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correlation_K2.R
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correlation_K2.R
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##### Performance in characterizing the correlation among the traits (two traits) #####
# Vary alpha (0.2, 0.4, 0.6), r (0.25, 1, 4) and rho (0, 0.05, 0.1, 0.15, 0.2, 0.25)
# to get Supplementary Figure S7
library(MASS)
library(LPM)
library(pbivnorm)
library(mvtnorm)
# 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))
}
K <- 2 # 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 <- 0.2 # parameter in the Beta distribution
rho <- 0 # correlation between the two traits
R <- matrix(c(1, rho, rho, 1), K, K) # correlation matrix for the traits
rep <- 500 # repeat times
pvalue_rho <- numeric(rep)
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)
pvalue_rho[i] <- test_rho(fit)
}
result <- sum(pvalue_rho < 0.05)/rep