Design evaluation and optimization 01"
In PFIM: Population Fisher Information Matrix

backup_options <- options()
options(width = 3000)
knitr::opts_chunk$set(collapse = TRUE,
comment = "#>",echo = FALSE, warning = FALSE, message = FALSE,
cache = FALSE, tidy = FALSE, size = "small")
library(PFIM)

Overview

Data for this example result from a PKPD population study on a non-steroidal molecule [@FloresMurrieta1998]. Single doses of 1, 3.2, 10, 31.6, 56.2, or 100mg/kg per os were given respectively to 6 groups, each of which contained at least 6 rats (weighing 200g on average), following a parallel design. Blood sampling and drug response (DI score) evaluation were conducted at 0, 15, 30, and 45 min and at 1, 1.25, 1.5, 2, 3 and 4 hours after administration.

Based on the evaluation results, we choose to optimize a design for 30 rats receiving a single dose of either 100mg/kg or 320 mg/kg, selecting only 3 from previously defined time points for blood sampling and response evaluation by using Fedorov-Wynn method and Multiplicative Algorithm.

Reports of the design evaluation and optimization are available at https://github.com/iame-researchCenter/PFIM

Design evaluation

outputPath = getwd()

Define the model equations of the PKPD model

modelEquations = list(

  outcomes = list( "RespPK"  = "Cc",
                   "RespPD"  = "E" ),

  equations = list(  "Deriv_Cc" = "dose_RespPK/V*ka*exp(-ka*t) - Cl/V*Cc",
                     "Deriv_E" = "Rin*(1-Imax*(Cc**gamma)/(Cc**gamma + IC50**gamma))-kout*E" ) )

Set mu and omega for each parameter

modelParameters = list(

  ModelParameter( name = "V",
                  distribution = LogNormal( mu = 0.74, omega = 0.316 ) ),

  ModelParameter( name = "Cl",
                  distribution = LogNormal( mu = 0.28, omega = 0.456 ) ),

  ModelParameter( name = "ka",
                  distribution = LogNormal( mu = 10, omega = sqrt( 0 ) ), fixedMu = TRUE ),

  ModelParameter( name = "kout",
                  distribution = LogNormal( mu = 6.14, omega = 0.947 ) ),

  ModelParameter( name = "Rin",
                  distribution = LogNormal( mu = 614, omega = sqrt( 0 ) ), fixedMu = TRUE ),

  ModelParameter( name = "Imax",
                  distribution = LogNormal( mu = 0.76, omega = 0.439 ) ),

  ModelParameter( name = "IC50",
                  distribution = LogNormal( mu = 9.22, omega = 0.452 ) ),

  ModelParameter( name = "gamma",
                  distribution = LogNormal( mu = 2.77, omega = 1.761 ) )

  )

Create the error model to the responses PK and PD.

errorModelRespPK = Combined1( outcome = "RespPK", sigmaInter = 0, sigmaSlope = 0.21 )
errorModelRespPD = Constant( outcome = "RespPD", sigmaInter = 9.6 )
modelError = list( errorModelRespPK, errorModelRespPD )

Define the arms and for each arm

- create the administration parameters for the response PK
- create the sampling times for the responses PK and PD

# sampling times
samplingTimesRespPK = SamplingTimes( outcome = "RespPK",
                                     samplings = c( 0.25, 0.5, 0.75, 1, 1.25, 1.5, 2, 3, 4 ) )

samplingTimesRespPD = SamplingTimes( outcome = "RespPD",
                                     samplings = c( 0.25, 0.5, 0.75, 1, 1.25, 1.5, 2, 3, 4 ) )

## arms

# Administrations
administrationRespPK1 = Administration( outcome = "RespPK", timeDose = c(0), dose = c( 0.2 ) )

arm1 = Arm( name = "0.2mg Arm",
            size = 6,
            administrations = list( administrationRespPK1 ) ,
            samplingTimes   = list( samplingTimesRespPK, samplingTimesRespPD ),
            initialCondition = list( "Cc" = 0,
                                     "E" = 100 ) )


