Scientific Background
This example is based on PK study of Remdesivir (Sukeishi et al.
2022). The PK is described by a 1-compartment model, with
linear elimination, following an IV infusion.
Considered original design.
A single arm with 150 subjects received multiple IV doses: a loading
dose of 400mg, then 200mg per day. Blood samples were collected at 6
time points: 1, 12, 24, 44, 72, and 120 h.
Objectives
- Evaluation – Compute the Population, Individual and Bayesian Fisher
Information Matrices (FIM) for the original design. Assess parameter
precision (RSE%) and Shrinkage.
- Optimization – Find the D-optimal design with only 4 sampling times,
using possible sampling time windows and a continuous design space
optimization. The number of subjects and the dosing regimen is
unchanged.
Design Evaluation
Model Equations from from Library of Models
PFIM provides a library of pre-implemented standard PK/PD structural
models. modelFromLibrary replaces
modelEquations — the two arguments are mutually exclusive.
The key "PKModel" is used for pharmacokinetic models.
The string "Linear1InfusionSingleDose_ClV" decodes
as:
Linear |
First-order (linear) elimination |
1 |
One-compartment disposition |
Infusion |
IV infusion route; requires Tinf in
Administration() |
ClV |
Parameterised by clearance \(Cl\) and volume \(V\) |
The predicted concentration follows:
\[C_c(t) = \begin{cases}
\dfrac{D}{T_{inf} \cdot Cl}\!\left(1 - e^{-\frac{Cl}{V}t}\right) & 0
\leq t \leq T_{inf} \\[6pt]
C_c(T_{inf})\,e^{-\frac{Cl}{V}(t - T_{inf})} & t > T_{inf}
\end{cases}\]
modelFromLibrary = list("PKModel" = "Linear1InfusionSingleDose_ClV")
Model Parameters
The model has two structural parameters, both log-normally
distributed:
| \(V\) |
Volume of distribution (L) |
50 |
\(\sqrt{0.26} \approx
0.51\) |
No |
No |
| \(Cl\) |
Elimination clearance (L/h) |
5 |
\(\sqrt{0.34} \approx
0.58\) |
No |
No |
modelParameters = list(
ModelParameter(name = "V", distribution = LogNormal(mu = 50, omega = sqrt(0.26))),
ModelParameter(name = "Cl", distribution = LogNormal(mu = 5, omega = sqrt(0.34)))
)
Residual Error Model
A Combined1 error model is used for the PK response.
errorModelRespPK = Combined1( output = "RespPK", sigmaInter = 0.5, sigmaSlope = sqrt( 0.15 ) )
modelError = list( errorModelRespPK )
Administration Parameters
The dosing schedule encodes the full multiple-dose regimen. The
loading dose (400 mg = 2× maintenance) rapidly raises \(C_c\) toward the therapeutic target;
subsequent 200 mg doses maintain near-steady-state concentrations.
administrationRespPK = Administration(
outcome = "RespPK",
Tinf = rep(1, 5), # 1-hour infusion for each of the 5 doses
timeDose = seq(0, 96, 24), # dosing at t = 0, 24, 48, 72, 96 h
dose = c(400, rep(200, 4)) # 400 mg loading + 4 × 200 mg maintenance
)
Sampling Times
Six sampling times cover distinct phases of the multi-dose
concentration profile:
| 1 |
End of first infusion — \(C_{max}\) of dose 1 |
| 12 |
Mid-interdose Day 1 — early elimination |
| 24 |
Trough before dose 2 — \(C_{min}\) after dose 1 |
| 44 |
Near \(C_{min}\) of
dose 2 (dose at 24 h + ~20 h) |
| 72 |
Trough before dose 4 — approaching steady state |
| 120 |
CTrough after last dose - at-Steady state |
samplingTimesRespPK = SamplingTimes(
outcome = "RespPK",
samplings = c(1, 12, 24, 44, 72, 120)
)
Arm and Design
A single arm with all 150 subjects on the same regimen. No
initialCondition is required: the library model sets \(C_c(0) = 0\) internally for IV infusion
models.
