Replicability is a cornerstone of science. The partial conjunction (PC) hypothesis testing framework objectively quantifies replicability across disciplines. Although several statistical methodologies for testing PC hypotheses exist, it is not clear which method performs well under which circumstances. In this paper, we consider the PC hypothesis testing problem from a neuroimaging perspective. Identifying the brain regions activated by a specific cognitive task constitutes a central challenge in neuroimaging. This problem becomes complex when the objective is to evaluate whether activation patterns are consistent across different cognitive tasks or subjects. In this paper, we cast this question as a PC hypothesis testing problem, assessing, for each location in the brain, whether it is activated in at least $γ$ subjects, for a pre-specified granularity $γ$. In our comparative study, we consider three methods, namely: adaFilter, CoFilter, and a method proposed by Benjamini, Heller, and Yekutieli (BHY). In equi-correlated simulated data, the BHY procedure tends to outperform the competing methods for high values of $γ$, while CoFilter performs well for low values of $γ$. In the real-data analysis, CoFilter dominates the other methods for intermediate values of $γ$.

翻译：可重复性是科学的基石。部分合取（PC）假设检验框架为跨学科的可重复性提供了客观量化方法。尽管存在多种检验PC假设的统计方法，但尚不清楚何种方法在何种情况下表现更优。本文从神经影像学的视角探讨PC假设检验问题。识别特定认知任务激活的脑区是神经影像学中的一个核心挑战。当目标是评估不同认知任务或受试者之间的激活模式是否一致时，该问题变得尤为复杂。本文将这一问题构建为PC假设检验问题，针对大脑中的每个位置，评估其是否在至少 $γ$ 名受试者中被激活，其中 $γ$ 为预先设定的粒度参数。在本比较研究中，我们考虑了三种方法：adaFilter、CoFilter以及由Benjamini、Heller和Yekutieli（BHY）提出的方法。在等相关的模拟数据中，BHY方法在 $γ$ 值较高时往往优于其他方法，而CoFilter在 $γ$ 值较低时表现良好。在真实数据分析中，CoFilter在中等 $γ$ 值范围内优于其他方法。