Two-stage adaptive designs in nonlinear mixed-effects models: an evaluation by simulation for a pharmacokinetic (PK) and pharmacodynamic (PD) model in oncology
Giulia Lestini (1), Cyrielle Dumont (1), France Mentré (1)
(1) IAME, UMR 1137, INSERM, University Paris Diderot, Paris, France
Objectives: Optimal design in population PKPD is based on prior information on the models and parameters. Adaptive designs [1,2] are a promising alternative to local or robust designs [3]. Two-stage designs are easier to implement than fully adaptive designs and can be as efficient [4]. Here, we compared by simulation one and two-stage designs using a PKPD model in oncology.
Methods: The PKPD model is the one developed for a TGF-β inhibitor [5]. We assumed that the model is known, and we defined two set of population parameters. A priori wrong values of the parameters, Ψ0, were obtained after an animal study and human scaled allometry as in [5]. “True” parameters, Ψ*, are those obtained in an clinical study [6].
We considered various designs with a total of N=50 patients with the same elementary design ξ in all patients within the same cohort (i.e. the same stage). We first consider a rich design ξrich with 6 sampling times. We then optimized various sparse design with 3 samples: i) ξ0 optimized with Ψ0, ii) ξ*optimized with Ψ*, iii) two-stage designs that combined N1=25 patients in first cohort with design ξ0 and N2=25 patients in second cohort with design ξ2, where ξ2 was optimized after the results of the first stage. Design optimization was performed using determinant of the Fisher Information Matrix (FIM) using PFIM 4.0 [7]. For the two-stage design prior information obtained after first stage was incorporated in the evaluation of FIM.
We simulated 100 datasets for each scenario using true parameters Ψ*. Parameters were then estimated using the SAEM algorithm in MONOLIX 4.3. Relative Bias (RB) and Relative Root Mean Square Error (RRMSE) were used to compare the various designs.
Results: RB and RRMSE were relatively small for designs ξrich and ξ*, whereas they were large with the design ξ0, showing first the importance of the prior parameters in the optimisation of the design and second the poor performance of the design if the choice is wrong. For the two-stage design we obtained results close to the one-stage design, ξ*, showing the ability of the two-stage design to correct the design after the first cohort.
Conclusions: With a two-stage design, results are close to those of the one-stage design using true parameters and are much better than those using wrong prior parameter. Study on the best balance between sizes of each cohort is ongoing.
This work was supported by the DDMoRe project (www.ddmore.eu).
References:
[1] Foo L, Duffull S. Adaptive optimal design for bridging studies with an application to population pharmacokinetic studies. Pharm Res (2012) 29(6): 1530 -1543.
[2] Dumont C, Chenel M, Mentré F. Two-stage optimal designs in nonlinear mixed effect models: application to pharmacokinetics in children. PAGE (2012) Abstr 2426 [www.page-meeting.org/?abstract=2426].
[3] Mentré F, Chenel M, Comets E, Grevel J, Hooker A, Karlsson M, Lavielle M, Gueorguieva I. Current use and developments needed for optimal design in pharmacometrics: a study performed among DDMoRe’s EFPIA members. CPT Pharmacometrics Syst Pharmacol (2013) 2(6): e46.
[4] Fedorov V, Wu Y, Zhang R. Optimal dose-finding designs with correlated continuous and discrete responses. Stat Med (2012) 31(3): 217 - 234.
[5] Gueorguieva I, Ogungbenro K, Graham G, Glatt S, Aarons L. A program for individual and population optimal design for univariate and multivariate response pharmacokinetic–pharmacodynamic models. Comput Methods Programs Biomed (2007) 86(1): 51 - 61.
[6] Gueorguieva I, Cleverly A, Stauber A, Pillay N, Rodon J, Miles C, Yingling J, Lahn M. Defining a therapeutic window for the novel TGF-β inhibitor LY2157299 monohydrate based on a pharmacokinetic/pharmacodynamic model. Br J Clin Pharmacol (2014) in press.
[7] www.pfim.biostat.fr