arm1 = Arm(
name = "arm1",
size = 150,
administrations = list(administrationRespPK),
samplingTimes = list(samplingTimesRespPK)
)
design1 = Design(name = "design1", arms = list(arm1))
FIM Evaluation: Population, Individual, and Bayesian FIM
# --- Population FIM ---
evaluationPop = Evaluation(
name = "evaluationPop",
modelFromLibrary = modelFromLibrary,
modelParameters = modelParameters,
modelError = modelError,
outputs = list("RespPK"),
designs = list(design1),
fimType = "population",
odeSolverParameters = list(atol = 1e-8, rtol = 1e-8)
)
evaluationPopResults = run(evaluationPop)
# --- Individual FIM ---
evaluationInd = Evaluation(
name = "evaluationInd",
modelFromLibrary = modelFromLibrary,
modelParameters = modelParameters,
modelError = modelError,
outputs = list("RespPK"),
designs = list(design1),
fimType = "individual",
odeSolverParameters = list(atol = 1e-8, rtol = 1e-8)
)
evaluationIndResults = run(evaluationInd)
# --- Bayesian FIM ---
evaluationBay = Evaluation(
name = "evaluationBay",
modelFromLibrary = modelFromLibrary,
modelParameters = modelParameters,
modelError = modelError,
outputs = list("RespPK"),
designs = list(design1),
fimType = "Bayesian",
odeSolverParameters = list(atol = 1e-8, rtol = 1e-8)
)
evaluationBayResults = run(evaluationBay)
show(evaluationPopResults)
***************************************
Population Fisher Matrix
***************************************
μ_V μ_Cl ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
μ_V 0.1393880 -0.2899109 0.00000 0.00000 0.00000 0.0000
μ_Cl -0.2899109 14.3204999 0.00000 0.00000 0.00000 0.0000
ω²_V 0.0000000 0.0000000 404.77110 17.51007 51.06227 259.6216
ω²_Cl 0.0000000 0.0000000 17.51007 427.24316 54.71243 80.1080
σ_inter_RespPK 0.0000000 0.0000000 51.06227 54.71243 1982.21804 1361.3658
σ_slope_RespPK 0.0000000 0.0000000 259.62165 80.10800 1361.36582 1648.5030
***************************************
Fixed effects
***************************************
μ_V μ_Cl
μ_V 0.1393880 -0.2899109
μ_Cl -0.2899109 14.3204999
***************************************
Variance components
***************************************
ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
ω²_V 404.77110 17.51007 51.06227 259.6216
ω²_Cl 17.51007 427.24316 54.71243 80.1080
σ_inter_RespPK 51.06227 54.71243 1982.21804 1361.3658
σ_slope_RespPK 259.62165 80.10800 1361.36582 1648.5030
*********************************************
Determinant, condition numbers and D-criterion
***********************************************
Determinant: 380849659427.786
D-criterion: 85.1384217619946
Condition number of the fixed effects: 107.343235280232
Condition number of the random effects: 12.6420305367204
***************************************
Parameters estimation
***************************************
parametersValues SE RSE
μ_V 50.0000000 2.73670901 5.473418
μ_Cl 5.0000000 0.26999904 5.399981
ω²_V 0.2600000 0.05481857 21.084067
ω²_Cl 0.3400000 0.04861157 14.297522
σ_inter_RespPK 0.5000000 0.03570392 7.140784
σ_slope_RespPK 0.3872983 0.04131312 10.667003
show(evaluationIndResults)
***************************************
Individual Fisher Matrix
***************************************
μ_V μ_Cl σ_inter_RespPK σ_slope_RespPK
μ_V 0.003831386 -0.03578704 0.00000 0.00000
μ_Cl -0.035787035 0.74495930 0.00000 0.00000
σ_inter_RespPK 0.000000000 0.00000000 16.79391 12.15818
σ_slope_RespPK 0.000000000 0.00000000 12.15818 20.61786
***************************************
Fixed effects
***************************************
μ_V μ_Cl
μ_V 0.003831386 -0.03578704
μ_Cl -0.035787035 0.74495930
***************************************
Variance components
