Identifying signals that replicate across multiple studies is essential for establishing robust scientific evidence, yet existing methods for high-dimensional replicability analysis either rely on restrictive modeling assumptions, are limited to two-study settings, or lack statistical power. We propose a general empirical Bayes framework for multi-study replicability analysis that jointly models summary-level $p$-values while explicitly accounting for between-study heterogeneity. Within each study, non-null $p$-value densities are estimated nonparametrically under monotonicity constraints, enabling flexible and tuning-free inference. For two studies, we develop a local false discovery rate (Lfdr) statistic for the composite null of non-replicability and establish identifiability, consistency, and a cubic-rate convergence of the nonparametric MLE, along with minimax optimality. Extending replicability analysis to $n$ studies typically requires estimating $2^n$ latent configurations, which is computationally infeasible. To address this challenge, we introduce a scalable pairwise rejection strategy that decomposes the exponentially large composite null into disjoint components, yielding linear complexity in the number of studies. We prove asymptotic FDR control under mild regularity conditions and show that Lfdr-based thresholding is power-optimal. Extensive simulations demonstrate that our method provides substantial power gains while maintaining valid FDR control, outperforming state-of-the-art alternatives across a wide range of scenarios. Applying our framework to East Asian- and European-ancestry genome-wide association studies of type 2 diabetes reveals replicable genetic associations that competing approaches fail to detect, illustrating the method's practical utility in large-scale biomedical research.

翻译：识别多个研究中可重复的信号对于建立稳健的科学证据至关重要，然而现有高维可重复性分析方法要么依赖于限制性建模假设，要么仅限于双研究设置，或缺乏统计功效。我们提出了一个通用的经验贝叶斯框架，用于多研究可重复性分析，该框架联合建模汇总水平的$p$值，同时明确考虑研究间的异质性。在每个研究内部，非空$p$值的密度在单调性约束下以非参数方式估计，从而实现灵活且无需调参的推断。针对双研究情况，我们开发了一种用于非可重复性复合零假设的局部错误发现率（Lfdr）统计量，并建立了非参数极大似然估计的可识别性、一致性、三次速率收敛性以及极小极大最优性。将可重复性分析扩展到$n$个研究通常需要估计$2^n$个潜在配置，这在计算上是不可行的。为解决这一挑战，我们引入了一种可扩展的成对拒绝策略，将指数级增长的复合零假设分解为不相交的分量，使得计算复杂度在研究数量上呈线性增长。我们在温和的正则性条件下证明了渐近FDR控制，并表明基于Lfdr的阈值处理是功效最优的。大量模拟实验表明，我们的方法在保持有效FDR控制的同时，提供了显著的功效提升，在多种广泛场景下优于现有先进方法。将我们的框架应用于东亚和欧洲血统人群的2型糖尿病全基因组关联研究，揭示了竞争方法未能检测到的可重复遗传关联，这说明了该方法在大规模生物医学研究中的实际效用。