# Administrations
administrationRespPK2 = Administration( outcome = "RespPK", timeDose = c(0), dose = c( 0.64 ) )

arm2 = Arm( name = "0.64mg Arm",
            size = 6,
            administrations = list( administrationRespPK2 ) ,
            samplingTimes   = list( samplingTimesRespPK, samplingTimesRespPD ),
            initialCondition = list( "Cc" = 0,
                                     "E" = 100 ) )

# Administrations
administrationRespPK3 = Administration( outcome = "RespPK", timeDose = c(0), dose = c( 2 ) )

arm3 = Arm( name = "2mg Arm",
            size = 6,
            administrations = list( administrationRespPK3 ) ,
            samplingTimes   = list( samplingTimesRespPK, samplingTimesRespPD ),
            initialCondition = list( "Cc" = 0,
                                     "E" = 100 ) )

# Administrations
administrationRespPK4 = Administration( outcome = "RespPK", timeDose = c(0), dose = c( 6.24 ) )

arm4 = Arm( name = "6.24mg Arm",
            size = 6,
            administrations = list( administrationRespPK4 ) ,
            samplingTimes   = list( samplingTimesRespPK, samplingTimesRespPD ),
            initialCondition = list( "Cc" = 0,
                                     "E" = 100 ) )

# Administrations
administrationRespPK5 = Administration( outcome = "RespPK", timeDose = c(0), dose = c( 11.24 ) )

arm5 = Arm( name = "11.24mg Arm",
            size = 6,
            administrations = list( administrationRespPK5 ) ,
            samplingTimes   = list( samplingTimesRespPK, samplingTimesRespPD ),
            initialCondition = list( "Cc" = 0,
                                     "E" = 100 ) )

# Administrations
administrationRespPK6 = Administration( outcome = "RespPK", timeDose = c(0), dose = c( 20 ) )

arm6 = Arm( name = "20mg Arm",
            size = 6,
            administrations = list( administrationRespPK6 ) ,
            samplingTimes   = list( samplingTimesRespPK, samplingTimesRespPD ),
            initialCondition = list( "Cc" = 0,
                                     "E" = 100 ) )

Add the arms to the design `design1`

design1 = Design( name = "design1", arms = list( arm1, arm2, arm3, arm4, arm5, arm6 ) )

Evaluate the population FIM

evaluationFIM = Evaluation( name = "",
                            modelEquations = modelEquations,
                            modelParameters = modelParameters,
                            modelError = modelError,
                            outcomes = list( "RespPK"  = "Cc", "RespPD"  = "E" ),
                            designs = list( design1 ),
                            fim = "population",
                            odeSolverParameters = list( atol = 1e-4, rtol = 1e-4 ) )

evaluationFIM = run( evaluationFIM )

Display the results of the design evaluation

show( evaluationFIM )

Create and save the report for the design evaluation

outputFile = "Example01_EvaluationPopFIM.html"
plotOptions = list( unitTime=c("hour"), unitResponses= c("mcg/mL","DI%") )

Report( evaluationFIM, outputPath, outputFile, plotOptions )

Evaluate the individual and Bayesian FIMs

evaluationInd = Evaluation( name = "",
                            modelEquations = modelEquations,
                            modelParameters = modelParameters,
                            modelError = modelError,
                            outcomes = list( "RespPK"  = "Cc", "RespPD"  = "E" ),
                            designs = list( design1 ),
                            fim = "individual",
                            odeSolverParameters = list( atol = 1e-4, rtol = 1e-4 ) )

evaluationInd = run( evaluationInd )

evaluationBay = Evaluation( name = "",
                            modelEquations = modelEquations,
                            modelParameters = modelParameters,
                            modelError = modelError,
                            outcomes = list( "RespPK"  = "Cc", "RespPD"  = "E" ),
                            designs = list( design1 ),
                            fim = "Bayesian",
                            odeSolverParameters = list( atol = 1e-4, rtol = 1e-4 ) )

evaluationBay = run( evaluationBay )

Display the results of the design evaluation

show( evaluationInd )
show( evaluationBay )