***************************************
σ_inter_RespPK σ_slope_RespPK
σ_inter_RespPK 16.79391 12.15818
σ_slope_RespPK 12.15818 20.61786
***********************************************
Determinant, condition numbers and D-criterion
***********************************************
Determinant: 0.312237623200518
D-criterion: 0.747517403243219
Condition number of the fixed effects: 354.325216014069
Condition number of the variance effects: 4.84715360183152
***************************************
Parameters estimation
***************************************
parametersValues SE RSE
μ_V 50.0000000 21.7585945 43.51719
μ_Cl 5.0000000 1.5604237 31.20847
σ_inter_RespPK 0.5000000 0.3223403 64.46806
σ_slope_RespPK 0.3872983 0.2909168 75.11439
show(evaluationBayResults)
***************************************
Bayesian Fisher Matrix
***************************************
μ_V μ_Cl
μ_V 9.580004 -8.946759
μ_Cl -8.946759 18.741630
***************************************
Fixed effects
***************************************
μ_V μ_Cl
μ_V 9.580004 -8.946759
μ_Cl -8.946759 18.741630
***********************************************
Determinant, condition numbers and D-criterion
***********************************************
Determinant: 99.5003949119652
D-criterion: 9.9749884667585
Condition number of the fixed effects: 5.89169416176677
***************************************
Shrinkage
***************************************
Shrinkage
μ_V 0.02897805
μ_Cl 1.13271843
***************************************
Parameters estimation
***************************************
parametersValues SE RSE
μ_V 50 0.4340015 0.8680031
μ_Cl 5 0.3102919 6.2058381
cat("--- Fisher Information Matrix (population FIM) ---\n")
print(getFisherMatrix(evaluationPopResults))
cat("--- Correlation Matrix (population FIM) ---\n")
print(getCorrelationMatrix(evaluationPopResults))
cat("--- Standard Errors ---\n")
print(getSE(evaluationPopResults))
cat("--- Relative Standard Errors ---\n")
print(getRSE(evaluationPopResults))
cat("--- Shrinkage ---\n")
print(getShrinkage(evaluationPopResults))
cat("--- D-Criterion ---\n")
print(getDcriterion(evaluationPopResults))
Response profiles
plotOptions = list(unitTime = "hour", unitOutcomes = "mcg/mL")
# plot() is the unified OO entry point -- dispatches on class, returns a named list:
# $evaluation -> nested [["design"]][["arm"]][["outcome"]]
# $sensitivityIndices -> nested [["design"]][["arm"]][["outcome"]][["param"]]
# $SE / $RSE -> ggplot2 bar charts
# Predicted concentration profile with sampling times overlaid
plotsEval = plot(evaluationPopResults,
plotOptions = plotOptions,
which = c("evaluation", "sensitivityIndices", "SE", "RSE"))
plotOutcomesRespPK = plotsEval$evaluation[["design1"]][["arm1"]][["RespPK"]]
print(plotOutcomesRespPK)
Sensitivity indices
# $sensitivityIndices is computed in the same plot() call above
print(plotsEval$sensitivityIndices[["design1"]][["arm1"]][["RespPK"]][["V"]])
print(plotsEval$sensitivityIndices[["design1"]][["arm1"]][["RespPK"]][["Cl"]])
Standard errors and Relative Standard errors
# Standard error and RSE bar charts -- computed in the same plot() call above
print(plotsEval$SE)
print(plotsEval$RSE)
Design Optimization in Continuous Space
Objective. Find 4 optimal sampling times (instead of
the original 6), constrained to two disjoint time windows, maximizing
the D-criterion of the population FIM \(M_{PF}\):
\[\max_{t_1,\ldots,t_4} \;
|M_{PF}(\xi)|^{1/P}
\quad \text{s.t.} \quad
t_1, t_2 \in [1,\,48], \quad t_3, t_4 \in [72,\,120], \quad |t_i - t_j|
\geq 5\,\text{h}\]
Three algorithms - PSO, PGBO, Simplex - are used.
