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## Variance-weighted adaptive Sum of powered score (SPUw) test; using bootstrapping to get the p-values
##
## It gives the p-values of the SPUw test and aSPUw test based on based on the permutation of residuals.
##
## @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 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 <- aSPUW(exdat$Y, exdat$X, pow = c(1:8, Inf), n.perm = 1000)
## out
##
## @seealso \code{\link{aSPU}}, \code{\link{aSPUperm2}}, \code{\link{aSPUboot}}, \code{\link{aSPUboot2}}
aSPUwboot2 <- 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)
if (is.null(cov)){
## NO nuisance parameters:
##cov of the score stats:
XUs <- Xg <- X
Xbar<-apply(Xg, 2, mean)
subtract<-function(x, y) { x - y }
Xgb=t(apply(Xg, 1, subtract, Xbar))
r=Y-mean(Y)
yresids <- Y-mean(Y)
U<-as.vector( t(Xg) %*% r)
if( model == "binomial" ) {
CovS <- mean(Y)*(1-mean(Y))*(t(Xgb) %*% Xgb)
} else {
CovS <- var(Y)*(t(Xgb) %*% Xgb)
}
} else {
## with nuisance parameters:
tdat1<-data.frame(trait=Y, cov)
fit1<-glm(trait~.,family=model,data=tdat1)
pis<-fitted.values(fit1)
yresids <- Y - pis
XUs<-matrix(0, nrow=n, ncol=k)
for(i in 1:k){
tdat2<-data.frame(X1=X[,i], cov)
fit2<-glm(X1~.,data=tdat2)
X1mus<-fitted.values(fit2)
XUs[, i] <- (X[,i] - X1mus)
}
U <- t(XUs) %*% (Y - pis)
if( model == "binomial" ) {
CovS <- mean(pis*(1-pis))*(t(XUs) %*% XUs)
} else {
CovS <- var(yresids)*(t(XUs) %*% XUs)
}
}
Vs<-diag(CovS)
diagSDs<-ifelse(Vs>1e-20, sqrt(Vs), 1e-10)
# test stat's:
Ts <- rep(0, length(pow))
for(j in 1:length(pow)){
if (pow[j] < Inf)
Ts[j] = sum((U/diagSDs)^pow[j]) else Ts[j] = max(abs(U/diagSDs))
}
# bootstrap:
T0s = matrix(0, nrow=n.perm, ncol=length(pow))
Y0 = Y
for(b in 1:n.perm){
if (is.null(cov)) {
Y0 <- sample(Y, length(Y))
#########Null score vector:
U0 <- t(Xg) %*% (Y0-mean(Y0))
} else {
## with nuisance parameters:
if ( model == "gaussian") {
Y0 <- pis + sample(yresids, n, replace = F )
tdat0<-data.frame(trait=Y0, cov)
fit0<-glm(trait~., data=tdat0)
yfits0<-fitted.values(fit0)
U0<-t(XUs) %*% (Y0 - yfits0)
} else {
## with nuisance parameters:
for(i in 1:n) Y0[i] <- sample(c(1,0), 1, prob=c(pis[i], 1-pis[i]) )
tdat0<-data.frame(trait=Y0, cov)
fit0<-glm(trait~., family=model, data=tdat0)
yfits0<-fitted.values(fit0)
U0<-t(XUs) %*% (Y0 - yfits0)
}
}
## test stat's:
for(j in 1:length(pow))
if (pow[j] < Inf)
T0s[b, j] = sum((U0/diagSDs)^pow[j]) else T0s[b, j] = max(abs(U0/diagSDs))
}
pPerm0 = rep(NA,length(pow))
for ( j in 1:length(pow))
{
pPerm0[j] = sum(abs(Ts[j])<=abs(T0s[,j])) / n.perm
P0s = ( ( n.perm - rank( abs(T0s[,j]) ) ) + 1 ) / (n.perm)
