🤖 AI Summary
Existing methods for two-sample multi-quantile equivalence testing suffer from several limitations: mean-based approaches are inapplicable; tests for extreme quantiles are overly conservative; and statistical power is low under heteroscedasticity, especially with small or unbalanced samples. To address these challenges, this paper proposes the α-qTOST method—a quantile-based extension of the Two One-Sided Tests (TOST) framework—incorporating finite-sample correction to enable joint equivalence testing across multiple quantiles, including extreme ones. The method rigorously controls the nominal Type I error rate while substantially improving statistical power. Theoretical analysis and extensive simulations demonstrate its valid inference properties under heteroscedastic Gaussian models. The α-qTOST method has been successfully applied in HIV drug bridging trials and local drug delivery distribution assessments, providing robust support for equivalence decisions across diverse populations and operational conditions.
📝 Abstract
Testing the equivalence of multiple quantiles between two populations is important in many scientific applications, such as clinical trials, where conventional mean-based methods may be inadequate. This is particularly relevant in bridging studies that compare drug responses across different experimental conditions or patient populations. These studies often aim to assess whether a proposed dose for a target population achieves pharmacokinetic levels comparable to those of a reference population where efficacy and safety have been established. The focus is on extreme quantiles which directly inform both efficacy and safety assessments. When analyzing heterogeneous Gaussian samples, where a single quantile of interest is estimated, the existing Two One-Sided Tests method for quantile equivalence testing (qTOST) tends to be overly conservative. To mitigate this behavior, we introduce $α$-qTOST, a finite-sample adjustment that achieves uniformly higher power compared to qTOST while maintaining the test size at the nominal level. Moreover, we extend the quantile equivalence framework to simultaneously assess equivalence across multiple quantiles. Through theoretical guarantees and an extensive simulation study, we demonstrate that $α$-qTOST offers substantial improvements, especially when testing extreme quantiles under heteroskedasticity and with small, unbalanced sample sizes. We illustrate these advantages through two case studies, one in HIV drug development, where a bridging clinical trial examines exposure distributions between male and female populations with unbalanced sample sizes, and another in assessing the reproducibility of an identical experimental protocol performed by different operators for generating biodistribution profiles of topically administered and locally acting products.