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dense_diff_SNR_N.R
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library(mvtnorm)
library(iGREX)
# set.seed(1)
rm(list=ls())
gc()
set.seed(100)
n1 <- 800
n2 <- 4000
p1 <- 100 #number of SNPs in each gene
p2 <- 200 #number of genes
r <- 0 #number of overlapped snps in each gene
p <- (p1-r)*(p2-1)+p1
n_block <- 50
block_cut <- c(0,(1:n_block)*(p%/%n_block),p) #block cutoff
sb2_true <- 0.3
sy2_true <- 0.7
sg2_true <- 0.2
sa2_true <- 0.3
# sz2_true <- 0.2
f <- runif(p, 0.05, 0.5)
m <- 500
n_rep <- 50
# out <- matrix(0,n_rep,4)
# out_se <- matrix(0,n_rep,4)
# colnames(out) <- colnames(out_se) <- c("PVE_G", "PVE_A","PVE_G_ss", "PVE_A_ss")
out <- matrix(0,n_rep,20)
for(i in 1:n_rep){
cat(i,"-th loop\n")
# sigma <- 0.3^(abs(outer(1:p, 1:p, "-")))
# X <- rmvnorm(n1+n2,mean=rep(0,p),sigma=sigma)
# X <- matrix(rnorm((n1+n2)*p),n1+n2,p)
X_tmp <- matrix(rnorm((n1+n2)*p),n1+n2,p)
X <- matrix(1, n1+n2, p)
X[t(t(X_tmp) - quantile(X_tmp, f^2)) < 0] <- 2
X[t(t(X_tmp) - quantile(X_tmp, 1-(1-f)^2)) > 0] <- 0
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-1)*(p1-r)+1):((g-1)*(p1-r)+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
gamma <- as.matrix(rnorm(p,0,sqrt(sa2_true/p)))
z1 <- X2%*%gamma
z <- z0 + z1 + rnorm(n2,0,sqrt(var(z0+z1)))
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)$coefficients[2,3]
}
# Data: gene expr Y, phenotype z, genotype1 X1, genotype2 X2
# fit LMM for step 1 and get K_g for each gene
K <- K0 <- Km <- Km0 <- 0
# K_diag <- vector("numeric",0)
Km_diag <- vector("numeric",0)
idx <- sample(1:n2,m,replace = F)
q1_vec <- rep(0,p2)
for(g in 1: p2){
cat(g,"/",p2," gene\n")
y_g <- Y[,g]
X1tmp <- X1[,((g-1)*(p1-r)+1):((g-1)*(p1-r)+p1)]
X2tmp <- X2[,((g-1)*(p1-r)+1):((g-1)*(p1-r)+p1)]
ztmp <- z_score[((g-1)*(p1-r)+1):((g-1)*(p1-r)+p1)]
W1 <- matrix(1,n1,1)
W2 <- matrix(1,n2,1)
fit_g <- iGREX_Kg(y_g,X1tmp,X2tmp,W1,1e-5,500)
K <- K + fit_g$K_g
K0 <- K0 + fit_g$K_g0
q1_vec[g] <- t(ztmp/sqrt(n2))%*%fit_g$weight%*%ztmp/sqrt(n2) / p1
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
Km_diag <- c(Km_diag,sum(diag(fitrd_g$K_g)))
}
q2_vec <- (z_score/sqrt(n2))^2
mdiag <- mean(diag(K))
K <- K/mdiag
mdiagm <- mean(diag(Km))
Km <- Km/mdiagm
# X2s <- scale(X2)
Ka <- X2 %*% t(X2) / ncol(X2)
Xm <- scale(X2[idx,])
