Multiple testing of interval composite null hypotheses using randomized p-values

IF 1.2 3区 数学 Q2 STATISTICS & PROBABILITY Statistical Papers Pub Date : 2024-07-02 DOI:10.1007/s00362-024-01591-9
Daniel Ochieng
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Abstract

Equivalence tests are statistical hypothesis testing procedures that aim to establish practical equivalence rather than the usual statistical significant difference. These testing procedures are frequent in “bioequivalence studies," where one would wish to show that, for example, an existing drug and a new one under development have comparable therapeutic effects. In this article, we propose a two-stage randomized (RAND2) p-value that depends on a uniformly most powerful (UMP) p-value and an arbitrary tuning parameter \(c\in [0,1]\) for testing an interval composite null hypothesis. We investigate the behavior of the distribution function of the two p-values under the null hypothesis and alternative hypothesis for a fixed significance level \(t\in (0,1)\) and varying sample sizes. We evaluate the performance of the two p-values in estimating the proportion of true null hypotheses in multiple testing. 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 our multiple hypotheses under consideration. The various claims in this research are verified using a simulation study and real-world data analysis.

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使用随机 p 值对区间复合零假设进行多重检验
等效性测试是一种统计假设检验程序,旨在确定实际等效性,而不是通常的统计显著差异。这些测试程序在 "生物等效性研究 "中很常见,例如,人们希望证明现有药物和正在开发的新药具有可比的治疗效果。在本文中,我们提出了一种两阶段随机(RAND2)p 值,它取决于均匀最强(UMP)p 值和任意调整参数 (c/in [0,1]\),用于检验区间复合零假设。我们研究了在固定显著性水平(t/in (0,1))和不同样本量下,两个 p 值在零假设和备择假设下的分布函数行为。我们评估了两个 p 值在多重检验中估计真实零假设比例的性能。我们使用带有插件估计器的自适应 Bonferroni 程序对误差率进行家族式控制,以考虑我们所考虑的多重假设所产生的多重性。通过模拟研究和实际数据分析,我们验证了本研究中的各种主张。
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来源期刊
Statistical Papers
Statistical Papers 数学-统计学与概率论
CiteScore
2.80
自引率
7.70%
发文量
95
审稿时长
6-12 weeks
期刊介绍: The journal Statistical Papers addresses itself to all persons and organizations that have to deal with statistical methods in their own field of work. It attempts to provide a forum for the presentation and critical assessment of statistical methods, in particular for the discussion of their methodological foundations as well as their potential applications. Methods that have broad applications will be preferred. However, special attention is given to those statistical methods which are relevant to the economic and social sciences. In addition to original research papers, readers will find survey articles, short notes, reports on statistical software, problem section, and book reviews.
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