of the same length to observations.
`Data`	Data table which will be used in Fx. Fx should access this with `e$DATA`.
`pNames`	Parameter names in the order of Fx arguments
`IE`	Initial estimates of parameters
`LB`	Lower bound for `optim` function. The default value is 0.
`UB`	Upper bound for `optim` function. The default value is 1e+06.
`Error`	Error model. One of `"POIS"` for Poisson error, `"P"` for proportional error, and others for additive error model.
`ObjFx`	Objective function to be minimized. The default is least square function.

Details

This uses scaled transformed parameters and environment e internally. Here we do not provide standard error. If you want standard error, use nlr.

Value

`PE`	Point estimates
`WRSS`	Weighted Residual Sum of Square
`run$m`	Count of positive residuals
`run$n`	Count of negative residuals
`run$run`	Count of runs of residuals
`run$p.value`	P value of run test with excluding zero points
`Objective Function Value`	Minimum value of the objective function
`AIC`	Akaike Information Criterion
`SBC`	Schwarz Bayesian Information Criterion
`Condition Number`	Condition number
`Message`	Message from `optim`.
`Prediction`	Fitted(predicted) values
`Residuals`	Residuals
`Elapsed Time`	Consumed time by minimization

Author(s)

Kyun-Seop Bae <[email protected]>

Examples

tData = Theoph
colnames(tData) = c("ID", "BWT", "DOSE", "TIME", "DV")

fPK = function(THETA) # Prediction function
{
  DOSE = 320000 # in microgram
  TIME = e$DATA[,"TIME"] # use data in e$DATA

  K  = THETA[1]
  Ka = THETA[2]
  V  = THETA[3]
  Cp  = DOSE/V*Ka/(Ka - K)*(exp(-K*TIME) - exp(-Ka*TIME))
  return(Cp)
}

IDs = unique(tData[,"ID"])
nID = length(IDs)
for (i in 1:nID) {
  Data = tData[tData$ID == IDs[i],]
  Res = wnl5(fPK, Data, pNames=c("k", "ka", "V"), IE=c(0.1, 3, 500))
  print(paste("## ID =", i, "##"))
  print(Res)
}

tData = Theoph
colnames(tData) = c("ID", "BWT", "DOSE", "TIME", "DV")

fPK = function(THETA) # Prediction function
{
  DOSE = 320000 # in microgram
  TIME = e$DATA[,"TIME"] # use data in e$DATA

  K  = THETA[1]
  Ka = THETA[2]
  V  = THETA[3]
  Cp  = DOSE/V*Ka/(Ka - K)*(exp(-K*TIME) - exp(-Ka*TIME))
  return(Cp)
}

IDs = unique(tData[,"ID"])
nID = length(IDs)
for (i in 1:nID) {
  Data = tData[tData$ID == IDs[i],]
  Res = wnl5(fPK, Data, pNames=c("k", "ka", "V"), IE=c(0.1, 3, 500))
  print(paste("## ID =", i, "##"))
  print(Res)
}

Package 'wnl'

Help Index

Minimization Tool for Pharmacokinetic-Pharmacodynamic Data Analysis

Description

Details

Author(s)

References

Examples

Compare model with Chi-square test

Description

Usage

Arguments

Details

Value

Author(s)

One compartment model - analytical

Description

Usage

Arguments

Details

Value

Author(s)

Examples

An Example of Dosing History Table

Description

Usage

Format

Details

Simplest diagnostic plot for minimization result

Description

Usage

Arguments

Details

Value

Author(s)

Environment's Objects

Description

Usage

Arguments

Details

Value

Author(s)

Expand Dosing History Table

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Hougaard Measure of Skewness

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Get Amounts of Each Compartments using Lambdas and Coefficients of Multi-compartment Model

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Nonlinear Regression in R

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Plot Compartment Model Diagram

Description

Usage

Arguments

Details