Shared Optimization Setup
samplingTimesOptim = SamplingTimes(
outcome = "RespPK",
samplings = c(1, 48, 72, 120) # initial guess: window boundaries
)
samplingConstraintsRespPK = SamplingTimeConstraints(
outcome = "RespPK",
initialSamplings = c(1, 48, 72, 120),
numberOfTimesByWindows = c(2, 2),
samplingsWindows = list(c(1, 48), # Window 1: post-dose 1 to pre-dose 3
c(72, 120)), # Window 2: near-SS to post-last-dose
minSampling = 5 # min 5 h between consecutive samples
)
arm2 = Arm(
name = "arm2",
size = 150,
administrations = list(administrationRespPK),
samplingTimes = list(samplingTimesOptim),
samplingTimesConstraints = list(samplingConstraintsRespPK)
)
# numberOfArms = 150: upper bound on distinct elementary protocols
design2 = Design(name = "design2", arms = list(arm2), numberOfArms = 150)
PSO Algorithm (Particle Swarm Optimization)
optimizationPSO = Optimization(
name = "PSO",
modelFromLibrary = modelFromLibrary,
modelParameters = modelParameters,
modelError = modelError,
optimizer = "PSOAlgorithm",
optimizerParameters = list(
maxIteration = 100,
populationSize = 50,
personalLearningCoefficient = 2.05,
globalLearningCoefficient = 2.05,
seed = 42,
showProcess = FALSE
),
designs = list(design2),
fimType = "population",
outputs = list("RespPK")
)
optimizationPSO = run(optimizationPSO)
=====================================
Initial design
=====================================
Arms name Number of subjects Outcome Dose Sampling times
1 arm2 150 RespPK 400, 200, 200, 200, 200 (1, 48, 72, 120)
***************************************
Population Fisher Matrix
***************************************
μ_V μ_Cl ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
μ_V 0.1354839 -0.3248313 0.00000 0.00000 0.00000 0.00000
μ_Cl -0.3248313 12.1107623 0.00000 0.00000 0.00000 0.00000
ω²_V 0.0000000 0.0000000 382.41404 21.98237 44.63647 264.88128
ω²_Cl 0.0000000 0.0000000 21.98237 305.56368 105.52177 79.50987
σ_inter_RespPK 0.0000000 0.0000000 44.63647 105.52177 1392.16105 653.06837
σ_slope_RespPK 0.0000000 0.0000000 264.88128 79.50987 653.06837 634.97897
***************************************
Fixed effects
***************************************
μ_V μ_Cl
μ_V 0.1354839 -0.3248313
μ_Cl -0.3248313 12.1107623
***************************************
Variance components
***************************************
ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
ω²_V 382.41404 21.98237 44.63647 264.88128
ω²_Cl 21.98237 305.56368 105.52177 79.50987
σ_inter_RespPK 44.63647 105.52177 1392.16105 653.06837
σ_slope_RespPK 264.88128 79.50987 653.06837 634.97897
*********************************************
Determinant, condition numbers and D-criterion
***********************************************
Determinant: 41386277548.9818
D-criterion: 58.8133694373923
Condition number of the fixed effects: 95.6713072499344
Condition number of the random effects: 18.4576745614613
***************************************
Parameters estimation
***************************************
parametersValues SE RSE
μ_V 50.0000000 2.80859742 5.617195
μ_Cl 5.0000000 0.29706229 5.941246
ω²_V 0.2600000 0.07073645 27.206328
ω²_Cl 0.3400000 0.05824621 17.131237
σ_inter_RespPK 0.5000000 0.04347975 8.695951
σ_slope_RespPK 0.3872983 0.07639997 19.726386
=====================================
Optimal design
=====================================
Arms name Number of subjects Outcome Dose Sampling times
1 arm2 150 RespPK 400, 200, 200, 200, 200 (1, 24, 97, 120)
***************************************
Population Fisher Matrix
***************************************
μ_V μ_Cl ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
