New Model–Based Bioequivalence Statistical Approaches for Pharmacokinetic Studies with Sparse Sampling

Abstract

Introduction: In traditional pharmacokinetic (PK) bioequivalence analysis, two one-sided tests (TOST) are conducted on the area under the concentration-time curve and the maximal concentration derived using a non-compartmental approach. When rich sampling is unfeasible, a model-based (MB) approach, using nonlinear mixed effect models (NLMEM) is possible. However, MB-TOST using asymptotic standard errors (SE) presents increased type I error when asymptotic conditions do not hold. Methods : In this work, we propose three alternative calculations of the SE based on i) an adaptation to NLMEM of the correction proposed by Gallant, ii) the a posteriori distribution of the treatment coefficient using the Hamiltonian Monte Carlo algorithm, and iii) parametric random effects and residual errors bootstrap. We evaluate these approaches by simulations, for two-arms parallel and two-periods two-sequences cross-over design with rich (n=10) and sparse (n=3) sampling under the null and the alternative hypotheses, with MB-TOST.Results: All new approaches correct for the inflation of MB-TOST type I error in PK studies with sparse designs. The approach based on the a posteriori distribution appears to be the best compromise between controlled type I errors and computing times.Conclusion: MB-TOST using non-asymptotic SE controls type I error rate better than when using asymptotic SE estimates for bioequivalence on PK studies with sparse sampling.

Impact of model misspecification on model-based tests in PK studies with parallel design: real case and simulation studies

“…Indeed, it can be hard to compute individual AUC and if we only have a few points per subject. In an effort to leverage population data over time to inform predictions for individuals, a model-based alternative has been proposed [ 8 , 10 ], in which we build a structural PK model and use a non-linear mixed effect model (NLMEM) to estimate the treatment effect. The corresponding statistical model can be written as follows in the case of parallel studies: with: : time j for individual i ; : concentration for individual i at time ; : vector of parameters for individual i (typically of size 3 to 10); : non-linear structural PK model depending on ; : error model; : residual error; : fixed effect for parameter l ; : treatment covariate variable; : coefficient of treatment effect for parameter l ; : between subject random effect for parameter l ; : standard deviation of the inter-individual random effect for parameter l .…”

“…In this study, we used and compared three different methods of computation of SE in the MB approach, that are described below, and called ”Asympt”, ”Gallant” and ”Post”. These three methods have also been evaluated in the context of BE studies by Loingeville et al [ 10 ].…”

“…To address this, several methods of correction of the asymptotic standard errors have been suggested. Here, we use two methods of correction, designated Gallant and Post, which were proposed for equivalence tests by Loingeville et al [ 10 ].…”

“…This method (MB-TOST Post) uses posterior distribution samples to compute the standard errors of treatment effects [ 10 ].…”

“…As such, FDA has actively supported research focused on MBBE approaches for PK BE studies with sparse designs [ 9 – 11 ]. Indeed, MB tests can lead to an inflation of the type I error because of an underestimation of the standard error (SE) of treatment effects on sparse designs in presence of large variability, which led Loingeville et al to propose and evaluate methods of correction of the standard errors in MB studies [ 10 ]. Shen et al [ 12 ] also proposed a MB alternative to traditional BE tests.…”