Reports for the design evaluation

plotOptions = list( unitTime=c("hour"), unitResponses= c("mcg/mL","DI%") )

outputFile = "Example01_EvaluationIndFIM.html"
Report( evaluationInd, outputPath, outputFile, plotOptions )

outputFile = "Example01_EvaluationBayFIM.html"
Report( evaluationBay, outputPath, outputFile, plotOptions )

Design optimization

Create an administration for response PK and samplings times

We create sampling times that will be used in the initial design for comparison during the optimization process.

samplingTimesRespPK = SamplingTimes( outcome = "RespPK", samplings = c( 0.25, 0.75, 1, 1.5, 2, 4, 6 ) )
samplingTimesRespPD = SamplingTimes( outcome = "RespPD", samplings = c( 0.25, 0.75, 1.5, 2, 3, 6, 8, 12 ) )

Create a sampling constraint for the responses PK and PD

Set the vector of allowed sampling times for the responses PK and PD
Fix certain time values
Set the number of optimisable sampling times

samplingConstraintsRespPK  = SamplingTimeConstraints( outcome = "RespPK",
                                                     initialSamplings = c( 0.25, 0.75, 1, 1.5, 2, 4, 6 ),
                                                     fixedTimes = c( 0.25, 4 ),
                                                     numberOfsamplingsOptimisable = 3 
                                                     )

samplingConstraintsRespPD  = SamplingTimeConstraints( outcome = "RespPD",
                                                     initialSamplings = c( 0.25, 0.75, 1.5, 2, 3, 6, 8, 12 ),
                                                     fixedTimes = c( 2, 6 ),
                                                     numberOfsamplingsOptimisable = 3 )

Set the initial vectors for the FedorovWynn algorithm

initialElementaryProtocols = list( c( 0.25, 1, 4 ), c( 1.5, 2, 6 ) )

Create an administration constraint with the vector of allowed amount of doses for the response PK

administrationConstraintsResp = AdministrationConstraints( outcome = "RespPK",
                                                             doses = c( 0.2, 0.64, 2, 6.24, 11.24, 20 )
                                                           )

Create the constraint design to the project

total number of individuals to be considered
administration constraint
sampling constraint

armConstraint = Arm( name = "armConstraint",
            size = 30,
            administrations = list( administrationRespPK1 ),
            samplingTimes   = list( samplingTimesRespPK, samplingTimesRespPD ),
            administrationsConstraints = list( administrationConstraintsResp ),
            samplingTimesConstraints = list( samplingConstraintsRespPK, samplingConstraintsRespPD ),
            initialCondition = list( "Cc" = 0,
                                     "E" = "Rin/kout"  )
            )

designConstraint = Design( name = "designConstraint", 
                           arms = list( armConstraint ), numberOfArms = 30 )

Set the vector of initial proportions or numbers of subjects for each elementary design

numberOfSubjects = c(30)
proportionsOfSubjects = c(30)/30

Set the the parameters of the FedorovWynn algorithm and run the algorithm for the design optimization with a population FIM

optimizationFWPopFIM = Optimization( name = "PKPD_ODE_multi_doses_populationFIM",
                             modelEquations = modelEquations,
                             modelParameters = modelParameters,
                             modelError = modelError,
                             optimizer = "FedorovWynnAlgorithm",
                             optimizerParameters = list( elementaryProtocols = initialElementaryProtocols,
                                                         numberOfSubjects = numberOfSubjects,
                                                         proportionsOfSubjects = proportionsOfSubjects,
                                                         showProcess = T ),
                             designs = list( designConstraint ),
                             fim = "population",
                             outcomes = list( "RespPK" = "Cc","RespPD" = "E" ),
                             odeSolverParameters = list( atol = 1e-8, rtol = 1e-8 ) )

optimizationFWPopFIM = run( optimizationFWPopFIM )

Display the results of the design optimization

show( optimizationFWPopFIM )

Reports for the design optimization

outputFile = "Example01_OptimizationFWPopFIM.html"
Report( optimizationFWPopFIM, outputPath, outputFile, plotOptions )