μ_V 0.1553579 -0.1841623 0.000000 0.000000 0.00000 0.00000
μ_Cl -0.1841623 12.4931400 0.000000 0.000000 0.00000 0.00000
ω²_V 0.0000000 0.0000000 502.835221 7.065782 52.29275 247.79202
ω²_Cl 0.0000000 0.0000000 7.065782 325.163639 101.06946 95.55499
σ_inter_RespPK 0.0000000 0.0000000 52.292752 101.069458 698.92855 623.89899
σ_slope_RespPK 0.0000000 0.0000000 247.792018 95.554992 623.89899 1641.69761
***************************************
Fixed effects
***************************************
μ_V μ_Cl
μ_V 0.1553579 -0.1841623
μ_Cl -0.1841623 12.4931400
***************************************
Variance components
***************************************
ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
ω²_V 502.835221 7.065782 52.29275 247.79202
ω²_Cl 7.065782 325.163639 101.06946 95.55499
σ_inter_RespPK 52.292752 101.069458 698.92855 623.89899
σ_slope_RespPK 247.792018 95.554992 623.89899 1641.69761
*********************************************
Determinant, condition numbers and D-criterion
***********************************************
Determinant: 207256273436.376
D-criterion: 76.9280305604956
Condition number of the fixed effects: 81.881392644448
Condition number of the random effects: 6.92393338504603
***************************************
Parameters estimation
***************************************
parametersValues SE RSE
μ_V 50.0000000 2.55953621 5.119072
μ_Cl 5.0000000 0.28542513 5.708503
ω²_V 0.2600000 0.04654285 17.901095
ω²_Cl 0.3400000 0.05674885 16.690838
σ_inter_RespPK 0.5000000 0.04739386 9.478773
σ_slope_RespPK 0.3872983 0.03156589 8.150277
PGBO Algorithm (Population genetic-based optimization)
optimizationPGBO = Optimization(
name = "PGBO",
modelFromLibrary = modelFromLibrary,
modelParameters = modelParameters,
modelError = modelError,
optimizer = "PGBOAlgorithm",
optimizerParameters = list(
N = 30,
muteEffect = 0.65,
maxIteration = 1000,
purgeIteration = 200,
seed = 42,
showProcess = FALSE
),
designs = list(design2),
fimType = "population",
outputs = list("RespPK")
)
optimizationPGBO = run(optimizationPGBO)
=====================================
Initial design
=====================================
Arms name Number of subjects Outcome Dose Sampling times
1 arm2 150 RespPK 400, 200, 200, 200, 200 (1, 48, 72, 120)
***************************************
Population Fisher Matrix
***************************************
μ_V μ_Cl ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
μ_V 0.1354839 -0.3248313 0.00000 0.00000 0.00000 0.00000
μ_Cl -0.3248313 12.1107623 0.00000 0.00000 0.00000 0.00000
ω²_V 0.0000000 0.0000000 382.41404 21.98237 44.63647 264.88128
ω²_Cl 0.0000000 0.0000000 21.98237 305.56368 105.52177 79.50987
σ_inter_RespPK 0.0000000 0.0000000 44.63647 105.52177 1392.16105 653.06837
σ_slope_RespPK 0.0000000 0.0000000 264.88128 79.50987 653.06837 634.97897
***************************************
Fixed effects
***************************************
μ_V μ_Cl
μ_V 0.1354839 -0.3248313
μ_Cl -0.3248313 12.1107623
***************************************
Variance components
***************************************
ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
ω²_V 382.41404 21.98237 44.63647 264.88128
ω²_Cl 21.98237 305.56368 105.52177 79.50987
σ_inter_RespPK 44.63647 105.52177 1392.16105 653.06837
σ_slope_RespPK 264.88128 79.50987 653.06837 634.97897
*********************************************
Determinant, condition numbers and D-criterion
***********************************************
Determinant: 41386277548.9818
D-criterion: 58.8133694373923
