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

Trambak Banerjee, Bowen Gang, Jianliang He

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 highly20
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.