A General Framework for Multiple Testing via E-value Aggregation and Data-Dependent Weighting

Abstract

Motivated by recent findings in Li and Zhang (2025), which established an equivalence between certain p-value-based multiple testing procedures and the e-Benjamini-Hochberg procedure (Wang and Ramdas, 2022), we introduce a general framework for constructing novel multiple testing methods through the aggregation and combination of e-values. Specifically, we propose methodologies for three distinct scenarios: (i) assembly of e-values obtained from different subsets of data, simultaneously controlling group-wise and overall false discovery rates; (ii) aggregation of e-values derived from different procedures or the same procedure employing different test statistics; and (iii) adaptive multiple testing methods that incorporate external structural information to enhance statistical power. A notable feature of our approach is the use of data-dependent weighting of e-values, significantly improving the efficiency of the resulting e-Benjamini-Hochberg procedures. The construction of these weights is non-trivial and inspired by leave-one-out analysis, a widely utilized technique for proving false discovery rate control in p-value-based methodologies. We theoretically establish that the proposed e-Benjamini-Hochberg procedures, when equipped with data-dependent weights, guarantee finite-sample false discovery rate control across all three considered applications. Additionally, numerical studies illustrate the efficacy and advantages of the proposed methods within each application scenario.