A Bayesian Informative Shrinkage Approach for Large-scale Multiple Hypothesis Testing (BISHOT): with Applications in Differential Analysis of Omics Data

A major goal of many omics studies is to identify differential features, e.g. differentially expressed genes, between experimental groups. When performing differential analysis for a given dataset, relevant information from another platform or species is often available. Incorporating such prior information can help identify features that show consistent differential patterns across platforms or species, which are more likely to reflect shared biological processes, and thereby enhance the robustness and generalizability of the findings. However, existing differential analysis methods typically analyze only the data from the current study and do not leverage prior knowledge about the magnitude or direction of changes from other platforms or species. We address this challenge, and the associated multiple testing problem, using a Bayesian framework that enables the incorporation of prior knowledge obtained from different platforms or species. We propose a new test statistic, Bayesian Credible Ratio (BCR), based on a heteroscedastic global local shrinkage prior, and a new multiple testing criterion, sign-adjusted FDR (SFDR), that emphasize information regarding the direction of the differentially features. We prove that BCR achieves the largest count of sign-based true positives among all legitimate SFDR-controlling methods. Simulation results offer numerical evidence of its advantage compared to an empirical Bayesian method. The approach is demonstrated through the analysis of RNAseq and single-cell RNAseq datasets.