Adaptive Optimal Design in PET Occupancy Studies
Stefano Zamuner (1), Vincenzo L. Di Iorio (1), Joakim Nyberg (2), Roger N. Gunn (3), Vincent J. Cunningham (3), Andrew Hooker (2) and Roberto Gomeni (1)
(1) GlaxoSmithKline, Clinical Pharmacokinetics/Modeling&Simulation, Verona, Italy. 2Div. of Pharmacokinetics and Drug Therapy, Dept. of Pharmaceutical Biosciences, Uppsala University, Sweden. (3) GlaxoSmithKline, Clinical Imaging Centre, Hammersmith, UK.
Background: To increase the efficiency of trials in drug development, optimal experimental design has been used to successfully optimize dose allocation and sampling schedule [1,2]. Adaptive optimal design has recently been proposed as a method to improve the assessment of receptor occupancy time-courses in PET experiments . In this work we have further developed this concept, to include the optimisation of dose and also improve the adaptation/optimization algorithm. In addition, a kon-koff model using the binding potential (BP) estimates from PET studies  has been applied to account for baseline inter-subject variability in these experiments.
Aim: To investigate advantages of adaptive optimal designs vs. traditional designs with fixed or educated selection of PET scan allocations, when optimizing over both sampling schedule and dose.
Methods: Adaptive optimization was performed on the following PK-BP model (kon=0.088 hrs-1 and koff=0.221 hrs-1, BP0=3, inter-subject variability=30%, proportional error model):
dBP/dt=koff·BP0 - (Cp·kon+koff)·BP
A total of 12 subjects were considered with 5 possible doses (1.5, 3, 4, 6 and 8mg) and designs with 3, 4, and 6 adaptive steps were investigated. At each adaptive step, parameter estimates from the previous cohorts were determined and used to determine designs for the next cohort. The BP time-courses from these designs (empirical dummy using Tmax and trough, educated and optimal) were then simulated under the true model. Optimization was performed on scanning times only and scanning times and doses using a D-optimality criterion as implemented in the PopED software [2,5]. Information about previous cohorts were included in the optimal design program as a prior to the fisher information matrix.
Results: A clear improvement in terms of bias (SME), precision (CV) and accuracy (RMSE) of the population estimates (Kon and koff) was found when comparing dummy vs. educated vs. optimal. Unbiased mean estimates were found for the optimal designs; a great improvement in accuracy was found when comparing optimal vs. dummy designs (25-30 fold) and still a significant improvement was found when comparing optimal vs. educated designs (2-3 fold). No clear advantages were found when optimizing both time and dose. The number of adaptive steps was less influential on design performance than the method of designing the next step. No improvement was obtained for inter-subject variability estimates when comparing optimal vs. non optimal designs.
Discussion: Our results indicate that adaptive optimal design of PET occupancy studies provides more information on the PK-Occupancy relationship. In this work, doses were initially selected at high, medium and low occupancy levels based on previous knowledge of the system. Consequently, optimization of dose was not found to influence the results. In experiments where initial dose selection is misleading it is expected that dose optimization will have a greater impact.
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