Development of a Bayesian Adaptive Sampling Time strategy for PK studies with constrained number of samples to ensure accurate estimates.
B. Boulanger (1), A. Jullion (1), J. Jaeger (2), M. Lovern (1) and C. Otoul (1)
(1) Pharmacometrics, UCB Pharma, Belgium. (2) Universitť de Strasbourg.
Background: When designing a PK study in which both the typical pharmacokinetic behavior and between-subject variability of the compound are poorly-understood, the search of Bayesian optimal design suggests using large numbers of sampling times and patients to ensure credible estimation of model parameters. When, for ethical reasons, the number of samples per patient and the number of patients is constrained (ie small children), then finding an optimal sampling strategy may be problematic. Our objective was to develop a robust methodology for optimizing each patient's sample times based upon the PK information available from preceding subjects, and thereby simultaneously maximize the accuracy of parameter estimates and minimize the number of samples. The approach we employed was the Bayesian Adaptive Sampling Times (BAST) strategy, for which it was assumed that the functional form of the model was known with perfect certainty.
Methods: The method envisaged here can be decomposed into several steps as classically encountered in adaptive designs. First, priors on the parameters are established based on previous data or information. Based on these priors, an optimal design for non-linear mixed effect models is determined, using Pfim. Second, after collection of concentration values on a patient or a cohort of patients, a Bayesian PK model (Winbugs) is fitted to the data using the model and the priors elicited previously. Third, the posteriors from the Bayesian fit are then used as prior for finding the optimal design for the next patient of cohort. This process is iterated each time a patient is recruited and continues until confidence on parameter estimates is deemed satisfactory.
Results: This approach was found to be very efficient for estimating the parameters of a pharmacokinetic model. When the guesses about the priors are wrong or very uninformative, then the BAST provides significantly more accurate estimates of the parameters than those derived from a fixed design based upon the same (wrong) assumptions. When the guess is correct, then the BAST doesn't impact the original optimal plan and estimates are as accurate as the fixed design without loss of power. The BAST method also appears to converge rapidly to the optimal sampling schedule.
Conclusion: The BAST approach is found to be an easy and efficient way to obtain reliable estimates of PK parameters under uncertainty and sampling restrictions.