R/NONMEM Toolbox for Simulation from Posterior Parameter (Uncertainty) Distributions
Gibiansky, Leonid, Marc R. Gastonguay
Metrum Institute, Tariffville, CT, USA
Background: Model-based simulations are now a necessary part of the drug development process. They facilitate evaluation of the predictive ability of the model, optimization of study designs (dosing, sampling, sample size, probability of success, etc.), and prediction of possible ranges of study outcomes under various conditions. Model parameters (and models) are always known with some level of imprecision (uncertainty). Neglecting this uncertainty may lead to falsely narrow model prediction intervals, designs that are not robust to model assumptions, and biased simulation conclusions. Uncertainty in the current state of knowledge can be incorporated into the simulation framework quantitatively and explicitly as posterior probability distributions, thus allowing more realistic predictions. This also enables assessment of global sensitivity of simulation (trial) outcomes to underlying assumptions about model parameters (and even the model itself). The application of these methods to models developed in NONMEM (GloboMax/ICON, Ellicott City, MD) has been limited due to the lack of the off-the-shelf software that would allow easy and efficient implementation.
Methods: Parameter uncertainty was implemented as an additional level in the non-linear mixed effects model hierarchy. Simulations from posterior probability distributions across all parameters were implemented using R (R Development Core Team; www.r-project.org), with the system model simulation implemented in NONMEM.
Results: A toolbox of several R scripts that allow for an easy adaptation to a particular project was created. Simulations from posterior distributions were implemented in three steps. First, posterior parameter distributions were simulated. Fixed-effect parameters were simulated from a multivariate normal distribution. Inter-subject and residual variance parameters were simulated from inverse Wishart or inverse Chi-square distributions. Modes of these distributions reflected the expected values of the population parameters while the variance-covariance matrix (for the multivariate normal distribution) and degrees of freedom (for the inverse Wishart or inverse Chi-square distributions) reflected uncertainty of these expectations. Results of the parameter simulations were saved as ASCII parameter files. Alternatively, parameter files could be created outside of the toolbox by sampling from posterior distributions created by MCMC or bootstrap methods. Second, for each set of parameters from the parameter file, a NONMEM simulation control stream was created and run. Finally, simulation results were either output to text files for future data analysis, or summarized using custom R functions.
Conclusions: A flexible and relatively easy to use R/NONMEM package for simulating from posterior distributions has been developed (code available from authors).