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#-----------------------------------------------------------------------------------#
# Simulate a K-stage SMART data with n_cluster clusters characterized by the differential means in the pinfo variables
# Yuan Chen, June 2018
#-----------------------------------------------------------------------------------#
sim_Kstage = function(n, n_cluster, pinfo, pnoise, centroids=NULL, K) {
if(is.null(centroids))
centroids = matrix(rnorm(n_cluster * pinfo, 0, sqrt(5)), nrow = n_cluster)
y=list()
R=list()
A=list()
X=matrix(0, n, pinfo+pnoise)
sigma1 = ifelse(diag(pinfo), 1, 0.2) #covariance matrix for Xpinfo
for (k in 1:K){
y[[k]] = rep(0,n)
R[[k]] = rep(0,n)
A[[k]] = 2*rbinom(n, 1, 0.5) - 1
}
# assign optimal treatment y and X, based on cluster
end = 1
for (l in 1:n_cluster){
start = end
end = end + n/n_cluster
for (k in 1:K) {
y[[k]][start:(end-1)] = 2 * (floor(l/(2*k-1)) %% 2) - 1
}
X[start:(end-1),1:pinfo] =
mvrnorm(n/n_cluster, centroids[l,], Sigma = sigma1)
}
X[, pinfo + (1:pnoise)] = mvrnorm(n, rep(0,pnoise), diag(pnoise))
for(k in 1:K) {
R[[K]] = R[[K]] + A[[k]]*y[[k]]
}
R[[K]] = R[[K]] + rnorm(n)
list(X=X, A=A, R=R, optA=y, centroids=centroids)
}
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