Cost-constrained optimal sampling for system identification in pharmacokinetics applications with population priors and nuisance parameters.

Pharmacokinetics (PK) applications can be seen as a special case of nonlinear, causal systems with memory. There are cases in which prior knowledge exists about the distribution of the system parameters in a population. However, for a specific patient in a clinical setting, we need to determine her system parameters so that the therapy can be personalized. This system identification is performed many times by measuring drug concentrations in plasma. The objective of this work is to provide an irregular sampling strategy that minimizes the uncertainty about the system parameters with a fixed amount of samples (cost constrained). We use Monte Carlo simulations to estimate the average Fisher's information matrix associated to the PK problem, and then estimate the sampling points that minimize the maximum uncertainty associated to system parameters (a minimax criterion). The minimization is performed employing a genetic algorithm. We show that such a sampling scheme can be designed in a way that is adapted to a particular patient and that it can accommodate any dosing regimen as well as it allows flexible therapeutic strategies.