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correlation_K8.R
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correlation_K8.R
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##### Performance in characterizing the correlation among the traits (eight traits) #####
# Figure 1b in the main text and Supplementary Figure S1
library(MASS)
library(pbivnorm)
library(mvtnorm)
K <- 8 # No. of traits
M <- 100000 # No. of SNPs
D <- 5 # No. of annotations
beta0 <- -1 # intercept of the probit model
beta0 <- rep(beta0, K)
set.seed(1)
beta <- matrix(rnorm(K*D), K, D) # coefficients of annotations
A.perc <- 0.2 # the proportion the entries in X is 1
A <- rep(0, M*D) # the design matrix of annotation
indexA <- sample(M*D, M*D*A.perc)
A[indexA] <- 1
A <- matrix(A, M, D)
r <- 1 # the relative signal strengh between annotated part and un-annotated part
sigmae2 <- var(A %*% t(beta))/r
beta <- beta/sqrt(diag(sigmae2))
beta <- cbind(as.matrix(beta0), beta)
alpha <- c(0.2, 0.35, 0.5, 0.3, 0.45, 0.55, 0.25, 0.4) # parameter in the Beta distribution
R <- matrix(0, K, K) # Correlation matrix for the traits
R[1, 2] <- 0.7
R[1, 3] <- 0.4
R[2, 3] <- 0.2
R[4, 5] <- 0.6
R[4, 6] <- 0.3
R[5, 6] <- 0.1
R[7, 8] <- 0.5
R <- R + t(R)
diag(R) <- 1
rep <- 50 # repeat times
##### LPM #####
library(LPM)
# function to generate data
generate_data <- function(M, K, D, A, beta, alpha, R){
Z <- cbind(rep(1, M), A) %*% t(beta) + mvrnorm(M, rep(0, K), R)
indexeta <- (Z > 0)
eta <- matrix(as.numeric(indexeta), M, K)
Pvalue <- NULL
for (k in 1:K){
Pvalue_tmp <- runif(M)
Pvalue_tmp[indexeta[, k]] <- rbeta(sum(indexeta[, k]), alpha[k], 1)
Pvalue <- c(Pvalue, list(data.frame(SNP = seq(1, M), p = Pvalue_tmp)))
}
names(Pvalue) <- paste("P", seq(1, K), sep = "")
A <- data.frame(SNP=seq(1,M), A)
return( list(Pvalue = Pvalue, A = A, beta = beta, eta = eta))
}
est_bLPM <- NULL
est_LPM <- NULL
for (i in 1:rep){
data <- generate_data(M, K, D, A, beta, alpha, R)
Pvalue <- data$Pvalue
X <- data$A
fit <- bLPM(Pvalue, X = X, coreNum = 10)
est_bLPM <- c(est_bLPM, list(fit))
fitLPM <- LPM(fit)
est_LPM <- c(est_LPM, list(fitLPM))
}
est_rho_LPM <- array(0, c(K, K, rep))
test_rho_LPM <- array(0, c(K, K, rep))
for(i in 1:rep){
est_rho_LPM[, , i] <- est_LPM[[i]]$R
rho_pvalue <- test_rho(est_blPM[[i]])
test_rho_LPM[, , i] <- (rho_pvalue < 0.05/((K-1)*K/2))
}
# results to get Figure 1b
est_LPM <- apply(est_rho_LPM, c(1, 2), mean)
colnames(est_LPM) <- paste("P", 1:8, sep = "")
rownames(est_LPM) <- colnames(est_LPM)
# results to get Supplementary Figure S1a
test_rho_LPM <- apply(test_rho_LPM, c(1, 2), mean)
colnames(test_rho_LPM) <- paste("P", 1:8, sep = "")
rownames(test_rho_LPM) <- colnames(test_rho_LPM)
##### GPA #####
library(GPA)
# function to generate data
generate_data_GPA <- function(M, K, D, A, beta, alpha, R){
Z <- cbind(rep(1, M), A) %*% t(beta) + mvrnorm(M, rep(0, K), R)
indexeta <- (Z > 0)
eta <- matrix(as.numeric(indexeta), M, K)
Pvalue <- matrix(0, M, K)
for (k in 1:K){
Pvalue[, k] <- runif(M)
Pvalue[indexeta[, k], k] <- rbeta(sum(indexeta[, k]), alpha[k], 1)
}
return( list(Pvalue = Pvalue, A = A, beta = beta, eta = eta))
}
test_rho_GPA <- array(0, c(K, K, rep))
for (k in 1:rep){
data <- generate_data_GPA(M, K, D, A, beta, alpha, R)
Pvalue <- data$Pvalue
X <- data$A
for (i in 1:(K-1)){
for (j in (i+1):K){
fit <- GPA(Pvalue[, c(i, j)], X)
fit.H0 <- GPA(Pvalue[, c(i, j)], X, pleiotropyH0 = TRUE)
test <- pTest(fit, fit.H0)
test_rho_GPA[i, j, k] <- (test$pvalue < 0.05/28)
}
}
}
# results to get Supplementary Figure S1b
test_rho_GPA <- apply(test_rho_GPA, c(1, 2), mean)
test_rho_GPA <- test_rho_GPA + t(test_rho_GPA)
diag(test_rho_GPA) <- 1
colnames(test_rho_GPA) <- paste("P", 1:8, sep = "")
rownames(test_rho_GPA) <- colnames(test_rho_GPA)
##### GGPA #####
library(GGPA)
# function to generate data
generate_data_GGPA <- function(M, K, D, A, beta, alpha, R){
Z <- cbind(rep(1, M), A) %*% t(beta) + mvrnorm(M, rep(0, K), R)
indexeta <- (Z > 0)
eta <- matrix(as.numeric(indexeta), M, K)
Pvalue <- matrix(0, M, K)
for (k in 1:K){
Pvalue[, k] <- runif(M)
Pvalue[indexeta[, k], k] <- rbeta(sum(indexeta[, k]), alpha[k], 1)
}
return( list(Pvalue = Pvalue, A = A, beta = beta, eta = eta))
}
est_GGPA <- NULL
for (i in 1:rep){
data <- generate_data_GGPA(M, K, D, A, beta, alpha, R)
fit_GGPA <- GGPA(data$Pvalue)
est_GGPA <- c(est_GGPA, list(fit_GGPA))
}
# result to get Supplementary Figure S1c
plot(est_GGPA[[1]])
plot(est_GGPA[[2]])