# R/p.tfisher.omni.R In TFisher: Optimal Thresholding Fisher's P-Value Combination Method

#### Documented in p.tfisher.omni

```#' CDF of omnibus thresholding Fisher's p-value combination statistic under the null hypothesis.
#' @param q - quantile, could be a vector.
#' @param n - dimension parameter, i.e. the number of p-values to be combined.
#' @param TAU1 - a vector of truncation parameters. Must be in non-descending order.
#' @param TAU2 - a vector of normalization parameters. Must be in non-descending order.
#' @param M - correlation matrix of the input statistics. Default = NULL assumes independence.
#' @param P0 - a vector of point masses of TFisher statistics. Default = NULL.
#' @return  The left-tail probability of the null distribution of omnibus thresholding Fisher's p-value combination statistic.
#' @seealso \code{\link{stat.tfisher.omni}} for the definition of the statistic.
#' @references 1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.
#' @examples
#' q = 0.05
#' n = 20
#' TAU1 = c(0.01, 0.05, 0.5, 1)
#' TAU2 = c(0.1, 0.2, 0.5, 1)
#' M = matrix(0.3,20,20) + diag(1-0.3,20)
#' p.tfisher.omni(q=q, n=n, TAU1=TAU1, TAU2=TAU2, M=M)
#' @export
#' @importFrom mvtnorm pmvnorm
#' @importFrom Matrix nearPD
#'
p.tfisher.omni <- function(q, n, TAU1, TAU2, M=NULL,P0=NULL){
if(is.null(M)){
E = 2*n*TAU1*(1+log(TAU2/TAU1))
nn = length(TAU1)

minTAU = pmin(matrix(TAU1,nn,nn), t(matrix(TAU1,nn,nn)))
part1 = 4*n*minTAU
part2 = part1*(1+log(matrix(TAU2,nn,nn)/minTAU))*(1+log(t(matrix(TAU2,nn,nn))/minTAU))
part3 = 4*n*matrix(TAU1,nn,nn)*t(matrix(TAU1,nn,nn))*(1+log(matrix(TAU2,nn,nn)/matrix(TAU1,nn,nn)))*(1+log(t(matrix(TAU2,nn,nn))/t(matrix(TAU1,nn,nn))))
COV = part1 + part2 - part3

COV[lower.tri(COV)] = t(COV)[lower.tri(COV)]
result = rep(NA, length(q))
for(i in 1:length(q)){
Q = mapply(function(x,y)q.tfisher(1-q, n, x,y),TAU1,TAU2)
result[i] = 1-pmvnorm(lower=-Inf,upper=Q,mean=E,sigma=COV,abseps=1e-6)[1]
}

return(result)
}else{
p = length(TAU1)
if(is.null(P0)){
#truncation parameter
bound = qnorm(1-TAU1/2)
P0 = sapply(1:p,function(x)pmvnorm(lower=-rep(bound[x],n),upper=rep(bound[x],n),sigma=M)[1])
}
if(1-min(P0)<q){
return("q is too large, impossible to obtain")
}else{
id = which(1-P0<q)
if(length(id>0)){
TAU1 = TAU1[-id]; TAU2 = TAU2[-id]
}

E = 2*n*TAU1*(1+log(TAU2/TAU1))

COV = getTFisherCovM(M, TAU1, TAU2)
if(any(eigen(COV)\$value<0)){
COV = as.matrix(nearPD(COV)\$mat)
}

#Q = mapply(function(x,y)q.tfisher(1-q, n, x,y, M),TAU1,TAU2)
Q = mapply(function(x,y)q.tfisher_N(1-q, n, x,y, M),TAU1,TAU2)
result = 1-pmvnorm(lower=-Inf,upper=Q,mean=E,sigma=COV,abseps=1e-6)[1]
return(result)
}
}
}
```

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TFisher documentation built on March 21, 2018, 5:11 p.m.