Estimate AUC and its standard error

Description

function to estimate AUC and compute standard error of this estimate

Usage

estimateAUCandStdErr(
  imputedData,
  timePoints,
  isMultiplicative = FALSE,
  na.rm = FALSE
)

Arguments

Value

vector of length 2 with estimated AUC and its standard error

Author(s)

Vahid Nassiri, Helen Yvette Barnett

Examples

# generate data from Beal model with only fixed effects
set.seed(111)
genDataFixedEffects <- simulateBealModelFixedEffects(10, 0.693,
+ 		1, 1, seq(0.5,3,0.5))
# Impute the data with BLOQ's with one of the provided methods,
# for example, here we use ROS
imputedDataROS <- imputeROS(genDataFixedEffects, 0.1)
# estimate AUC and its standard error
estimateAUCandStdErr(imputedDataROS,seq(0.5,3,0.5))

estimate AUC with censored maximum likelihood per time point

Description

function to estimate mean and standard error of each column of data with BLOQ's using a censored maximum likelihood (CML) approach, then use these estimates for estimating AUC and its standard error

Usage

estimateAUCwithCMLperTimePoint(
  inputData,
  LOQ,
  timePoints,
  isMultiplicative = FALSE,
  onlyFitCML = FALSE,
  printCMLmessage = TRUE,
  optimizationMethod = NULL,
  CMLcontrol = NULL
)

Arguments

Value

a list with three components: output of maxLik function, estimated parameters for each column using censored maximum likelihood, and estimated AUC and its standard error.

Author(s)

Vahid Nassiri, Helen Yvette Barnett

See Also

maxLik

Examples

# generate data from Beal model with only fixed effects
set.seed(111)
genDataFixedEffects <- simulateBealModelFixedEffects(10, 0.693,
 		1, 1, seq(0.5,3,0.5))
# Multiplicative error model
estimateAUCwithCMLperTimePoint(genDataFixedEffects, 0.1, seq(0.5,3,0.5), TRUE)

estimate AUC with Full censored maximum likelihood

Description

function to estimate mean and and covariance matrix of censored data using a full censored maximum likelihood approach (with a special structure for the covariance matrix which only allows correlations between successive time points), then use these estimates for estimating AUC and its standard error

Usage

estimateAUCwithFullCML(
  inputData,
  LOQ,
  timePoints,
  isMultiplicative = FALSE,
  onlyFitCML = FALSE,
  printCMLmessage = TRUE,
  optimizationMethod = NULL,
  CMLcontrol = NULL,
  na.rm = TRUE
)

Arguments

Value

a list with three components: output of maxLik function, estimated parameters (mean vector and the covariance matrix) using censored maximum likelihood, and estimated AUC and its standard error.

Author(s)

Vahid Nassiri, Helen Yvette Barnett

See Also

maxLik

Examples

#' # generate data from Beal model with only fixed effects
set.seed(123)
genDataFixedEffects <- simulateBealModelFixedEffects(10, 0.693,
	1, 1, seq(0.5,3,1.5))
estimateAUCwithFullCML(genDataFixedEffects, 0.15, seq(0.5,3,1.5))

estimate AUC with multivariate normal censored maximum likelihood

Description

function to estimate mean and and covariance matrix of censored data using a full censored maximum likelihood approach (with a special structure for the covariance matrix which only allows correlations between successive time points), then use these estimates for estimating AUC and its standard error

Usage

estimateAUCwithMVNCML(
  inputData,
  LOQ,
  timePoints,
  isMultiplicative = FALSE,
  onlyFitCML = FALSE,
  printCMLmessage = TRUE,
  optimizationMethod = NULL,
  CMLcontrol = NULL,
  na.rm = TRUE,
  isPairwise = FALSE
)

Arguments

Value

a list with three components: output of maxLik function, estimated parameters (mean vector and the covariance matrix) using censored maximum likelihood, and estimated AUC and its standard error.