Kma <- Xm %*% t(Xm) / ncol(Xm)
# REML
REML <- REML_3var(K,Ka,z)
out[i,1:2] <- REML$PVE[1,1:2]
out[i,11:12] <- REML$PVE[2,1:2]
# REML without acocunting for uncertainty
REML0 <- REML_3var(K0,Ka,z)
out[i,3:4] <- REML0$PVE[1,1:2]
out[i,13:14] <- REML0$PVE[2,1:2]
# exact estimate by MoM
MoM <- MoM_3var(K,Ka,z)
out[i,5:6] <- MoM$PVE[1,1:2]
out[i,15:16] <- MoM$PVE[2,1:2]
# exact estimate by MoM without accounting for uncertainty
MoM0 <- MoM_3var(K0,Ka,z)
out[i,7:8] <- MoM0$PVE[1,1:2]
out[i,17:18] <- MoM0$PVE[2,1:2]
# MoM using summary statisitcs
trK1 <- sum(diag(Km))
trK2 <- sum(diag(Kma))
trK12 <- sum(Km^2)
trK22 <- sum(Kma^2)
trK1K2 <- sum(Km*Kma)
c <- 1
S <- matrix(0,2,2)
S[1,1] <- (trK12-trK1^2/(m-c))/(m-c)^2
S[1,2] <- S[2,1] <- (trK1K2-trK1*trK2/(m-c))/(m-c)^2
S[2,2] <- (trK22-trK2^2/(m-c))/(m-c)^2
q_ss <- c(sum(q1_vec)/mdiagm - 1/n2, sum(q2_vec)/p - 1/n2)
invS <- solve(S)
med_H_ss <- invS%*%q_ss
group1 <- rep(0,p2)
group2 <- rep(0,p)
idx_group <- 1
n_block <- length(block_cut)-1
for(j in 1:n_block){
tmp1 <- rep(FALSE,p2)
tmp2 <- rep(FALSE,p)
for(g in 1: p2){
# cat(g,"/",p2," gene\n")
gstart <- (g-1)*(p1-r)+1
gend <- (g-1)*(p1-r)+p1
if(gstart>=(block_cut[j]+1) & gend<=block_cut[j+1]){
tmp1[g] <- TRUE
}
}
tmp2[(block_cut[j]+1):block_cut[j+1]] <- TRUE
if(sum(tmp1!=0)&sum(tmp2!=0)){
group1[tmp1] <- idx_group
group2[tmp2] <- idx_group
idx_group <- idx_group+1
}
}
ngroup <- idx_group-1
qj <- sapply(1:ngroup,function(j){
tmp1 <- group1==j
tmp2 <- group2==j
q1 <- sum(q1_vec[tmp1])
q2 <- sum(q2_vec[tmp2])
c(q1,q2,sum(Km_diag[tmp1])/m,sum(tmp2))
})
t1 <- sum(Km_diag[group1!=0])/m
pp <- sum(group2!=0)
q_j <- (c(sum(q1_vec[group1!=0]),sum(q2_vec[group2!=0])) - qj[1:2,])/(c(t1,pp)-qj[3:4,]) - 1/n2
var_h <- invS %*% var(t(q_j)) %*% invS * (ngroup-1)
out[i,9:10] <- med_H_ss
out[i,19:20] <- sqrt(diag(var_h))
}
out <- data.frame(out)
names(out) <- c("PVEg_REML", "PVEa_REML","PVEg_REML0", "PVEa_REML0","PVEg_MoM", "PVEa_MoM","PVEg_MoM0", "PVEa_MoM0","PVEg_ss", "PVEa_ss",
"se_PVEg_REML", "se_PVEa_REML","se_PVEg_REML0", "se_PVEa_REML0","se_PVEg_MoM", "se_PVEa_MoM","se_PVEg_MoM0", "se_PVEa_MoM0","se_PVEg_ss", "se_PVEa_ss")
setwd("/home/share/mingxuan/prediXcan/medH/simulation")
write.table(out,file=paste("5prop",sg2_true*10,sa2_true*10,"_SNRy",sb2_true,"_n",n1,"_",n2,".txt",sep=""),quote = F,col.names = T,row.names = F)