Optimal design of in vitro time kill curve experiments for the evaluation of antibiotic effects.
Anders Kristoffersson, Andrew Hooker, Mats O. Karlsson, Lena E. Friberg
Dept of Pharmaceutical Biosciences, Uppsala University, Sweden
Objectives: In order to integrate information of antibiotic effects from in vitro time kill curve experiments semi-mechanistic pharmacokinetic-pharmacodynamic (PKPD) models are of interest . While informative compared to basic MIC measurements, that provide only a point estimate of the antibiotic effect, these experiments are labour intensive as bacteria counts are measured at a range of different concentrations and time points. This work therefore aims at evaluating currently used experimental designs and providing generalized and efficient experimental plans for future time-kill curve experiments of antibiotics.
Methods: A previously developed model  was implemented in the PopED optimal design software . The original experimental design for five different antibiotics includes 9 unique sampling points studied at 9-10 concentrations. The optimization of the sampling schedule incorporated all five antibiotics in order to give a general design. A D-optimal design criterion with a reduced FIM calculation was utilized with parameters independent across sub-models. Designs were compared based on efficiency (the ratio of the FIM determinant between the optimized and the base design raised to the inverse of the number of unfixed parameters). Time dependent autocorrelation between sample points within one experiment was evaluated by implementing AR(1) residual autocorrelation  for the PKPD model using NONMEM 7 .
Results: The autocorrelation in the original model was high, a half-life of 7.5 h was estimated for these 24 h experiments and the impact on the optimal design was pronounced. When autocorrelation was considered the number of unique sample points increased from five to seven. The efficiency for the optimal design developed without consideration of autocorrelation was 102% when evaluated on a model with autocorrelation while the corresponding efficiency for the design that considered autocorrelation was 120%.
Conclusions: Inclusion of autocorrelation had a pronounced influence on the design. A design produced without consideration of autocorrelation had low performance on a model with autocorrelation. The determined general experimental setup for in vitro time kills curve experiments provided increased power at decreased experimental cost by a reduction of sampling points and a decrease in estimated parameter uncertainty. The proposed design was sufficient for a wide range of antibiotic classes, indicating the potential for application to novel antibiotics not previously studied.
 Nielsen EI, Viberg A, Lowdin E, Cars O, Karlsson MO, Sandstrom M. Semimechanistic Pharmacokinetic/Pharmacodynamic Model for Assessment of Activity of Antibacterial Agents from Time-Kill Curve Experiments. Antimicrob Agents Chemother. 2007 January 1, 2007;51(1):128-36.
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 Karlsson M, Beal S, Sheiner L. Three new residual error models for population PK/PD analyses. Journal of Pharmacokinetics and Pharmacodynamics. 1995;23(6):651-72.
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