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#' Pathway based Sum of Powered Score tests (SPUsPath) and adaptive SPUpath (aSPUsPath) test for single trait - pathway association with GWAS summary statistics.
#'
#' It gives p-values of the SPUsPath tests and aSPUsPath test with GWAS summary statistics.
#'
#' @param Zs Z-scores for each SNPs. It could be P-values if the Ps option is TRUE.
#'
#' @param corSNP Correlation matirx of the SNPs to be tested; estimated from a
#' reference panel (based on the same set of the reference alleles as
#' used in calculating Z-scores).
#'
#' @param snp.info SNP information matrix, the 1st column is SNP id, 2nd column is chromosome #, 3rd column indicates SNP location.
#'
#' @param gene.info GENE information matrix, The 1st column is GENE id, 2nd column is chromosome #, 3rd and 4th column indicate start and end positions of the gene.
#'
#' @param pow SNP specific power(gamma values) used in SPUpath test.
#'
#' @param pow2 GENE specific power(gamma values) used in SPUpath test.
#'
#' @param n.perm number of permutations.
#'
#' @param Ps TRUE if input is p-value, FALSE if input is Z-scores. The default is FALSE.
#'
#' @param prune if it is TRUE, do pruing before the test using pruneSNP function.
#'
#' @return P-values for SPUMpath tests and aSPUMpath test.
#'
#' @author Il-Youp Kwak and Wei Pan
#'
#' @references
#' Il-Youp Kwak, Wei Pan (2015)
#' Adaptive Gene- and Pathway-Trait Association Testing with GWAS Summary Statistics,
#' Bioinformatics, 32(8):1178-1184
#'
#' @examples
#' data(kegg9)
#'
#' # p-values of SPUpath and aSPUpath tests.
#' out.a <- aSPUsPath(kegg9$nP, corSNP = kegg9$ldmatrix, pow=c(1:8, Inf),
#' pow2 = c(1,2,4,8),
#' snp.info=kegg9$snp.info, gene.info = kegg9$gene.info,
#' n.perm=5, Ps = TRUE)
#'
#' out.a
#'
#' @seealso \code{\link{aSPUs}}
#'
#' @export
aSPUsPath <- function(Zs, corSNP, pow=c(1,2,4,8, Inf),
pow2 = c(1,2,4,8),
snp.info, gene.info, n.perm=1000,
Ps = FALSE, prune=TRUE) {
if(prune== TRUE) {
pr <- pruneSNP(corSNP)
if( length(pr$to.erase) > 0 ) {
Zs <- Zs[-pr$to.erase]
corSNP <- corSNP[-pr$to.erase, -pr$to.erase]
snp.info <- snp.info[ snp.info[,1] %in% names(Zs), ]
}
}
if( length(Zs) <= 1 ) {
stop("less than 1 SNP.")
}
if ( !( length(Zs) == dim(corSNP)[1] & dim(corSNP)[2] == dim(corSNP)[1] ) ) {
stop("dimension do not match. Check dimension of Zs and corSNP.")
}
ko <- length(Zs)
n.gene <- nrow(gene.info)
GL <- list(0)
GLch <- NULL
# GL.CovSsqrt <- list(0)
i = 1
for(g in 1:n.gene) { # g = 1
snpTF <- ( snp.info[,2] == gene.info[g,2] &
gene.info[g,3] <= as.numeric(snp.info[,3]) &
gene.info[g,4] >= as.numeric(snp.info[,3]) )
if( sum(snpTF) != 0){
GL[[i]] <- which(snpTF)
GLch <- c(GLch, gene.info[g,2])
i = i + 1
}
}
chrs <- unique(GLch)
CH <- list(0)
CH.CovSsqrt <- list(0)
for( i in 1:length(chrs) ) { # i = 2
c = chrs[i]
CH[[i]] <- unlist(GL[which( GLch == c )])
Covtemp <- corSNP[CH[[i]], CH[[i]]]
eS <- eigen(Covtemp, symmetric = TRUE)
ev <- eS$values
k1 <- length(ev)
CH.CovSsqrt[[i]] <- eS$vectors %*% diag(sqrt(pmax(ev, 0)), k1)
}
# for( i in 1:length(chrs) ) { # c = 16
# c = chrs[i]
# CH[[c]] <- unlist(GL[which( GLch == c )])
# }
Zs = Zs[unlist(GL)]
nSNPs0=unlist(lapply(GL,length))
k <- length(Zs)
if(Ps == TRUE)
Zs <- qnorm(1 - Zs/2)
U <- Zs
nGenes=length(nSNPs0)
TsUnnorm<-Ts<-StdTs<-rep(0, length(pow)*nGenes)
for(j in 1:length(pow))
for(iGene in 1:nGenes){
if (iGene==1) SNPstart=1 else SNPstart=sum(nSNPs0[1:(iGene-1)])+1
indx=(SNPstart:(SNPstart+nSNPs0[iGene]-1))
if (pow[j] < Inf){
a= (sum(U[indx]^pow[j]))
TsUnnorm[(j-1)*nGenes+iGene] = a
Ts[(j-1)*nGenes+iGene] = sign(a)*((abs(a)) ^(1/pow[j]))
StdTs[(j-1)*nGenes+iGene] = sign(a)*((abs(a)/nSNPs0[iGene]) ^(1/pow[j]))
