Sequential versus simultaneous optimal experimental design on dose and sample times
Joakim Nyberg, Mats O Karlsson, Andrew Hooker
Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Background: To increase the efficiency of trials in drug development, optimal experimental design has been used to optimize the sampling schedule. This produces a sampling schedule that will give the most information possible, given a model . In addition, optimizing other model dependent variables, e.g. dose, has recently been possible with some optimal design software .
Aim: To investigate different optimization strategies, simultaneous vs. sequential optimization, when optimizing over both sampling schedule and dose.
Methods: The PKPD model used is a one-compartment PK model with first-order absorption and linear elimination linked with a sigmoidal Emax PD model . Dose and sampling times are varied between groups with one dose, 2 PK and 3 PD samples taken within each group. Initial dose and sample times are evenly spread across the design space. Optimization is performed in POPED  on 1-5 groups with 20 individuals each. Three different optimization strategies are used; (i) dose-sampling times sequentially, (ii) sampling times-dose sequentially and (iii) dose-sampling times at the same time. When using the sequential approach, e.g. dose first, the dose is fixed after optimization and the optimal sampling schedule is calculated with the fixed optimized dose.
Results: Different doses give different optimal sampling schedules and vice versa. When optimizing the dose first and then sampling schedule, the efficiency  in some cases was 55 % of the efficiency using the simultaneous optimization technique. Sequential optimization of time first has at minimum in our setup an efficiency of 75 % of the simultaneous approach. The coefficients of variance (CV) of the model parameters are increased in most of the parameters when optimizing in sequence, with some parameters this increase can be as much as 190 %.
Discussion: Optimizing over both dose and sampling times could change the optimal experimental design with respect to sampling schedules and hence a whole trial. The large differences in efficiency with different optimization strategies indicate that these strategies are of importance. Furthermore, the decrease in efficiency also reflects an over-all increase in CV of the model parameters indicating a higher uncertainty to the model.
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