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

TL;DR

This paper presents the IRT framework that fuses evidence from multiple testing procedures by converting binary decisions into e-values, ensuring FDR control across diverse data sources, and offering a flexible meta-analysis tool.

Contribution

The paper introduces a novel IRT method that transforms binary test decisions into e-values for effective evidence fusion across studies with different reporting formats.

Findings

IRT guarantees FDR control when individual studies do so

The method is flexible for meta-analysis with varied data types

Extensions to other error measures are discussed

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.