Harnessing the collective wisdom: fusion learning using decision sequences from diverse sources

Summary We introduce an integrative ranking and thresholding 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 our new framework ensures overall false discovery rate control, provided that the individual studies maintain their respective false discovery rate levels. The proposed approach is highly flexible and offers a powerful method for fusing inferences in meta-analyses where some studies report summary statistics while the rest reveal only the rejections under a prespecified false discovery rate level. Extensions to alternative Type I error control measures are explored.