R/stat.soft.omni.R

In TFisher: Optimal Thresholding Fisher's P-Value Combination Method

#' Construct omnibus soft-thresholding Fisher's p-value combination statistic.
#' @param p - input p-values.
#' @param TAU1 - a vector of truncation parameters (=normalization parameters). Must be in non-descending order.
#' @param M - correlation matrix of the input statistics. Default = NULL assumes independence.
#' @return  omni - omnibus soft-thresholding statistic.
#' @return  pval - p-values of each soft-thresholding tests.
#' @details Let \eqn{x_{i}}, \eqn{i = 1,...,n} be a sequence of individual statistics with
#' correlation matrix M, \eqn{p_{i}} be the corresponding two-sided p-values, then the soft-thresholding statistics
#' \deqn{Soft_j = \sum_{i=1}^n -2\log(p_i/\tau_{1j})I(p_i\leq\tau_{1j})}, \eqn{j = 1,...,d}.
#' The omnibus test statistic is the minimum p-value of these soft-thresholding tests,
#' \deqn{W_o = min_j G_j(Soft_j)}, where \eqn{G_j} is the survival function of \eqn{Soft_j}.
#' @references 1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.
#'
#' @examples
#' pval = runif(20)
#' TAU1 = c(0.01, 0.05, 0.5, 1)
#' stat.soft.omni(p=pval, TAU1=TAU1)
#' M = matrix(0.3,20,20) + diag(1-0.3,20)
#' stat.soft.omni(p=pval, TAU1=TAU1, M=M)
#' @export
#' @importFrom mvtnorm pmvnorm

stat.soft.omni <- function(p, TAU1, M=NULL){
  stat.tfisher.omni(p,TAU1,TAU1,M)
}