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 $\alpha$-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 $\alpha$-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.

翻译：检验两个总体间多个分位数的等效性在诸多科学应用中具有重要意义，例如在传统基于均值的方法可能不适用的临床试验中。这在桥接研究中尤为相关，此类研究旨在比较不同实验条件或患者群体间的药物反应。这些研究通常旨在评估为目标人群提出的剂量是否达到与已确立疗效和安全性的参考人群相当的药代动力学水平。研究重点在于直接反映疗效和安全性评估的极端分位数。当分析异质性高斯样本（其中仅估计单个目标分位数）时，现有的分位数等效性检验双重单侧检验方法（qTOST）往往过于保守。为改善此特性，我们提出$\alpha$-qTOST，一种有限样本调整方法，在将检验水平维持在名义水平的同时，实现了相较于qTOST均匀更高的检验效能。此外，我们将分位数等效性框架扩展至同时评估多个分位数的等效性。通过理论保证和广泛的模拟研究，我们证明$\alpha$-qTOST能带来显著改进，尤其在异方差性下检验极端分位数且样本量小而不平衡时。我们通过两个案例研究阐明这些优势：其一在HIV药物研发中，一项桥接临床试验以不平衡样本量考察男性和女性群体的暴露量分布；另一案例评估不同操作者执行相同实验协议生成局部给药局部作用产品生物分布谱的可重复性。