One class of statistical hypothesis testing procedures is the indisputable equivalence tests, whose main objective is to establish practical equivalence rather than the usual statistical significant difference. These hypothesis tests are prone in bioequivalence studies, where one would wish to show that, for example, an existing drug and a new one under development have the same therapeutic effect. In this article, we consider a two-stage randomized (RAND2) p-value utilizing the uniformly most powerful (UMP) p-value in the first stage when multiple two-one-sided hypotheses are of interest. We investigate the behavior of the distribution functions of the two p-values when there are changes in the boundaries of the null or alternative hypothesis or when the chosen parameters are too close to these boundaries. We also consider the behavior of the power functions to an increase in sample size. Specifically, we investigate the level of conservativity to the sample sizes to see if we control the type I error rate when using either of the two p-values for any sample size. In multiple tests, we evaluate the performance of the two p-values in estimating the proportion of true null hypotheses. We conduct a family-wise error rate control using an adaptive Bonferroni procedure with a plug-in estimator to account for the multiplicity that arises from the multiple hypotheses under consideration. We verify the various claims in this research using simulation study and real-world data analysis.

翻译：一类统计假设检验程序是无可争议的等效性检验，其主要目标是建立实际等效性而非通常的统计显著性差异。这类假设检验常用于生物等效性研究，例如，研究者希望证明现有药物与正在开发的新药具有相同的治疗效果。本文针对多重双单侧假设检验，提出一种利用第一阶段中最优功效(UMP)p值的两阶段随机化(RAND2)p值方法。我们研究了当原假设或备择假设边界发生变化，或所选参数过于接近这些边界时，两种p值分布函数的行为特征。同时，我们考察了功效函数随样本量增加的变化规律。具体而言，我们分析了保守性程度与样本量的关系，以验证任意样本量下使用两种p值是否都能控制第一类错误率。在多重检验中，我们评估了两种p值在估计真实原假设比例方面的表现。我们采用含插件估计量的自适应Bonferroni程序控制族系错误率，以处理多重假设带来的多重性问题。通过模拟研究与真实数据分析验证了本文的各项结论。