Estimating the genetic correlation with GWAS summary association statistics

Jianqiao Wang 2/27/2022

Input

To estimate the genetic correlation, the proposed method requires the information of summary association statistics and external LD matrix

summary statistics

The summary statistics file should have the following information:

SNP: the name of the genetic variants
A1: the effect allele.
n: number of samples used when testing the predictor.
Z: The z test staitistics of the genetic variants.

Note that the Z statistics could be calculated based on estimate of effect size (or log odds) of a predictor, and its standard deviation, or converted from the p values along with effects size.

external LD matrix

The external LD matrix could be calculated from external genotype data. The corresponding variant name and the effect allele should also be kept

Before the input

The summary statistics for outcome 1
The summary statistics for outcome 2
external LD information

We note theat two summary statistics should come from differet studies so that they are independent with each other. Make sure that all files have the same genetic variants and effect alleles

implement the method

source('./R/LDScore.R')
source('./R/Genetic_Correlation_class_v2.R')
source('./R/SummaryStatistics.R')
source('./R/Precsion_Matrix_Estimation.R')
source('./R/Helper.R')

# read the sumstat file 
sumstat.beta = read.table("./data/FG_female.sumstats", header = T) 
sumstat.gamma = read.table("./data/HG_male.sumstats", header = T)
n = mean(sumstat.beta$N, na.rm = T)
m = mean(sumstat.gamma$N, na.rm = T)

# convert to beta_mg and gamma_mg
beta_mg = Z.to.Mg(sumstat.beta$Z, n = n)
gamma_mg = Z.to.Mg(sumstat.gamma$Z, n = m)


# Omega0, SIGMA #  LD matrix calculated from the external genotype data
SIGMA = readRDS("./data/SIGMA.rds")
Omega0 = readRDS("./data/Omega0.rds")


# Inititate the estimation object
GeCor.Analysis = GeCov$new(Beta_mg = beta_mg,
                             Gamma_mg = gamma_mg,
                             N1 = n,
                             N2 = m)

# plug-in the external Omega and Sigma
# Estimation 
GeCor.Analysis$Estimation(Omega = Omega0, Sigma = SIGMA, Type = "proposed")
# variance
GeCor.Analysis$Var.Est(TRUE)
# print out the result 
print(GeCor.Analysis)

If we ignore the dependence, the estimator is

ldscore = read.table("./data/simu.l2.ldscore", header = T)

# ignore the dependence
GeCor.Analysis$Estimation(Omega = I, Sigma = SIGMA, LDSCORE = ldscore$LD, Type = "Identity")

GeCor.Analysis$Var.Est(TRUE)

print(GeCor.Analysis)

JianqiaoWang / GeCr_Sumstat