标题： 独立离散$p$值的最优调整与组合 显示英文标题

标题： Optimal Adjustment and Combination of Independent Discrete $p$-Values

摘要： 将多个独立检验的p值结合起来是统计推断中的基本任务，但当p值是离散的时候会带来独特的挑战。 我们扩展了一个最近提出的基于最优传输的框架，用于结合离散p值，该框架通过最小化变换后的离散零假设与其连续类比之间的Wasserstein距离来构建一个连续的替代分布。 我们提供了一种统一的方法，适用于几种经典的组合方法，包括Fisher统计量、Pearson统计量、George统计量、Stouffer统计量和Edgington统计量。 我们的理论分析和大量模拟结果显示，当调整后的离散统计量的方差与连续情况下的方差紧密匹配时，可以实现精确的I类错误控制。 我们进一步证明，当似然比检验是组合统计量的单调函数时，所提出的近似方法在功效上可以与一致最有力（UMP）检验相媲美。 该方法通过使用病例对照数据进行罕见变异的遗传关联研究进行了说明，并在R包DPComb中实现。 显示英文摘要

摘要： Combining p-values from multiple independent tests is a fundamental task in statistical inference, but presents unique challenges when the p-values are discrete. We extend a recent optimal transport-based framework for combining discrete p-values, which constructs a continuous surrogate distribution by minimizing the Wasserstein distance between the transformed discrete null and its continuous analogue. We provide a unified approach for several classical combination methods, including Fisher's, Pearson's, George's, Stouffer's, and Edgington's statistics. Our theoretical analysis and extensive simulations show that accurate Type I error control is achieved when the variance of the adjusted discrete statistic closely matches that of the continuous case. We further demonstrate that, when the likelihood ratio test is a monotonic function of a combination statistic, the proposed approximation achieves power comparable to the uniformly most powerful (UMP) test. The methodology is illustrated with a genetic association study of rare variants using case-control data, and is implemented in the R package DPComb.