#' The adjusted p-values for Modified Hochberg step-up FWER controlling procedure.
#'
#' The function for calculating the adjusted p-values based on original available p-values and all attaianble p-values.
#'
#' @usage
#' MHoch.p.adjust(p, p.set, alpha, make.decision)
#' @param p numeric vector of p-values (possibly with \code{\link[base]{NA}}s). Any other R is coerced by \code{\link[base]{as.numeric}}. Same as in \code{\link[stats]{p.adjust}}.
#' @param p.set a list of numeric vectors, where each vector is the vector of all attainable p-values containing the available p-value for the corresponding hypothesis..
#' @param alpha significant level used to compare with adjusted p-values to make decisions, the default value is 0.05.
#' @param make.decision logical; if \code{TRUE}, then the output include the decision rules compared adjusted p-values with significant level \eqn{\alpha}
#' @return
#' A numeric vector of the adjusted p-values (of the same length as \code{p}).
#' @seealso \code{\link{Roth.p.adjust}}, \code{\link[stats]{p.adjust}}.
#' @author Yalin Zhu
#' @references
#' Zhu, Y., & Guo, W. (2017).
#' Familywise error rate controlling procedures for discrete data
#' \emph{arXiv preprint} arXiv:1711.08147.
#'
#' Hochberg, Y. (1988).
#' A sharper Bonferroni procedure for multiple tests of significance.
#' \emph{ Biometrika}, \strong{75}: 800-803.
#' @examples
#' p <- c(pbinom(1,8,0.5),pbinom(1,5,0.75),pbinom(1,6,0.6))
#' p.set <-list(pbinom(0:8,8,0.5),pbinom(0:5,5,0.75),pbinom(0:6,6,0.6))
#' MHoch.p.adjust(p,p.set)
#' ## Compare with the traditional Hochberg adjustment
#' p.adjust(p,method = "hochberg")
#' ## Compare with the Roth adjustment
#' Roth.p.adjust(p,p.set)
#' @export
MHoch.p.adjust <- function(p,p.set, alpha = 0.05, make.decision = FALSE){
o <- order(p); ro <- order(o); m <- length(p)
sort.p <- p[o]; sort.p.set <- p.set[o]
adjP <- numeric(m); pCDF <- matrix(NA,m,m)
for (i in m:1){
for (j in i:m){
pCDF[i,j] <- max(sort.p.set[[j]][sort.p.set[[j]] <= sort.p[i]],0)
}
c <- sum(pCDF[i,i:m])
adjP[i] <- ifelse(i==m, c, min(adjP[i+1],c))
}
if (make.decision==FALSE){
return(adjP[ro])
} else{
return(list(method= "Modified Hochberg", significant.level = alpha, Result = data.frame(raw.p = p, adjust.p=adjP[ro], decision=ifelse(adjP[ro]<=alpha, "reject","accept"))))
}
}
#' The number of rejected hypotheses for Roth's step-up FWER controlling procedure.
#'
#' The function for calculating the number of rejected hypotheses (rejection region) based on original available p-values, all attaianble p-values and the given significant level.
#'
#' @usage
#' Roth.rej(p,p.set,alpha)
#' @param p numeric vector of p-values (possibly with \code{\link[base]{NA}}s). Any other R is coerced by \code{\link[base]{as.numeric}}. Same as in \code{\link[stats]{p.adjust}}.
#' @param p.set a list of numeric vectors, where each vector is the vector of all attainable p-values containing the available p-value for the corresponding hypothesis..
#' @param alpha the given significant level for Roth's procedure, the default value is 0.05.
#' @return
#' An integer value of the number of rejected hypotheses.
#' @author Yalin Zhu
#' @references
#' Roth, A. J. (1999).
#' Multiple comparison procedures for discrete test statistics.
#' \emph{Journal of statistical planning and inference}, \strong{82}: 101-117.
#'
#' Hochberg, Y. (1988).
#' A sharper Bonferroni procedure for multiple tests of significance.
#' \emph{ Biometrika}, \strong{75}: 800-803.
