EBMMT:The Eigen Higher Criticism and Eigen Berk–Jones Tests for Multiple Trait Association Studies Based on GWAS Summary Statistics
EBMMT includs nine approches (i.e., the OMNI, eHC, eBJ, iHC, GHC, GBJ, MinP, Wald and PCFisher tests) for detecting the association between a single SNP and multiple traits based on GWAS summary statistics while accounting for the correlation structure among multiple traits.
Please use the following command in R to install the package:
library(usethis)
library(devtools)
install_github("Vivian-Liu-Wei64/EBMMT")
The EBMMT performs the multiple traits association test based on GWAS summary statistics.
The eHC function is used to calculate the P_values of the eHC test.
The eBJ function is used to calculate the P_values of the eBJ test.
The iHC function is used to calculate the P_values of the iHC test.
The Wald function is used to calculate the P_values of the Wald test.
The PCFisher function is used to calculate the P_values of the PCFisher tests.
The Eigen_ana function is used to calculate the P_values of the eHC, eBJ, iHC, GHC, GBJ, MinP, Wald and PCFisher tests.
Eigen_ana(Z_score, Sigma)
Given Z_score and Sigma, the Eigen_ana function provids the P-values of the eHC, eBJ, iHC, GHC, GBJ, MinP, Wald and PCFisher tests.
library(EBMMT) # load the EBMMT package
# Z_score shold be a vector of test statistics for each factor in the set (i.e. marginal test statistic for each trait).
# Sigma shpuld be a matrix of the correlations between all the test statistics in the set.
#example
library(mvtnorm)
Sigma<-matrix(c(1,-0.08,-0.42,-0.08,1,0.27,-0.42,0.27,1),3,3)
Z_score<- as.vector(rmvnorm(1,mean=c(1.3,1.3,1.3),sigma=Sigma) )
Eigen_ana(Z_score,Sigma)
-----------The p_values of eHC, eBJ, iHC, GHC, GBJ, MinP, Wald and PCFisher tests-----------
OMNI_p eHC_p eBJ_p iHC_p GHC_p GBJ_p MinP_p Wald_p PCFisher_p
[1] 0.027059710 0.013585974 0.024266871 0.023478188 0.045186983 0.066075545 0.036742809 0.008783658 0.009267857
Liu, W., Xu, Y., Wang, A., Huang, T.# and Liu, Z.#, 2021. The Eigen Higher Criticism and Eigen Berk–Jones Tests for Multiple Trait Association Studies Based on GWAS Summary Statistics. Genetic Epidemiology. https://doi.org/10.1002/gepi.22439
Our proposed eigen higher criticism (eHC) has similar name with the test statistic "eigenHC" in those two papers (Donoho, D. et al., Ke, Z.T.). Note that eHC is fundamentally different from eigenHC.
Donoho, D. and Jin, J., 2015. Higher criticism for large-scale inference, especially for rare and weak effects. Statistical Science, 30(1), 1-25.
Ke, Z.T., 2016. Detecting rare and weak spikes in large covariance matrices. arXiv preprint arXiv:1609.00883.