Harnessing The Collective Wisdom: Fusion Learning Using Decision Sequences From Diverse Sources

Abstract

We introduce an Integrative Ranking and Thresholding (IRT) framework for fusing evidence from multiple testing procedures. The key innovation is a method that transforms binary testing decisions into compound $e-$values, enabling the combination of findings across diverse data sources or studies. We demonstrate that IRT ensures overall false discovery rate (FDR) control, provided the individual studies maintain their respective FDR levels. This approach is highly flexible and is a powerful alternative for fusing inferences in meta-analysis where some studies report summary statistics while the rest reveal only the rejections under a pre-specified FDR level. Extensions to alternative Type I error control measures are explored.