Global Sensitivity Analysis in Physiologically Based Kinetic Modeling • pksensi

pksensi implements the global sensitivity analysis workflow to investigate the parameter uncertainty and sensitivity in physiologically based kinetic (PK) models, especially the physiologically based pharmacokinetic/toxicokinetic model with multivariate outputs. The package also provides some functions to check the convergence and sensitivity of model parameters.

Through pksensi, you can:

Run sensitivity analysis for PK models in R with script that were written in C or GNU MCSim.
Decision support: The output results and visualization tools can be used to easily determine which parameters have “non-influential” effects on the model output and can be fixed in following model calibration.

Installation

You can install the released version of pksensi from CRAN with:

install.packages("pksensi")

And the development version from GitHub with:

# install.packages("remotes")
remotes::install_github("nanhung/pksensi")

This package includes a function that can help you install GNU MCSim more easily through the function mcsim_install().
All updated details can be found in NEWS.md.
NOTE: Windows users need to install Rtools40 to compile the model code.

Workflow

Note: The parameter correlation (e.g., V_max and K_M in metabolism) might be an issue in the global sensitivity analysis. If you have experiment data, suggest using small datasets as a sample in Markov Chain Monte Carlo Simulation. Then, check correlation before conducting the sensitivity analysis. The issue will try to address in the future version.

Example

This is a basic example of applying pksensi in one-compartment pbtk model:

library(pksensi)

Step 1. Construct 1-cpt pbtk model

pbtk1cpt <- function(t, state, parameters) {
  with(as.list(c(state, parameters)), {
    dAgutlument = - kgutabs * Agutlument
    dAcompartment = kgutabs * Agutlument - ke * Acompartment
    dAmetabolized = ke * Acompartment
    Ccompartment = Acompartment / vdist * BW;
    list(c(dAgutlument, dAcompartment, dAmetabolized), 
         "Ccompartment" = Ccompartment) 
  })
}

Step 2. Define initial conditions, output time steps and variable

initState <- c(Agutlument = 10, Acompartment = 0, Ametabolized = 0)
t <- seq(from = 0.01, to = 24.01, by = 1)
outputs <- c("Ccompartment")

Step 3. Generate parameter matrix

3.1. (Optional) Extract parameter value from httk package

library(httk)
pars1comp <- (parameterize_1comp(chem.name = "acetaminophen"))
#> Human volume of distribution returned in units of L/kg BW.

3.2. Set parameter distributions

q <- c("qunif", "qunif", "qunif", "qnorm")
q.arg <- list(list(min = pars1comp$Vdist / 2, max = pars1comp$Vdist * 2),
              list(min = pars1comp$kelim / 2, max = pars1comp$kelim * 2),
              list(min = pars1comp$kgutabs / 2, max = pars1comp$kgutabs * 2),
              list(mean = pars1comp$BW, sd = 5))

3.3. Create parameter matrix

set.seed(1234)
params <- c("vdist", "ke", "kgutabs", "BW")
x <- rfast99(params, n = 200, q = q, q.arg = q.arg, replicate = 1)

Step 4. Conduct simulation (will take few minutes with more replications)

out <- solve_fun(x, time = t, func = pbtk1cpt, initState = initState, outnames = outputs)
#> Starting time: 2022-01-13 09:47:44
#> Ending time: 2022-01-13 09:47:52

Step 5. Uncertainty analysis

pksim(out)  # Use to compare with "real" data (if any)

Step 6. Check and visualize the result of sensitivity analysis

plot(out)   # Visualize result

check(out)  # Print result to console
#> 
#> Sensitivity check ( Index > 0.05 )
#> ----------------------------------
#> First order:
#>  vdist ke kgutabs 
#> 
#> Interaction:
#>  vdist ke kgutabs 
#> 
#> Total order:
#>  vdist ke kgutabs 
#> 
#> Unselected factors in total order:
#>  BW 
#> 
#> 
#> Convergence check ( Index > 0.05 )
#> ----------------------------------
#> First order:
#>   
#> 
#> Interaction:
#>   
#> 
#> Total order:
#>

Citation

To cite pksensi in publications use:

  Hsieh, N-H., Reisfeld B., and Chiu W.A., (2020). pksensi: An R
  package to apply global sensitivity analysis in physiologically based
  kinetic modeling SoftwareX, 12, 100609.
  https://doi.org/10.1016/j.softx.2020.100609

A BibTeX entry for LaTeX users is

  @Article{,
    title = {{pksensi}: An R package to apply global sensitivity analysis in physiologically based kinetic modeling},
    author = {Nan-Hung Hsieh and Brad Reisfeld and Weihsueh A. Chiu},
    journal = {SoftwareX},
    year = {2020},
    volume = {12},
    pages = {100609},
    doi = {10.1016/j.softx.2020.100609},
  }