# (-1)^(1/3)=NaN!
#Ts[(j-1)*nGenes+iGene] = (sum(U[indx]^pow[j]))^(1/pow[j])
}
else {
TsUnnorm[(j-1)*nGenes+iGene] = Ts[(j-1)*nGenes+iGene] = StdTs[(j-1)*nGenes+iGene] =max(abs(U[indx]))
}
}
## Permutations:
T0sUnnorm=T0s = StdT0s = matrix(0, nrow=n.perm, ncol=length(pow)*nGenes)
for(b in 1:n.perm){
U00<-rnorm(k, 0, 1)
U0 <- NULL;
for( ss in 1:length(CH)) { # ss = 21
U0 <- c(U0, CH.CovSsqrt[[ss]] %*% U00[CH[[ss]]] )
}
if(Ps == TRUE)
U0 <- abs(U0)
## test stat's:
for(j in 1:length(pow))
for(iGene in 1:nGenes){
if (iGene==1) SNPstart=1 else SNPstart=sum(nSNPs0[1:(iGene-1)])+1
indx=(SNPstart:(SNPstart+nSNPs0[iGene]-1))
if (pow[j] < Inf){
a = (sum(U0[indx]^pow[j]))
StdT0s[b, (j-1)*nGenes+iGene] = sign(a)*((abs(a)/nSNPs0[iGene]) ^(1/pow[j]))
}
else StdT0s[b, (j-1)*nGenes+iGene] = max(abs(U0[indx]))
}
}
#combine gene-level stats to obtain pathway-lelev stats:
Ts2<-rep(0, length(pow)*length(pow2))
T0s2<-matrix(0, nrow=n.perm, ncol=length(pow)*length(pow2))
for(j2 in 1:length(pow2)){
for(j in 1:length(pow)){
if(pow2[j2] < Inf) {
Ts2[(j2-1)*length(pow) +j] = sum(StdTs[((j-1)*nGenes+1):(j*nGenes)]^pow2[j2])
for(b in 1:n.perm){
T0s2[b, (j2-1)*length(pow) +j] = sum(StdT0s[b, ((j-1)*nGenes+1):(j*nGenes)]^pow2[j2])
}
} else {
Ts2[(j2-1)*length(pow) +j] = max(StdTs[((j-1)*nGenes+1):(j*nGenes)])
for(b in 1:n.perm){
T0s2[b, (j2-1)*length(pow) +j] = max(StdT0s[b, ((j-1)*nGenes+1):(j*nGenes)])
}
}
}
}
# permutation-based p-values:
pPerm2 = rep(NA, length(pow)*length(pow2));
pvs = NULL;
for(j in 1:(length(pow)*length(pow2))) {
pPerm2[j] = sum( abs(Ts2[j]) < abs(T0s2[,j]))/n.perm
}
P0s2 = PermPvs(T0s2)
minP0s2 = apply(P0s2, 1, min)
minP2 = sum( min(pPerm2) > minP0s2 )/n.perm
minP2s <- rep(NA, length(pow2))
for(j2 in 1:length(pow2)){
minP0s2 = apply(P0s2[, ((j2-1)*length(pow)+1):(j2*length(pow))], 1, min)
minP2s[j2] = sum( min(pPerm2[((j2-1)*length(pow)+1):(j2*length(pow))]) > minP0s2 )/n.perm
}
pvs=c(pPerm2, minP2)
nmvec <- NULL;
for(ii in pow2) {
for(jj in pow) {
nmvec <- c(nmvec, paste("SPUsPath",jj,",",ii,sep=""))
}
}
nmvec <- c(nmvec, "aSPUsPath")
names(pvs) <- nmvec
pvs
}
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