Model‐based analyses of bioequivalence crossover trials using the stochastic approximation expectation maximisation algorithm

Abstract

In this work, we develop a bioequivalence analysis using nonlinear mixed effects models (NLMEM) that mimics the standard noncompartmental analysis (NCA). We estimate NLMEM parameters, including between-subject and within-subject variability and treatment, period and sequence effects. We explain how to perform a Wald test on a secondary parameter, and we propose an extension of the likelihood ratio test for bioequivalence. We compare these NLMEM-based bioequivalence tests with standard NCA-based tests. We evaluate by simulation the NCA and NLMEM estimates and the type I error of the bioequivalence tests. For NLMEM, we use the stochastic approximation expectation maximisation (SAEM) algorithm implemented in monolix. We simulate crossover trials under H(0) using different numbers of subjects and of samples per subject. We simulate with different settings for between-subject and within-subject variability and for the residual error variance. The simulation study illustrates the accuracy of NLMEM-based geometric means estimated with the SAEM algorithm, whereas the NCA estimates are biased for sparse design. NCA-based bioequivalence tests show good type I error except for high variability. For a rich design, type I errors of NLMEM-based bioequivalence tests (Wald test and likelihood ratio test) do not differ from the nominal level of 5%. Type I errors are inflated for sparse design. We apply the bioequivalence Wald test based on NCA and NLMEM estimates to a three-way crossover trial, showing that Omnitrope®; (Sandoz GmbH, Kundl, Austria) powder and solution are bioequivalent to Genotropin®; (Pfizer Pharma GmbH, Karlsruhe, Germany). NLMEM-based bioequivalence tests are an alternative to standard NCA-based tests. However, caution is needed for small sample size and highly variable drug.