Set the the parameters of the Multiplicative Algorithm algorithm and run the algorithm for the design optimization with a population FIM

optimizationMultPopFIM = Optimization( name = "PKPD_ODE_multi_doses_populationFIM",
                             modelEquations = modelEquations,
                             modelParameters = modelParameters,
                             modelError = modelError,
                             optimizer = "MultiplicativeAlgorithm",
                             optimizerParameters = list( lambda = 0.99,
                                                         numberOfIterations = 1000,
                                                         delta = 1e-04, showProcess = T ),
                              designs = list( designConstraint ),
                             fim = "population",
                             outcomes = list( "RespPK" = "Cc","RespPD" = "E" ),
                             odeSolverParameters = list( atol = 1e-8, rtol = 1e-8 ) )

Run the Multiplicative Algorithm algorithm for the optimization with a population FIM

optimizationMultPopFIM = run( optimizationMultPopFIM )

Display the results of the design optimization

show( optimizationMultPopFIM )

Create and save the report for the design optimization

plotOptions = list( unitTime=c("hour"), unitResponses= c("mcg/mL","DI%"), threshold = 0.01 )

outputFile = "Example01_OptimizationMultPopFIM.html"
Report( optimizationMultPopFIM, outputPath, outputFile, plotOptions )

References

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PFIM
Population Fisher Information Matrix

Design evaluation and optimization 01"
In PFIM: Population Fisher Information Matrix

Overview

Design evaluation

Define the model equations of the PKPD model

Set mu and omega for each parameter

Create the error model to the responses PK and PD.

Define the arms and for each arm

Add the arms to the design `design1`

Evaluate the population FIM

Display the results of the design evaluation

Create and save the report for the design evaluation

Evaluate the individual and Bayesian FIMs

Display the results of the design evaluation

Reports for the design evaluation

Design optimization

Create an administration for response PK and samplings times

Create a sampling constraint for the responses PK and PD

Set the initial vectors for the FedorovWynn algorithm

Create an administration constraint with the vector of allowed amount of doses for the response PK

Create the constraint design to the project

Set the vector of initial proportions or numbers of subjects for each elementary design

Set the the parameters of the FedorovWynn algorithm and run the algorithm for the design optimization with a population FIM

Display the results of the design optimization

Reports for the design optimization

Set the the parameters of the Multiplicative Algorithm algorithm and run the algorithm for the design optimization with a population FIM

Run the Multiplicative Algorithm algorithm for the optimization with a population FIM

Display the results of the design optimization

Create and save the report for the design optimization

References

Try the PFIM package in your browser

R Package Documentation

Browse R Packages

We want your feedback!

PFIM Population Fisher Information Matrix

Design evaluation and optimization 01" In PFIM: Population Fisher Information Matrix

Overview

Design evaluation

Define the model equations of the PKPD model

Set mu and omega for each parameter

Create the error model to the responses PK and PD.

Define the arms and for each arm

Add the arms to the design design1

Evaluate the population FIM

Display the results of the design evaluation

Create and save the report for the design evaluation

Evaluate the individual and Bayesian FIMs

Display the results of the design evaluation

Reports for the design evaluation

Design optimization

Create an administration for response PK and samplings times

Create a sampling constraint for the responses PK and PD

Set the initial vectors for the FedorovWynn algorithm

Create an administration constraint with the vector of allowed amount of doses for the response PK

Create the constraint design to the project

Set the vector of initial proportions or numbers of subjects for each elementary design

Set the the parameters of the FedorovWynn algorithm and run the algorithm for the design optimization with a population FIM

Display the results of the design optimization

Reports for the design optimization

Set the the parameters of the Multiplicative Algorithm algorithm and run the algorithm for the design optimization with a population FIM

Run the Multiplicative Algorithm algorithm for the optimization with a population FIM

Display the results of the design optimization

Create and save the report for the design optimization

References

Try the PFIM package in your browser

R Package Documentation

Browse R Packages

We want your feedback!

PFIM
Population Fisher Information Matrix

Design evaluation and optimization 01"
In PFIM: Population Fisher Information Matrix

Add the arms to the design `design1`