Evaluation of designs for biosimilarity crossover trials analysed by nonlinear mixed effects models
Anne Dubois (1), Thu Thuy Nguyen (1), Philip Lowe (2) and France Mentré (1)
(1) UMR 738, INSERM - University Paris Diderot, Paris, France; (2) Modeling and Simulation Department, Novartis Pharma AG, Basel, Switzerland
Objectives: To assess the similarity between different formulations of a biologic drug, a pharmacokinetic (PK) bioequivalence trial is usually performed as for chemical drugs [1,2]. Nonlinear mixed effects models (NLMEM) can be used to analyse such data [3,4]. Before performing these trials, it is important to define an appropriate design which has an impact on the precision of parameter estimates and the power of tests. The approach for design evaluation and optimisation based on the expression of the Fisher information matrix (MF) was extended to NLMEM including within subject variability (WSV) and discrete covariates changing between periods [5]. The power of equivalence Wald test can be computed using the predicted standard error (SE). These developments are implemented in the R function PFIM 3.2 [6]. Our objectives were to evaluate and apply this evaluation design approach to biosimilarity crossover trials.
Methods: We simulated 1000 replicates of crossover trials using simulation settings of Dubois et al [4]. Crossover trials with 2 and 4 periods were simulated under the equivalence test H0 with different numbers of subjects (N) and of samples, and two variability levels. We estimated the NLMEM parameters by the SAEM algorithm implemented in MONOLIX 2.4 [7,8]. We compared the predicted SE obtained by PFIM to the distribution of SE estimated by MONOLIX and the corresponding empirical SE. We then computed the power of equivalence test on clearance (CL) for different H1 and simulated designs. We applied this approach to a crossover trial on 16 monkeys comparing 2 formulations of drug X. We evaluated then optimised its design by NLMEM using about twice less samples than originally.
Results: For all simulated scenarii, the predicted SE computed by PFIM and the empirical SE obtained from simulations are close, for all fixed effects including treatment, period and sequence effects. For variance parameters, predicted SE of WSV are slightly underestimated even for 4-period trials. The power of equivalence test decreases with N or for high variability. For the application, the predicted power of the equivalence test on CL is 90% and 85%, for the original and optimised designs.
Conclusion: This extension of MF for NLMEM is relevant to predict SE of treatment effect and power in crossover trials. PK similarity trials analysed through NLMEM allow sparse designs and can be performed in patients. PFIM can be used to efficiently design these trials.
References:
[1] FDA. Guidance for industry - statistical approaches to establishing bioequivalence. Technical report, FDA 2001.
[2] EMEA. Guideline on the investigation of bioequivalence. Technical report, EMEA 2010
[3] Dubois A, Gsteiger S, Pigeolet E and Mentré F. Bioequivalence tests based on individual estimates using non compartmental of model-based analyses: evaluation of estimates of sample means and type I error for different designs. Pharmaceutical Research. 2010; 27:92-104
[4] Dubois A, Lavielle M, Gsteiger S, Pigeolet E and Mentré F. Model-based analyses of bioequivalence crossover trials using the SAEM algorithm. Statistics in Medicine. 2010; in press
[5] Nguyen TT, Bazzoli C and Mentré F. Design evaluation and optimization in crossover pharmacokinetic studies analysed by nonlinear mixed effects models: application to bioequivalence or interaction trials. Poster for American Conference on Pharmacometrics. 2009, Foxwoods, Connecticut, USA
[6] http://www.pfim.biostat.fr/
[7] Panhard X and Samson A. Extension of the SAEM algorithm for nonlinear mixed effects models with two levels of random effects. Biostatistics. 2009; 10:121-135
[8] www.monolix.org
