Powerful large scale inference in high dimensional mediation analysis.

In genome-wide epigenetic studies, determining how exposures (e.g., Single Nucleotide Polymorphisms) affect outcomes (e.g., gene expression) through intermediate variables, such as DNA methylation, is a key challenge. Mediation analysis provides a framework to identify these causal pathways; however, testing for mediation effects involves a complex composite null hypothesis. Existing methods, such as Sobel's test or the Max-P test, are often underpowered in this context because they rely on null distributions determined under only a subset of the null space and are not optimized for the multiple testing burden inherent in high-dimensional data. To address these limitations, we introduce MLFDR (Mediation Analysis using Local False Discovery Rates), a novel method for high-dimensional mediation analysis. MLFDR leverages local false discovery rates, calculated from the coefficients of structural equation models, to construct an optimal rejection region. We demonstrate theoretically and through simulation that MLFDR asymptotically controls the false discovery rate and achieves superior statistical power compared to recent high-dimensional mediation methods. In real data applications, MLFDR identified 20%-50% more significant mediators than existing methods, demonstrating its ability to uncover biological signals missed by conventional approaches.