# Joint Local False Discovery Rate in GWAS

##### Posted on (Update: )

\[\newcommand\Jlfdr{\mathrm{Jlfdr}} \newcommand\Fdr{\mathrm{Fdr}}\]propose a novel summary-statistics-based joint analysis method based on controlling the joint local false discovery rate (Jlfdr).

- prove that the method is the most powerful summary-statistics-based joint analysis method when controlling the false discovery rate at a certain level
- the Jlfdr-based method achieves higher power than commonly used meta-analysis methods when analyzing heterogeneous datasets from multiple GWASs

two kinds of joint analysis methods:

- individual-level
- summary-statistics-based

Jlfdr generalizes the concept of the local false discovery rate (Jlfdr) from the analysis of single study to the joint analysis of multiple studies

## Methods

### Jlfdr and optimal rejection region

\[\Jlfdr(z) = P(H_0\mid \bfz)\]Fdr is the expectation of Jlfdr, given that the test statistic vector is in the rejection region $R$.

\[\Fdr(R) = E(\Jlfdr(z)\mid z\in R)\]