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

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. 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-period, two-sequence cross-over design with rich (n = 10) and sparse (n = 3) sampling under the null and the alternative hypotheses, with MB-TOST. 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. 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.