Simulate marginal Z-scores from joint Z-score vector

Simulate marginal z-scores (\(Z_m\)) from the joint z-scores (\(Z_j\)) using \(E(Z_m) = Z_j \times \Sigma\) and \(Z* \sim MVN(E(Z_m), \Sigma)\)

z_sim(Zj, Sigma, nrep)

Arguments

Zj

Vector of joint Z-scores (a vector of 0s except at the CV)
Sigma

SNP correlation matrix
nrep

Number of Z-score systems to simulate

Value

Matrix of simulated posterior probabilties, one simulation per row

Examples


set.seed(1)
nsnps <- 100

# derive joint Z score vector
Zj <- rep(0, nsnps)
iCV <- 4 # index of CV
mu <- 5 # true effect at CV
Zj[iCV] <- mu

## generate example LD matrix
library(mvtnorm)
nsamples = 1000

simx <- function(nsnps, nsamples, S, maf=0.1) {
    mu <- rep(0,nsnps)
    rawvars <- rmvnorm(n=nsamples, mean=mu, sigma=S)
    pvars <- pnorm(rawvars)
    x <- qbinom(1-pvars, 1, maf)
}

S <- (1 - (abs(outer(1:nsnps,1:nsnps,`-`))/nsnps))^4
X <- simx(nsnps,nsamples,S)
LD <- cor2(X)

res <- z_sim(Zj, Sigma = LD, nrep = 100)
res[c(1:5), c(1:5)]
#>          [,1]     [,2]     [,3]     [,4]     [,5]
#> [1,] 3.718183 3.690915 3.591499 4.885386 3.868505
#> [2,] 5.557154 5.020218 5.803891 5.429848 4.264808
#> [3,] 3.498198 3.556396 4.206735 5.507531 4.739869
#> [4,] 5.811572 5.143549 5.750160 6.988442 5.427503
#> [5,] 2.554965 2.720556 2.625123 4.353644 2.902586