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## Adaptive Sum of powered score (SPU) tests (SPU and aSPU) (simulation, version 1, vector used in permutation)
##
## It gives the p-values of the SPU tests and aSPU test based on the simulations of U from the null distribution. (This is version 1, matrix version is faster but if it doesn't work, we should use version 1, vector version)
##
## @param Y phenotype data. It can be disease lables; =0 for controls, =1 for cases.
## or It can be any quantitative traits. Vector with length n (number of observations)
##
## @param X genotype data; each row for a subject, and each column
## for an SNP. The value of each element is the # of the copies
## for an allele. Matrix with dimension n by k (n : number of observation, k : number of genotype data)
##
## @param cov covariates. Matrix with dimension n by p (n :number of observation, p : number of covariates)
##
## @param model Use "gaussian" for quantitative trait (Default)
## , and Use "binomial" for binary trait.
##
## @param pow power used in SPU test. Vector of g number of power.
##
## @param n.perm number of permutation
##
## @export
## @return Test Statistics and p-values for SPU tests and aSPU test.
##
## @examples
##
## data(exdat)
## out <- aSPUsim1(exdat$Y, exdat$X, cov = NULL, model = "binomial",
## pow = c(1:8, Inf), n.perm = 1000)
## out
##
## @seealso \code{\link{aSPU}}, \code{\link{aSPUperm2}}, \code{\link{aSPUboot}}, \code{\link{aSPUboot2}}
aSPUsim1 <- function(Y, X, cov = NULL, model=c("gaussian","binomial"), pow=c(1:8, Inf), n.perm=1000){
model = match.arg(model)
n <- length(Y)
if (is.null(X) && length(X)>0) X=as.matrix(X, ncol=1)
k <- ncol(X)
#### Score vector:
if (is.null(cov)){
## NO nuisance parameters:
XUs<-Xg <- X
r<-Y-mean(Y)
U<-as.vector(t(Xg) %*% r)
Xgb <- apply(X, 2, function(x)(x-mean(x)) )
if( model == "binomial" ) {
CovS <- mean(Y)*(1-mean(Y))*(t(Xgb) %*% Xgb)
} else {
CovS <- var(Y)*(t(Xgb) %*% Xgb)
}
} else {
tdat1<-data.frame(trait=Y, cov)
if(is.null(colnames(cov))) {
colnames(tdat1) = c("trait", paste("cov",1:dim(cov)[2],sep=""))
} else {
colnames(tdat1) = c("trait", colnames(cov))
}
fit1<-glm(trait~.,family=model,data=tdat1)
pis<-fitted.values(fit1)
XUs<-matrix(0, nrow=n, ncol=k)
Xmus = X
for(i in 1:k){
tdat2<-data.frame(X1=X[,i], cov)
fit2<-glm(X1~.,data=tdat2)
Xmus[,i]<-fitted.values(fit2)
XUs[, i]<-(X[,i] - Xmus[,i])
}
r<-Y - pis
U<-t(XUs) %*% r
if( model == "binomial" ) {
CovS <- mean(pis*(1-pis))*(t(Xgb) %*% Xgb)
} else {
CovS <- var(r)*(t(Xgb) %*% Xgb)
}
# CovS<-matrix(0, nrow=k, ncol=k)
# for(i in 1:n)
# CovS<-CovS + XUs[i,] %*% t(XUs[i,])
}
svd.CovS<-svd(CovS)
CovSsqrt<-svd.CovS$u %*% diag(sqrt(svd.CovS$d))
##observed statistics
Ts=rep(NA,length(pow))
for (j in 1:length(pow)){
if (pow[j]<Inf) Ts[j] = sum(U^pow[j]) else Ts[j] = max(abs(U))
}
## cat("statistic calculated","\n")
## simulation based
pPerm0 = rep(NA,length(pow))
T0s = numeric(n.perm)
s <- sample(1:10^5,1)
for (j in 1:length(pow)){
set.seed(s) # to ensure the same samples are drawn for each pow
for (b in 1:n.perm){
U00<-rnorm(k, 0, 1)
U0<-CovSsqrt %*% U00
# r0 <- sample(r, length(r))
# U0 <- as.vector(t(XUs) %*% r0)
if (pow[j] < Inf){ T0s[b] = sum( U0^pow[j]) }
if (pow[j] == Inf) {T0s[b] = max(abs(U0)) }
}
pPerm0[j] = sum(abs(Ts[j])<=abs(T0s)) / n.perm
P0s = ( (n.perm-rank(abs(T0s))) + 1 )/(n.perm)
if (j==1) minp0=P0s else minp0[which(minp0>P0s)]=P0s[which(minp0>P0s)]
}
# cat("P0s caculated","\n")
Paspu<-(sum(minp0<=min(pPerm0))+1)/(n.perm+1)
pvs <- c(pPerm0, Paspu)
Ts <- c(Ts, min(pPerm0))
names(Ts) <- c(paste("SPU", pow, sep=""), "aSPU")
names(pvs) = names(Ts)
list(Ts = Ts, pvs = pvs)
}
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