  In genome-wide epigenetic studies, exposures (e.g., Single Nucleotide
Polymorphisms) affect outcomes (e.g., gene expression) through intermediate
variables such as DNA methylation. Mediation analysis offers a way to study
these intermediate variables and identify the presence or absence of causal
mediation effects. Testing for mediation effects lead to a composite null
hypothesis. Existing methods like the Sobel's test or the Max-P test are often
underpowered because 1) statistical inference is often conducted based on
distributions determined under a subset of the null and 2) they are not
designed to shoulder the multiple testing burden. To tackle these issues, we
introduce a technique called MLFDR (Mediation Analysis using Local False
Discovery Rates) for high dimensional mediation analysis, which uses the local
False Discovery Rates based on the coefficients of the structural equation
model specifying the mediation relationship to construct a rejection region. We
have shown theoretically as well as through simulation studies that in the
high-dimensional setting, the new method of identifying the mediating variables
controls the FDR asymptotically and performs better with respect to power than
several existing methods such as DACT (Liu et al.)and JS-mixture (Dai et al).
