2013 - Glasgow - Scotland

PAGE 2013: Study Design
Cyrielle Dumont

Influence of the ratio of the sample sizes between the two stages of an adaptive design: application for a population pharmacokinetic study in children

Cyrielle Dumont (1,2), Marylore Chenel (2), France Mentré (1)

(1) UMR 738, INSERM, University Paris Diderot, Paris, France; (2) Department of Clinical Pharmacokinetics, Institut de Recherches Internationales Servier, Suresnes, France

Objectives: Nonlinear mixed-effect models are used to analyse pharmacokinetic (PK) data during drug development, notably in pediatric studies[1,2]. To optimise their design, adaptive designs[3], among which two-stage designs, allow to provide flexibility and could be more efficient than fully adaptive design[4]. We investigated, with a simulation approach, the impact of a two-stage design on the precision of parameter estimation, by varying sample size ratio of each stage, when the ‘true’ and the a priori PK parameters are different.

Methods: A two-stage design for a population PK study proceeds as follows. At the 1st stage, from a model and a priori population parameters Ψ0, data for N1 children are collected based on design ξ1, optimised with Ψ0. The same design is assumed for all children. At the 2nd stage, ξ2 for the remaining N2 children is optimised using a combined information matrix with the estimated Ψ1 after 1st stage. At the end, Ψ2 parameters are estimated using data of N=N1+N2 children. We evaluated this approach and the influence of the ratio between N1 and N2 by a clinical trial simulation in R. The PK model was a 2-compartment model with 1st-order absorption. Optimal one- and two-stage designs were derived using PFIM[5], assuming N=60 children with the same design (5 sampling times) at each stage. We assumed different ‘true’ Ψ* and a priori Ψ0 parameters. From Ψ0, we optimised ξ1. From 10 simulated data sets, 10 vectors Ψ1 were estimated with SAEMIX[6]. ξ2 was then optimised for each Ψ1. 10 simulations were performed with each of the 10 ξ2 designs. We obtained 100 data sets. Relative root mean square errors (RRMSE) for the 100 estimated Ψ2 were compared for the extremum designs 60-0 (ξ1) and 0-60 (ξ*, optimal design), and two-stage designs: 50-10 (ξ50-10), 30-30 (ξ30-30), 10-50 (ξ10-50). The standardized RRMSE was calculated for each parameter and each design as the RRMSE divided by the RRMSE of ξ*. For each design, mean standardized RRMSE was then computed.

Results: The mean standardized RRMSE equalled 2.48 for ξ1 optimised with the wrong Ψ0. Hopefully, the mean standardized RRMSE of the two-stage designs were very close to the one for ξ*, and equalled 1.15, 1.06, 1.07 for ξ10-50, ξ30-30 and ξ50-10, respectively.

Conclusions: The two-stage designs allowed to compensate from the unsatisfactory result obtained for ξ1. When the size of the 1st cohort was small, the result was slightly worse. The design with N1=N2 appears to be a good compromise.

References:
[1] Mentré F, Dubruc C, Thénot J.P. Population pharmacokinetic analysis and optimization of the experimental design for Mizolastine solution in children. Journal of Pharmacokinetics and Pharmacodynamics, 2001; 28(3): 299-319.
[2] EMEA. Guideline on the role of pharmacokinetics in the development of medicinal products in the paediatric population. Scientific guideline, 2006.
[3] Foo L.K, Duffull S. Adaptive optimal design for bridging studies with an application to population pharmacokinetic studies. Pharmaceutical Research, 2012; 29(6): 1530-1543.
[4] Federov V, Wu Y, Zhang R. Optimal dose-finding designs with correlated continuous and discrete responses. Statistics in Medicine, 2012; 31(3): 217-234.
[5] www.pfim.biostat.fr.
[6] Comets E, Lavenu A, Lavielle M. SAEMIX, an R version of the SAEM algorithm, Population Approach Group in Europe, 2011; Abstr 1695 [www.page-meeting.org/default.asp?abstract=2173].




Reference: PAGE 22 (2013) Abstr 2778 [www.page-meeting.org/?abstract=2778]
Poster: Study Design
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