Evaluation of the Pre-Posterior Distribution of Optimized Sampling Times for the Design of Pharmacokinetic Studies

Information theoretic methods are often used to design studies that aim to learn about pharmacokinetic and linked pharmacokinetic–pharmacodynamic systems. These design techniques, such as D-optimality, provide the optimum experimental conditions. The performance of the optimum design will depend on the ability of the investigator to comply with the proposed study conditions. However, in clinical settings it is not possible to comply exactly with the optimum design and hence some degree of unplanned suboptimality occurs due to error in the execution of the study. In addition, due to the nonlinear relationship of the parameters of these models to the data, the designs are also locally dependent on an arbitrary choice of a nominal set of parameter values. A design that is robust to both study conditions and uncertainty in the nominal set of parameter values is likely to be of use clinically. We propose an adaptive design strategy to account for both execution error and uncertainty in the parameter values. In this study we investigate designs for a one-compartment first-order pharmacokinetic model. We do this in a Bayesian framework using Markov-chain Monte Carlo (MCMC) methods. We consider log-normal prior distributions on the parameters and investigate several prior distributions on the sampling times. An adaptive design was used to find the sampling window for the current sampling time conditional on the actual times of all previous samples.