Faster ADVAN-style Analytical Solutions for

Simulations From Common Pharmacokinetic Models

PKADVAN package

INTRODUCTION• ADVAN-style analytical solutions for the 1, 2, and 3 compartment linear

pharmacokinetic models of intravenous bolus, infusion, and first-orderabsorption have been presented by Abuhelwa et al [1] and were coded inin the R programming language [2] and have been shown to have speedadvantages over solutions using differential equation solvers.

• The ADVAN-style analytical solutions are used to simulate the time-course of drug amounts in each compartment of a referencepharmacokinetic model and they “advance” the solution of apharmacokinetic model from one time point to the next, allowing for anydose or time-changing covariate factors to be accounted for.

1 Australian Centre for Pharmacometrics, University of South Australia Email: ahmad.abuhelwa@mymail.unisa.edu.au

METHODS• The ADVAN-style analytical solutions were derived using Laplace

transforms and then were coded in the C++ programming language andintegrated into R using the Rcpp package attributes [3].

• The integrated R/C++ ADVAN-style analytical functions were built into anopen-source R package (“PKADVAN” package).

• To assess computational speed, simulations for 1000 subjects using threecompartment IV bolus, infusion, and first-order absorption models wereperformed and compared to relative computational speed of theequivalent R-coded functions. For each subject, two doses weresimulated with the evaluations performed at 1 hour time intervals for 2days.

• All pharmacokinetic models incorporated into the “PKADVAN” packagehave been validated against the commercially available populationpharmacokinetic modelling software NONMEM.

• A total of 26 pharmacokinetic models were incorporated into the“PKADVAN” package library including the basic models published byAbuhelwa et al [1]. A list of all the models is presented in Table 1.

• To perform pharmacokinetic simulations using the “PKADVAN” package,two simple steps are required: (1) Supply a NONMEM-style simulationdata frame with the individual pharmacokinetic parameters including anycovariate effects on the PK parameters (2) Call the “PKADVAN” functionof the respective model to process simulations.

• The NONMEM-style data frame should have the following columns: ID,TIME, AMT, in addition to the individual pharmacokinetic parameters ofthe respective pharmacokinetic model (e.g., CL, V, Q).

• The PKADVAN functions returns the drug amounts in the respectivecompartments and the individual predicted concentrations (IPRED) in thecentral compartment of the pharmacokinetic system.

• The PKADVAN functions are capable of simulating arbitrary dosingregimens and can account for time-changing covariate structures;however, covariate effects on respective parameters must be calculatedprior processing simulations.

• All the PKADVAN functions were validated against NONMEM and bothoutputs were identical.

• Stochastic population pharmacokinetic model simulations using thePKADVAN functions are comparable to NONMEM. An example outputusing PKADVAN package versus NONMEM is presented in Figure 1.

• The “PKADVAN” package is available on GitHub and can be downloadedby scanning the quick reference (QR) code provided above or throughthe package URL: ( https://github.com/abuhelwa/PKADVAN_Rpackage ).

• Users are encouraged to read the package documentation and run thesimulation examples provided with the package.

REFERENCES

AIMS

Ahmad Y Abuhelwa1, David J.R Foster 1, Richard N Upton1

1. Abuhelwa AY, Foster DJ, Upton RN. 2015. ADVAN-style analytical solutions for common pharmacokinetic models. J Pharmacol Toxicol Methods 73:42-48.2. R Core Team. 2014. R: A Language and Environment for Statistical Computing R Foundation for Statistical Computing, Vienna, Austria.3. Eddelbuettel D, François R, Allaire J, Chambers J, Bates D, Ushey K. 2011. Rcpp: Seamless R and C++ integration. Journal of Statistical Software 40:1-18.4. Kümmel A, Abuhelwa AY, Dingemanse J, Krause A. PECAN, a Shiny application for calculating confidence and prediction intervals for pharmacokinetic

and pharmacodynamic models. The twenty-fifth Annual Population Approach Group Europe (PAGE) Meeting. 2016

Table 1. Pharmacokinetic models of the “PKADVAN” package library

APPLICATIONS

CONCLUSIONSWith its speed advantages and the capacity to handle arbitrary dosing regimens andcovariate structures, the “PKADVAN” package is expected to facilitate the investigationof a useful open-source software for modelling and simulating pharmacokinetic data.

• Simulations using the integrated R/C++ ADVAN-style analytical solutions were

substantially faster (8-34 times) than the equivalent R-coded functions (Table 2). Therelative speed of the integrated R/C++ functions was greater with the more complexmodels and with more extensive sample time evaluations (Table 2).

Table 2. Comparison of computation time: R-functions versus the integrated R/C++ PKADVAN functions

• The PKADVAN package can be used for performing simulations from stochasticpopulation pharmacokinetic models coded in R and incorporated into reactive ‘Shiny’web applications where speed is important as it allows for simulating largerpopulations without compromising the reactivity of the Shiny application.

• The PKADVAN package can be implemented for data fitting, and for calculatingconfidence and prediction intervals of pharmacokinetic models’ parameters [4].

• The PKADVAN package could be incorporated into an open-source mixed-effectmodelling framework to estimate population parameters where speed is alwaysdesirable.

TO DO LIST

The aims of this work were to:• Enhance the computational speed of the ADVAN-style analytical

functions through coding them in hybrid R/C++ programming languagesfor faster simulation processing.

• Present the ADVAN-style analytical functions in an R package,“PKADVAN” package, and make them available for the wider audience .

• Expand the “PKADVAN” package library to include other pharmacokineticmodels such as transit first-order absorption and metabolite models.

Implement steady-state functionality, as achieved with the SS and II data items inNONMEM. Implement analytical solutions for combined dosing regimens (e.g., IV bolusplus infusion).

Figure 1. Comparison of NONMEMand PKADVAN package simulationoutputs.

The median and 90% confidenceinterval of the concentration-timeprofiles of 1,000 simulated subjectsusing a two compartment-two transitfirst-order absorption model.Creatinine clearance was added as atime-changing covariate on centralclearance. Between subject variabilitywas added on all pharmacokineticmodel parameters. Proportional andadditive residual error model wasadded on the individual predictions.

The R-script for processing the simulations presented in this example are provided on GitHub.

Australian Centre for

Pharmacometrics

https://github.com/abuhelwa/PKADVAN_Rpackage