Extension of the SAEM algorithm and evaluation of Wald and likelihood ratio tests for interaction or bioequivalence studies
A. Dubois (1), M. Lavielle (2), S. Gsteiger (3), E. Pigeolet (3) and F. Mentré (1)
(1) INSERM, U738, Paris, France; University Paris Diderot, Paris, France.(2) INRIA, Saclay, France.(3) Novartis Pharma AG, Basel, Switzerland.
Objectives: The context of our work is the analysis of pharmacokinetic (PK) crossover trials using nonlinear mixed effects model (NLMEM) in similar way as the recommendations for results based on non compartmental approach [1]. In that context, our objectives are to adapt the SAEM algorithm and the MONOLIX software for the analysis of crossover trials, to develop the likelihood ratio test (LRT) for bioequivalence and to evaluate the type I error of global comparison and bioequivalence tests in crossover trials using those developments.
Methods: We extend the SAEM algorithm to any number of periods and to any structure of the matrix of random effects, based on the work done by Panhard and Samson [2]. This extended SAEM has been implemented in the version 2.4 of MONOLIX. For bioequivalence trials, Wald test based on NLMEM has been developed [3, 4] and we propose an extension of the LRT. The extension of SAEM and the type I error of these tests are evaluated by simulation using 1000 replicates. We use the theophylline example with a one-compartment PK model. Two-period two-sequence crossover trials are simulated under the null hypothesis with 40 subjects and two different numbers of samples. We call rich design the designs with 10 samples per subject and sparse design the designs with 3 samples per subject. We simulate with treatment effect on clearance and volume of distribution. We use two levels of between-subject (BSV) and within-subject variability (WSV): BSV=20%, WSV=10% and BSV=50%, WSV=15%.
Results: Estimations of all parameters by SAEM are satisfactory for both variability settings and both evaluated designs. The type I error of comparison and bioequivalence tests are rather similar, as the results of Wald tests and LRT. We present here results on bioequivalence Wald tests for the clearance. The type I errors are respectively 5.3% (6.6%) and 5.6% (8.6%) for the low (high) variability, respectively for the rich and sparse design.
Conclusion: The extension of SAEM is accurate for crossover trials that can be analyzed with NLMEM. The simulation study does not show advantage to use the LRT instead of the Wald test since the results for the type I error are similar and the LRT is time consuming. Further work is needed for the use of these tests for design with little information as a slight increase of the type I error was found for the sparse design with high variability.
References:
[1] FDA. Guidance for industry - statistical approaches to establishing bioequivalence. Technical report, FDA 2001.
[2] 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.
[3] Panhard X and Mentré F. Evaluation by simulation of tests based on non-linear mixed-effects models in pharmacokinetic interaction and bioequivalence crossover trials. Statistics in Medicine 2005, 24: 1509-1524.
[4] Panhard X Taburet AM, Piketti C and Mentré F. Impact of modeling intra-subject variability on tests based on non-linear mixed-effects models in crossover pharmacokinetic trials with application to the interaction of tenofovir on atazanavir in HIV patients. Statistics in Medicine 2007, 26: 1268-1284.
