Pharmacokinetic/pharmacodynamic (PK/PD) modelling is used to increase the understanding of drug concentration time courses and their interaction with the considered physiological response(s). PK/PD modelling is used mainly for data from pre-clinical and clinical trials during the development of a new drug but also for validation purposes during drug approval processes. Estimated parameter values can be used to classify, rank and evaluate drugs and fitted models can, e.g., be used to analyse the physiological response to different dosing regimes.
To incorporate differences in test subjects (e.g. higher or lower metabolism), some model parameters are typically considered to be distributed in the population. These parameters are assumed to follow a probabilistic model by hyperparameters, typically mean values and a covariance matrix of a normal or log-normal distribution. Together, the model for the data and the parameters create a hierarchy. This leads to hierarchical PK/PD models which are more commonly known as population PK/PD models or nonlinear-mixed effects (NLME) models.
A crucial part of my work with PK/PD models is uncertainty quantification which can be used as a foundation for the design of new experiments (e.g. to determine which additional measurements potentially lead to the most increase in information) or to better discern which parameters are hard to estimate from data.
Practitioners often apply methods based on maximum likelihood estimators (MLEs) for parameter estimation in PK/PD models. The main reason being that these methods deliver fast results. However, these are based on normal distribution approximations, as the parameter estimation problem cannot be solved analytically. Especially variance parameters, which are part of the hyperparameters in hierarchical PK/PD models, often have non-zero mass around zero and are bounded from below at zero. This can lead to their posterior distribution being far from normal distributed and optimization techniques used in MLE-based methods can experience numerical issues. As part of my PhD studies, I am using Bayesian methods, explicitly Hamiltonian Monte Carlo, to estimate parameters in PK/PD models to acquire a full picture of the posterior distribution of the estimated parameters. This allows me to fully explore the uncertainty present in the model fit while avoiding problematic topics as normal distribution approximations or numerical difficulties due to parameter values close to their lower bound.
Most considered PK/PD models are based on ordinary differential equations (ODEs) and the nature of Hamiltonian Monte Carlo requires the repeated solution of these ODEs for each iteration. This makes parameter estimation for these models time-intensive. Additionally, multiple instances of the same estimation process need to be run to assess the quality of the resulting distribution of parameter estimates.
To ease the development of new and useful models and to be able to properly assess uncertainty in these models, I hereby apply for computer resources to run the parameter estimation software efficiently.