Virtual Bioequivalence Assessment of Long-acting Injectable Suspensions Using PBPK Modeling: Part 2. Type 1 Error and Safe space Analyses

We present an analysis of statistical type I error and safe space calculations in virtual bioequivalence (VBE) assessments using a previously published physiologically-based pharmacokinetic (PBPK) model (1) for 3-month long-acting paliperidone palmitate (PP) injectable suspensions. The type I error for the two-one-sided t test (TOST) applied to virtual parallel design bioequivalence (BE) trials was estimated through approximation of ‘simulated BE boundaries’. This was defined as the range of formulation quality attribute values (here, mean drug particle radius), corresponding to simulated population-level geometric mean ratios (GMRs) for key pharmacokinetic (PK) metrics of between 0.8 to 1.25. Monte Carlo simulations were then used to combine these limits with power calculations to display estimates of the safe space for BE extending from a predefined particle radius. Type I error for detecting formulation difference in the model was controlled at 5% for PK endpoints. The simulated BE boundaries for 3-month PP LAI suspension mean particle radius extended over 5 micrometers, but acceptable statistical power (≥80%) was obtained only when the mean particle radius was within 1 micrometer of the reference formulation. For PBPK models, type I error calculations are notably more complex than power calculations because the simulated BE boundaries for CQAs need to be determined before the error assessment. This study appears to be the first to discuss the intersection of type I error control and safe space estimation in PBPK modeling for a BE assessment. Our case study shows the conditions that allow for a controlled type I error in a VBE assessment. Safe space is shown to depend on both formulation characteristics and the statistical power afforded by BE studies, offering valuable insights for formulation design considerations.