if (j == 1 ) minp0 = P0s else minp0[which(minp0>P0s)] = P0s[which(minp0>P0s)]
}
Paspu <- (sum(minp0 <= min(pPerm0)) + 1) / (n.perm+1)
pvs <- c(pPerm0, Paspu)
Ts <- c(Ts, min(pPerm0))
names(Ts) <- c(paste("SPUw", pow, sep=""), "aSPUw")
names(pvs) = names(Ts)
list(Ts = Ts, pvs = pvs)
}
aSPUwboot <- 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)
if (is.null(cov)){
## NO nuisance parameters:
XUs <- Xg <- X
Xbar<-apply(Xg, 2, mean)
subtract<-function(x, y) { x - y }
Xgb=t(apply(Xg, 1, subtract, Xbar))
r=Y-mean(Y)
U<-as.vector( t(Xg) %*% r)
##cov of the score stats:
if( model == "binomial" ) {
CovS <- mean(Y)*(1-mean(Y))*(t(Xgb) %*% Xgb)
} else {
CovS <- var(Y)*(t(Xgb) %*% Xgb)
}
} else {
## with nuisance parameters:
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)
yresids <- Y - pis
XUs<-matrix(0, nrow=n, ncol=k)
for(i in 1:k){
tdat2<-data.frame(X1=X[,i], cov)
fit2<-glm(X1~.,data=tdat2)
X1mus<-fitted.values(fit2)
XUs[, i] <- (X[,i] - X1mus)
}
U <- t(XUs) %*% (Y - pis)
if( model == "binomial" ) {
CovS <- mean(pis*(1-pis))*(t(XUs) %*% XUs)
} else {
CovS <- var(yresids)*(t(XUs) %*% XUs)
}
}
Vs<-diag(CovS)
diagSDs<-ifelse(Vs>1e-20, sqrt(Vs), 1e-10)
# svd.CovS<-svd(CovS)
# CovSsqrt<-svd.CovS$u %*% diag(sqrt(svd.CovS$d))
# test stat's:
Ts<-rep(0, length(pow))
for(j in 1:length(pow)){
if (pow[j] < Inf)
Ts[j] = sum((U/diagSDs)^pow[j]) else Ts[j] = max(abs(U/diagSDs))
# VarTs[j] = var(Upow)
}
# permutations:
pPerm0<-rep(0, length(pow))
T0s = numeric(n.perm)
s <- sample(1:10^5,1)
Y0 <- numeric(n)
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){
if (is.null(cov) ) {
Y0 <- sample(Y, length(Y))
## Null score vector:
U0<-t(Xg) %*% (Y0-mean(Y0))
} else {
if( model == "gaussian" ) {
Y0 <- pis + sample(fit1$residuals, n, replace = F )
tdat0 <- data.frame(trait=Y0, cov)
fit0 <- glm(trait ~., data = tdat0)
yfits0 <- fitted.values(fit0)
U0 <- t(XUs) %*% (Y0 - yfits0)
} else {
## with nuisance parameters:
for(i in 1:n) Y0[i] <- sample(c(1,0), 1, prob=c(pis[i], 1-pis[i]) )
tdat0<-data.frame(trait=Y0, cov)
fit0<-glm(trait~., family=model, data=tdat0)
yfits0<-fitted.values(fit0)
U0<-t(XUs) %*% (Y0 - yfits0)
}
}
# test stat's:
if (pow[j] < Inf) {T0s[b] = round( sum((U0/diagSDs)^pow[j]), digits=8) }
if (pow[j] == Inf) {T0s[b] = round( max(abs(U0/diagSDs)), digits=8)}
}
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("g=",g,"\n")
}
cat("P0s caculated","\n")
Paspu<-(sum(minp0<=min(pPerm0))+1)/(n.perm+1)
pvs <- round(c(pPerm0, Paspu), digits = 3)
Ts <- c(Ts, min(pPerm0))
names(Ts) <- c(paste("SPUw", pow, sep=""), "aSPUw")
names(pvs) = names(Ts)
list(Ts = Ts, pvs = pvs)
}
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