Author(s)

Vahid Nassiri, Helen Yvette Barnett

See Also

maxLik

Examples

# generate data from Beal model with only fixed effects
set.seed(111)
genDataFixedEffects <- simulateBealModelFixedEffects(10, 0.693,
		1, 1, seq(0.5,3,1.5))
estimateAUCwithMVNCML(genDataFixedEffects, 0.1, seq(0.5,3,1.5))
estimateAUCwithMVNCML(genDataFixedEffects, 0.1, seq(0.5,3,1.5),
isPairwise = TRUE)

estimate AUCwith pairwise censored maximum likelihood

Description

function to estimate mean and and covariance matrix of censored data using a full censored maximum likelihood approach via fitting all possible pairs, then use these estimates for estimating AUC and its standard error

Usage

estimateAUCwithPairwiseCML(
  inputData,
  LOQ,
  timePoints,
  isMultiplicative = FALSE,
  onlyFitCML = FALSE,
  optimizationMethod = NULL,
  CMLcontrol = NULL,
  na.rm = TRUE
)

Arguments

Value

a list with three components: output of maxLik function, estimated parameters (mean vector and the covariance matrix) using censored maximum likelihood, and estimated AUC and its standard error.

Author(s)

Vahid Nassiri, Helen Yvette Barnett

See Also

maxLik

Examples

# generate data from Beal model with only fixed effects
set.seed(111)
genDataFixedEffects <- simulateBealModelFixedEffects(10, 0.693,
		1, 1, seq(0.5,3,1.5))
estimateAUCwithPairwiseCML(genDataFixedEffects, 0.1, seq(0.5,3,1.5))

impute BLOQ's with various methods

Description

function to impute BLOQ's. The user can define column-specific methods to impute the BLOQ's.

Usage

imputeBLOQ(inputData, LOQ, imputationMethod, progressPrint = FALSE, ...)

Arguments

Value

a list with two components: imputed dataset, and the methods used to impute each column.

Author(s)

Vahid Nassiri, Helen Yvette Barnett

Examples

set.seed(111)
inputData <- simulateBealModelFixedEffects(10, 0.693,1, 1, seq(0.5,3,0.5))
LOQ = 0.125
imputeBLOQ(inputData, LOQ, 
		imputationMethod = c("cml", "ros", "kernel","constant", "constant", "constant"), 
		maxIter = 500, isMultiplicative = TRUE, constantValue = LOQ)
imputeBLOQ(inputData, LOQ, maxIter = 500, isMultiplicative = TRUE, 
constantValue = LOQ/5, epsilon = 1e-04)

imputing BLOQ's using censored maximum likelihood

Description

function to impute BLOQ's using quantiles of a normal distribution with mean and standard error estimates using censored maximum likelihood

Usage

imputeCML(
  inputData,
  LOQ,
  isMultiplicative = FALSE,
  useSeed = runif(1),
  printCMLmessage = TRUE,
  CMLcontrol = NULL
)

Arguments

Value

the imputed dataset: a numeric matrix or data frame of the size n by J (n the sample size and J the number of time points)

Author(s)

Vahid Nassiri, Helen Yvette Barnett

See Also

maxLik

Examples

# generate data from Beal model with only fixed effects
set.seed(111)
genDataFixedEffects <- simulateBealModelFixedEffects(10, 0.693,
+ 		1, 1, seq(0.5,3,0.5))
imputeCML(genDataFixedEffects, 0.1, FALSE, 1)

imputing BLOQ's with a constant value

Description

function to impute BLOQ observations by replacing them with a constant value.

Usage

imputeConstant(inputData, LOQ, constantValue)

Arguments

Value

the imputed dataset: a numeric matrix or data frame of the size n by J (n the sample size and J the number of time points)

Author(s)

Vahid Nassiri, Helen Yvette Barnett

Examples

# generate data from Beal model with only fixed effects
set.seed(111)
genDataFixedEffects <- simulateBealModelFixedEffects(10, 0.693,
+ 		1, 1, seq(0.5,3,0.5))
# replacing BLOQ's with LOQ/2
imputeConstant(genDataFixedEffects, 0.1, 0.1/2)

imputing BLOQ's using kernel density estimation

Description

function to impute BLOQ observations using kernel density estimation.

