Anders N. Kristofferson, Andrew C. Hooker, Mats O. Karlsson, Lena E. Friberg
Department of Pharmaceutical Biosciences, Uppsala University, Sweden
Objectives: Residual autocorrelation (AC) is shown to be of importance in optimal experimental design with different magnitudes of correlation resulting in markedly different designs [1]. While always present to some degree, the magnitude of AC in experimental data may be hard to estimate accurately [2]. This work aims to design efficient ciprofloxacin time-kill curve experiments robust in the vicinity of AC earlier quantified in similar experiments [3].
Methods: A previously developed model describing the kill and growth of a wildtype E. coli strain under exposure of ciprofloxacin [4] was implemented in the optimal design software PopED [5]. The model features two proportional errors, one independent and one shared either across replicate observations only (L2 correlated), or AR(1) correlated [2]. The D-optimal design of the sampling schedule over 24 h was investigated for AC half-lives (t1/2) ranging from 0 to 60h. In the case of no AC both a reduced model with one independent error and a full model with L2 correlated duplicate samples were investigated. Assuming an AC t1/2 of 7.5h [3] the design was further optimized for the variables study length, time of night pause, and the number of experimental concentrations vs. the number of samples per concentration.
Results: The scenarios of L2 correlated duplicate samples and no replicate samples resulted in identical designs. Higher AC resulted in less clustering and a wider spread of the sampling times, the design was constant for AC t1/2 of 1.5 h or greater. Evaluating models assuming AC for designs optimized without AC resulted in a distinctly larger information drop than the reverse case. At an AC t1/2 of 7.5 h, and an experimental duration of 32h, an optimal design including a 14h nighttime pause was computed. Â Compared to the current study design, the optimized design prolonged the night time pause and decreased the number of samples per concentration from 8 to 6 without an increase in parameter variance.
Conclusions: L2 correlated replicate errors may in optimal design be substituted by a single suitably scaled variance. Acknowledging AC resulted in a change of the optimal design and designs produced with AC were more robust to the lack of AC than the reverse. The optimal design remained stable across a wide range of AC t1/2, including the 7.5h t1/2Â found in similar experiments [3]. An optimized design was proposed decreasing the number of samples by 25% while maintaining parameter precision.
References:
[1] Nyberg J, Höglund R, Bergstrand M, Karlsson MO, Hooker AC. Serial correlation in optimal design for nonlinear mixed effects models. Submitted 2012.
[2] 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.
[3] Kristoffersson A, Hooker AC, Karlsson MO, Friberg LE. Optimal design of in vitro time kill curve experiments for the evaluation of antibiotic effects. 2011; Available from: PAGE 20 (2011) Abstr 2243 [www.page-meeting.org/?abstract=2243].
[4] Khan D, Lagerbäck P, Malmberg C, Cars O, Friberg LE. In silico predictions of in vitro growth competition experiments between wild type and mutant E.coli MG1655 exposed to ciprofloxacin. [Page abstract]. In press 2012.
[5] Nyberg J, Ueckert S, Karlsson MO, Hooker A. PopED v. 2.11. 2010.
Reference: PAGE 21 (2012) Abstr 2532 [www.page-meeting.org/?abstract=2532]
Poster: Study Design