#' @examples
#' p <- c(pbinom(1,8,0.5),pbinom(1,5,0.75),pbinom(1,6,0.6))
#' p.set <-list(pbinom(0:8,8,0.5),pbinom(0:5,5,0.75),pbinom(0:6,6,0.6))
#' Roth.rej(p,p.set,0.05)
#' @export
Roth.rej <- function(p,p.set,alpha=0.05){
m <- length(p); minP <- sapply(p.set,min)
p_R1 <- p[minP < alpha]
Q <-Inf
for (j in seq_along(p_R1)){
if(sort(p_R1,decreasing = T)[j] < alpha/j){
Q <- j; break
}
else{next}
}
M <- c()
for (j in seq_along(p)){
M[j] <- sum(minP<alpha/j)
if (M[j]<=j){
K <- j; break
}
else {next}
}
p_RK <- if(M[K]<K) c(sort(p[minP < alpha/K],decreasing = T),rep(0,K-M[K])) else sort(p[minP < alpha/K],decreasing = T)
W <- Inf
for (j in seq_along(p_RK)){
if(max(p_RK[j],p[minP<alpha/j & minP>=alpha/K]) < alpha/j){
W <- j; break
}
else{next}
}
return(min(Q,W))
}
#' The adjusted p-values for Roth's step-up FWER controlling procedure.
#'
#' The function for calculating the adjusted p-values based on original available p-values and all attaianble p-values.
#'
#' @usage
#' Roth.p.adjust(p, p.set, digits, alpha, make.decision)
#' @param p numeric vector of p-values (possibly with \code{\link[base]{NA}}s). Any other R is coerced by \code{\link[base]{as.numeric}}. Same as in \code{\link[stats]{p.adjust}}.
#' @param p.set a list of numeric vectors, where each vector is the vector of all attainable p-values containing the available p-value for the corresponding hypothesis..
#' @param digits minimal number of significant digits for the adjusted p-values, the default value is 4, see \code{\link[base]{print.default}}.
#' @param alpha significant level used to compare with adjusted p-values to make decisions, the default value is 0.05.
#' @param make.decision logical; if \code{TRUE}, then the output include the decision rules compared adjusted p-values with significant level \eqn{\alpha}
#' @return
#' A numeric vector of the adjusted p-values (of the same length as \code{p}).
#' @seealso \code{\link{MHoch.p.adjust}}, \code{\link[stats]{p.adjust}}.
#' @author Yalin Zhu
#' @references
#' Roth, A. J. (1999).
#' Multiple comparison procedures for discrete test statistics.
#' \emph{Journal of statistical planning and inference}, \strong{82}: 101-117.
#'
#' @examples
#' p <- c(pbinom(1,8,0.5),pbinom(1,5,0.75),pbinom(1,6,0.6))
#' p.set <-list(pbinom(0:8,8,0.5),pbinom(0:5,5,0.75),pbinom(0:6,6,0.6))
#' Roth.p.adjust(p,p.set,digits=5)
#' @export
Roth.p.adjust <- function(p,p.set,digits=4, alpha = 0.05, make.decision = FALSE){
m <- length(p)
adjP <- c()
for (i in 1:m){
##### setting the accuracy as 4 digitals
init.alpha <- numeric(); eps <- 10^(-1*c(1:digits))
init.alpha[1] <- 1
while(p[i] <= init.alpha[1]/Roth.rej(p,p.set,init.alpha[1]) & init.alpha[1] <= 1){
init.alpha[1] <- init.alpha[1]-eps[1]
}
for (j in 2:digits){
init.alpha[j] <- init.alpha[j-1]+eps[j-1]
while(p[i] <=init.alpha[j]/Roth.rej(p,p.set,init.alpha[j]) ){
init.alpha[j] <- init.alpha[j]-eps[j]
}
}
adjP[i] <- init.alpha[digits]+eps[digits]
}
if (make.decision==FALSE){
return(adjP)
} else{
return(list(method= "Roth-Hochberg", significant.level = alpha, Result = data.frame(raw.p = p, adjust.p=adjP, decision=ifelse(adjP<=alpha, "reject","accept"))))
}
}
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