Usage

imputeKernelDensityEstimation(
  inputData,
  LOQ,
  epsilon = 1e-07,
  maxIter = 1000,
  useSeed = runif(1)
)

Arguments

Value

the imputed dataset: a numeric matrix or data frame of the size n by J (n the sample size and J the number of time points)

Author(s)

Vahid Nassiri, Helen Yvette Barnett

Examples

# generate data from Beal model with only fixed effects
set.seed(111)
genDataFixedEffects <- simulateBealModelFixedEffects(10, 0.693,
+ 		1, 1, seq(0.5,3,0.5))
imputeKernelDensityEstimation(genDataFixedEffects, 0.1, epsilon = 1e-05)

imputing BLOQ's using regression on order statistics

Description

function to impute BLOQ's with regression on order statistics (ROS) approach.

Usage

imputeROS(inputData, LOQ, isMultiplicative = FALSE, useSeed = runif(1))

Arguments

Value

the imputed dataset: a numeric matrix or data frame of the size n by J (n the sample size and J the number of time points)

Author(s)

Vahid Nassiri, Helen Yvette Barnett

Examples

# generate data from Beal model with only fixed effects
set.seed(111)
genDataFixedEffects <- simulateBealModelFixedEffects(10, 0.693,
+ 		1, 1, seq(0.5,3,0.5))
imputeROS(genDataFixedEffects, 0.1)

simulate data from Beal model with fixed effects

Description

function to generate data from a Beal model with fixed effects

Usage

simulateBealModelFixedEffects(
  numSubjects,
  clearance,
  volumeOfDistribution,
  dose,
  timePoints
)

Arguments

Details

The model used to generate data at time t is as follows

y(t)=C(t)\exp(e(t)),

where C(t), the PK-model, is defined as follows:

C(t) = \frac{\mathrm{dose}}{V_d} \exp{(CL.t)},

with V_d the volume of distribution and CL as clearance. The error model is consdiered as e(t) \sim N(0, h(t)), with:

h(t) = 0.03 + 0.165 \frac{C(t)^{-1}}{C(1.5)^{-1} + C(t)^{-1}}

Value

generated sample with numSubjects as the number of rows and length of timePoints as the number of columns

Author(s)

Vahid Nassiri, Helen Yvette Barnett

See Also

Beal S. L., Ways to fit a PK model with some data below the quantification limit, Journal of Pharmacokinetics and Pharmacodynamics, 2001;28(5):481–504.

Examples

set.seed(111)
simulateBealModelFixedEffects(10, 0.693,
+ 		1, 1, seq(0.5,3,0.5))

simulate data from Beal model with fixed and random effects

Description

function to generate data from a Beal model with fixed effects

Usage

simulateBealModelMixedEffects(
  numSubjects,
  clearance,
  volumeOfDistribution,
  dose,
  varCompClearance,
  varCompVolumeOfDistribution,
  timePoints
)

Arguments

Details

The model used to generate data at time t is as follows

y(t)=C(t)\exp(e(t)),

where C(t), the PK-model, is defined as follows:

C(t) = \frac{\mathrm{dose}}{V_d} \exp{(CL.t)},

with V_d the volume of distribution and CL as clearance. The error model is consdiered as e(t) \sim N(0, h(t)), with:

h(t) = 0.03 + 0.165 \frac{C(t)^{-1}}{C(1.5)^{-1} + C(t)^{-1}}.

For the mixed effects model, CL=\widetilde{CL} \exp{(\eta_1)}, and V_d=\widetilde{V_d} \exp{(\eta_2)}, where \eta_1 \sim N(0, w_1^2) and \eta_1 \sim N(0, w_2^2). Note that w_1 and w_2 are specified by varCompClearance, and varCompVolumeOfDistribution in the arguments, respectively.

Value

generated sample with numSubjects as the number of rows and length of timePoints as the number of columns

Author(s)

Vahid Nassiri, Helen Yvette Barnett

See Also

Beal S. L., Ways to fit a PK model with some data below the quantification limit, Journal of Pharmacokinetics and Pharmacodynamics, 2001;28(5):481–504.

Examples

set.seed(111)
simulateBealModelMixedEffects(10, 0.693,
+ 		1, 1, 0.2,0.2, seq(0.5,3,0.5))