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iGREX_vs_RHOGE.R
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iGREX_vs_RHOGE.R
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library(mvtnorm)
library(iGREX)
# set.seed(1)
n1 <- 2000
n2 <- 4000
p1 <- 100 #number of SNPs in each gene
p2 <- 200 #number of genes
p <- p1*p2
sb2_true <- 0.9
sy2_true <- 0.1
sg2_true <- 0.2
sz2_true <- 0.8
m <- 500
n_rep <- 30
out <- matrix(0,n_rep,5)
for(i in 1:n_rep){
cat(i,"-th loop\n")
X <- matrix(rnorm((n1+n2)*p1*p2),n1+n2,p1*p2)
X <- scale(X)
Y0 <- matrix(0,n1+n2,p2)
for(g in 1:p2){
beta <- rnorm(p1,0,sqrt(sb2_true/p1))
Y0[,g] <- X[,(g*p1-p1+1):(g*p1)] %*% beta
}
Y <- Y0[1:n1,] + matrix(rnorm(n1*p2,0,sqrt(sy2_true)),n1,p2)
X1 <- X[1:n1,]
X2 <- X[(n1+1):(n1+n2),]
t <- mean(diag(Y0[(n1+1):(n1+n2),]%*%t(Y0[(n1+1):(n1+n2),])))
alpha <- as.matrix(rnorm(p2,0,sqrt(sg2_true/t)))
z0 <- Y0[(n1+1):(n1+n2),] %*% alpha
z <- z0 + rnorm(n2,0,sqrt(sz2_true))
med_H_true <- var(z0)/var(z)
z_score <- rep(0,p)
for(j in 1:p){
fit_lm <- lm(z~.,data = data.frame(z,X2[,j]))
z_score[j] <- summary(fit_lm)$coefficients[2,3]
}
# Data: gene expr Y, phenotype z, genotype1 X1, genotype2 X2
# fit LMM for step 1 and get K_g gor each gene
K <- K0 <- Km <- Km0 <- 0
idx <- sample(1:n2,m,replace = F)
q1_vec <- rep(0,p2)
q0_vec <- rep(0,p2)
z_TWAS <- rep(0,p2)
Y_hat <- matrix(0,n2,p2)
for(g in 1: p2){
cat(g,"/",p2," gene\n")
y_g <- Y[,g]
X1tmp <- X1[,(g*p1-p1+1):(g*p1)]
X2tmp <- X2[,(g*p1-p1+1):(g*p1)]
ztmp <- z_score[(g*p1-p1+1):(g*p1)]
W1 <- matrix(1,n1,1)
W2 <- matrix(1,n2,1)
fit_g <- iGREX_Kg(y_g,X1tmp,X2tmp,W1,1e-5,500)
K <- K + fit_g$K_g
K0 <- K0 + fit_g$K_g0
q1_vec[g] <- t(ztmp/sqrt(n2))%*%fit_g$weight%*%ztmp/sqrt(n2) / p1
q0_vec[g] <- sum(ztmp/sqrt(n2)*fit_g$mub)^2 / p1
z_TWAS[g] <- sum(ztmp*fit_g$mub)/sqrt(t(fit_g$mub)%*%cor(X2tmp[idx,])%*%fit_g$mub)
Y_hat[,g] <- X2tmp[idx,]%*%fit_g$mub
fitrd_g <- iGREX_Kg(y_g,X1tmp,X2tmp[idx,],W1,1e-5,500)
Km <- Km + fitrd_g$K_g
Km0 <- Km0 + fitrd_g$K_g0
}
mdiag <- mean(diag(K))
K <- K/mdiag
mdiagm <- mean(diag(Km))
Km <- Km/mdiagm
mdiagm0 <- mean(diag(Km0))
Km0 <- Km0/mdiagm0
# REML
REML <- REML_2var(K,z)
# exact estimate by MoM
trK <- sum(diag(K))
tr2K <- trK^2
trK2 <- sum(K^2)
temp <- K - trK/(n2-1)*diag(n2)
denom <- trK2 - tr2K/(n2-1)
sg2 <- drop((t(z) %*% temp %*% z) / denom)
sz2 <- drop((t(z) %*% (trK2/(n2-1)*diag(n2) - K*trK/(n2-1)) %*% z) / denom)
MoM_H <- trK*sg2/sum(z^2)
# Sigma <- sg2 * K + sz2 * diag(n2)
# temp <- t(z) %*% temp
# se_sg2 <- sqrt(2*temp %*% Sigma %*% t(temp))/denom
# se_H <- trK*se_sg2/sum(z^2)
# MoM using summary statisitcs
trK_ss <- sum(diag(Km))
tr2K_ss <- trK_ss^2
trK2_ss <- sum(Km^2)
S <- (trK2_ss- tr2K_ss/(m-1))/(m-1)^2
q_ss <- sum(q1_vec)/mdiagm - 1/n2
MoM_H_ss <- q_ss/S
# q <- (t(z)%*%K%*%z/(n2-1)^2 - trK/(n2-1)^3*sum(z^2))/sum(z^2)*trK
# med_H_Mq <- q/S
# ldsc-RHOGEn
corY2 <- cor(Y_hat)^2
r2_unbiased <- colSums(corY2-(1-corY2)/m)
fit_ldsc <- ldsc(z_TWAS,r2_unbiased/p2,n2)
# MoM using summary statisitcs without accounting for uncertainty
trK0_ss <- sum(diag(Km0))
tr2K0_ss <- trK0_ss^2
trK02_ss <- sum(Km0^2)
S <- (trK02_ss- tr2K0_ss/(m-1))/(m-1)^2
q_ss <- sum(q0_vec)/mdiagm0 - 1/n2
MoM_H_ss0 <- q_ss/S
out[i,] <- c(REML=REML$h,MoM_H,MoM_H_ss,MoM_H_ss0,fit_ldsc$fit$coefficients[1])
}
colnames(out) <- c("REML","MoM","iGREX_ss","iGREX_ss0","RHOGE")
# setwd("/home/mcaiad/iGREX/simulation")
setwd("/home/share/mingxuan/prediXcan/medH/simulation")
write.table(out,file=paste("iGREXvsRHOGE_SNRz",sg2_true,"_SNRy",sb2_true,"_n",n1,"_",n2,".txt",sep=""),quote = F,col.names = T,row.names = F)