A Tail Likelihood Ratio Method for Large-scale Causal Mediation Tests in Epigenome-Wide Studies

Large-scale mediation testing has attracted considerable attention in epigenome-wide studies, intending to determine whether the effect of an exposure on an outcome is mediated through specific DNA methylation sites. Statistical inference for the mediation effects is challenged by the complexity of testing a large number of composite null hypotheses. We propose a tail likelihood ratio (TLR) test that is robust to variations in the proportion of null cases, signal strength, and signal distribution, achieving higher power for marginal mediation testing than existing methods while maintaining robust error rate control across diverse scenarios, with false discovery rate control established theoretically under independence and supported by simulation under dependence. The proposed TLR method features a powerful test statistic whose distribution under the composite null is derived analytically. Meanwhile, since methylations are often correlated, we account for the correlation of dependent test statistics using a principal component-based approximation. Simulations demonstrate that the proposed method maintains accurate error rate control in multiple comparisons and exhibits power gains compared to existing methods. We apply the proposed method to the Normative Aging Epigenetic Study and identify 27 of the 484,548 CpG sites of DNA methylation measured on 632 men that mediate the effect of smoking on lung function.