Robust Optimal Design for the Estimation of Hyperparameters in Population Pharmacokinetics

The expectation of the determinant of the inverse of the population Fisher information matrix is proposed as a criterion to evaluate and optimize designs for the estimation of population pharmacokinetic (PK) parameters. Given a PK model, a measurement error model, a parametric distribution of the parameters and a prior distribution representing the belief about the hyperparameters to be estimated, the EID criterion is minimized in order to find the optimal population design. In this approach, a group is defined as a number of subjects to whom the same sampling schedule (i.e., the number of samples and their timing) is applied. The constraints, which are defined a priori, are the number of groups, the size of each group and the number of samples per subject in each group. The goal of the optimization is to determine the optimal sampling times in each group. This criterion is applied to a one-compartment open model with first-order absorption. The error model is either homoscedastic or heteroscedastic with constant coefficient of variation. Individual parameters are assumed to arise from a lognormal distribution with mean vectorMand covariance matrixC. Uncertainties about theMandCare accounted for by a prior distribution which is normal forMand Wishart forC. Sampling times are optimized by using a stochastic gradient algorithm. Influence of the number of different sampling schemes, the number of subjects per sampling schedule, the number of samples per subject in each sampling scheme, the uncertainties onMandCand the assumption about the error model and the dose have been investigated.