Condition number of the fixed effects: 95.6713072499344
Condition number of the random effects: 18.4576745614613
***************************************
Parameters estimation
***************************************
parametersValues SE RSE
μ_V 50.0000000 2.80859742 5.617195
μ_Cl 5.0000000 0.29706229 5.941246
ω²_V 0.2600000 0.07073645 27.206328
ω²_Cl 0.3400000 0.05824621 17.131237
σ_inter_RespPK 0.5000000 0.04347975 8.695951
σ_slope_RespPK 0.3872983 0.07639997 19.726386
=====================================
Optimal design
=====================================
Arms name Number of subjects Outcome Dose Sampling times
1 arm2 150 RespPK 400, 200, 200, 200, 200 (1, 48, 72.97, 120)
***************************************
Population Fisher Matrix
***************************************
μ_V μ_Cl ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
μ_V 0.1548932 -0.1689487 0.000000 0.000000 0.00000 0.00000
μ_Cl -0.1689487 11.6800910 0.000000 0.000000 0.00000 0.00000
ω²_V 0.0000000 0.0000000 499.831270 5.946593 56.06854 245.91576
ω²_Cl 0.0000000 0.0000000 5.946593 284.217764 122.82514 88.37993
σ_inter_RespPK 0.0000000 0.0000000 56.068542 122.825140 792.72088 609.27763
σ_slope_RespPK 0.0000000 0.0000000 245.915762 88.379926 609.27763 1578.56182
***************************************
Fixed effects
***************************************
μ_V μ_Cl
μ_V 0.1548932 -0.1689487
μ_Cl -0.1689487 11.6800910
***************************************
Variance components
***************************************
ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
ω²_V 499.831270 5.946593 56.06854 245.91576
ω²_Cl 5.946593 284.217764 122.82514 88.37993
σ_inter_RespPK 56.068542 122.825140 792.72088 609.27763
σ_slope_RespPK 245.915762 88.379926 609.27763 1578.56182
*********************************************
Determinant, condition numbers and D-criterion
***********************************************
Determinant: 190655846414.95
D-criterion: 75.8650394322679
Condition number of the fixed effects: 76.6486671491829
Condition number of the random effects: 7.78335282832985
***************************************
Parameters estimation
***************************************
parametersValues SE RSE
μ_V 50.0000000 2.56116249 5.122325
μ_Cl 5.0000000 0.29493763 5.898753
ω²_V 0.2600000 0.04668595 17.956133
ω²_Cl 0.3400000 0.06141230 18.062441
σ_inter_RespPK 0.5000000 0.04358091 8.716183
σ_slope_RespPK 0.3872983 0.03120088 8.056032
Simplex Algorithm (Nelder-Mead)
optimizationSimplex = Optimization(
name = "Simplex",
modelFromLibrary = modelFromLibrary,
modelParameters = modelParameters,
modelError = modelError,
optimizer = "SimplexAlgorithm",
optimizerParameters = list(
pctInitialSimplexBuilding = 10,
maxIteration = 1000,
tolerance = 1e-10,
showProcess = FALSE
),
designs = list(design2),
fimType = "population",
outputs = list("RespPK")
)
optimizationSimplex = run(optimizationSimplex)
show(optimizationSimplex)
=====================================
Initial design
=====================================
Arms name Number of subjects Outcome Dose Sampling times
1 arm2 150 RespPK 400, 200, 200, 200, 200 (1, 48, 72, 120)
***************************************
Population Fisher Matrix
***************************************
μ_V μ_Cl ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
μ_V 0.1354839 -0.3248313 0.00000 0.00000 0.00000 0.00000
μ_Cl -0.3248313 12.1107623 0.00000 0.00000 0.00000 0.00000
ω²_V 0.0000000 0.0000000 382.41404 21.98237 44.63647 264.88128
ω²_Cl 0.0000000 0.0000000 21.98237 305.56368 105.52177 79.50987
