We study how to combine p-values and e-values, and design multiple testing procedures where both p-values and e-values are available for every hypothesis. Our results provide a new perspective on multiple testing with data-driven weights: while standard weighted multiple testing methods require the weights to deterministically add up to the number of hypotheses being tested, we show that this normalization is not required when the weights are e-values that are independent of the p-values. Such e-values can be obtained in the meta-analysis setting wherein a primary dataset is used to compute p-values, and an independent secondary dataset is used to compute e-values. Going beyond meta-analysis, we showcase settings wherein independent e-values and p-values can be constructed on a single dataset itself. Our procedures can result in a substantial increase in power, especially if the non-null hypotheses have e-values much larger than one.

翻译：我们研究如何结合p值和e值，并设计在每一个假设检验中同时存在p值和e值的多重检验程序。我们的研究结果为数据驱动权重的多重检验提供了新视角：标准加权多重检验方法要求权重确定性总和等于被检验假设的数量，而本研究表明当权重为独立于p值的e值时，无需进行此归一化。这类e值可在元分析场景中获得——即用主数据集计算p值，用独立辅助数据集计算e值。除元分析外，我们还展示了在单一数据集上独立构造e值与p值的场景。我们的程序能显著提升检验效能，尤其在备择假设对应的e值远大于1的情况下。