σ_inter_RespPK 0.0000000 0.0000000 44.63647 105.52177 1392.16105 653.06837
σ_slope_RespPK 0.0000000 0.0000000 264.88128 79.50987 653.06837 634.97897
***************************************
Fixed effects
***************************************
μ_V μ_Cl
μ_V 0.1354839 -0.3248313
μ_Cl -0.3248313 12.1107623
***************************************
Variance components
***************************************
ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
ω²_V 382.41404 21.98237 44.63647 264.88128
ω²_Cl 21.98237 305.56368 105.52177 79.50987
σ_inter_RespPK 44.63647 105.52177 1392.16105 653.06837
σ_slope_RespPK 264.88128 79.50987 653.06837 634.97897
*********************************************
Determinant, condition numbers and D-criterion
***********************************************
Determinant: 41386277548.9818
D-criterion: 58.8133694373923
Condition number of the fixed effects: 95.6713072499344
Condition number of the random effects: 18.4576745614613
***************************************
Parameters estimation
***************************************
parametersValues SE RSE
μ_V 50.0000000 2.80859742 5.617195
μ_Cl 5.0000000 0.29706229 5.941246
ω²_V 0.2600000 0.07073645 27.206328
ω²_Cl 0.3400000 0.05824621 17.131237
σ_inter_RespPK 0.5000000 0.04347975 8.695951
σ_slope_RespPK 0.3872983 0.07639997 19.726386
=====================================
Optimal design
=====================================
Arms name Number of subjects Outcome Dose Sampling times
1 arm2 150 RespPK 400, 200, 200, 200, 200 (1, 48, 72, 108)
***************************************
Population Fisher Matrix
***************************************
μ_V μ_Cl ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
μ_V 0.1348140 -0.2668512 0.00000 0.00000 0.00000 0.00000
μ_Cl -0.2668512 12.7511475 0.00000 0.00000 0.00000 0.00000
ω²_V 0.0000000 0.0000000 378.64174 14.83533 51.14649 269.76601
ω²_Cl 0.0000000 0.0000000 14.83533 338.73284 90.52798 91.56249
σ_inter_RespPK 0.0000000 0.0000000 51.14649 90.52798 1082.56615 725.21291
σ_slope_RespPK 0.0000000 0.0000000 269.76601 91.56249 725.21291 892.90492
***************************************
Fixed effects
***************************************
μ_V μ_Cl
μ_V 0.1348140 -0.2668512
μ_Cl -0.2668512 12.7511475
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Variance components
***************************************
ω²_V ω²_Cl σ_inter_RespPK σ_slope_RespPK
ω²_V 378.64174 14.83533 51.14649 269.76601
ω²_Cl 14.83533 338.73284 90.52798 91.56249
σ_inter_RespPK 51.14649 90.52798 1082.56615 725.21291
σ_slope_RespPK 269.76601 91.56249 725.21291 892.90492
*********************************************
Determinant, condition numbers and D-criterion
***********************************************
Determinant: 57264569164.007
D-criterion: 62.0841871782222
Condition number of the fixed effects: 98.7579745041842
Condition number of the random effects: 13.8859868390161
***************************************
Parameters estimation
***************************************
parametersValues SE RSE
μ_V 50.0000000 2.78175798 5.563516
μ_Cl 5.0000000 0.28603036 5.720607
ω²_V 0.2600000 0.06457386 24.836098
ω²_Cl 0.3400000 0.05516612 16.225328
σ_inter_RespPK 0.5000000 0.05010192 10.020383
σ_slope_RespPK 0.3872983 0.06227156 16.078448
References
Sukeishi, Asami, Kotaro Itohara, Atsushi Yonezawa, Yuki Sato, Katsuyuki
Matsumura, Yoshiki Katada, Takayuki Nakagawa, et al. 2022.
“Population Pharmacokinetic Modeling of GS-441524, the Active
Metabolite of Remdesivir, in Japanese COVID-19 Patients with Renal
Dysfunction.” CPT: Pharmacometrics & Systems
Pharmacology 11 (1): 94–103.
