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#' Calculation of permutation p-value
#' @name permute_pvalue
#'
#' @description Calculates the permutation p-value for a fitted GEM. See more detail in \cite{E Petkova, T Tarpey, Z Su, and RT Ogden. Generated effect modifiers (GEMs) in randomized clinical trials. Biostatistics, (First published online: July 27, 2016). doi: 10.1093/biostatistics/kxw035.}
#'
#'
#' @param dat Data frame with first column as the treatment index, second column as the outcome, and the
#' remaining columns as the covariates design matrix. The elements of the treatment index take \eqn{K} distinct values, where \eqn{K} is the number of treatment groups.
#' The outcome has to be a continuous variable.
#' @param permuteN Number of permutation
#' @param method Choice of the criterion that the generated effect modifier optimizes. This is a string in
#' \code{c("nu","de","F")}, which corresponde to the numerator, denominator and F-statistics
#' criteria respectively. The default method is the F-statistics method.
#'
#'
#' @return \code{perm_p} Permutation p-value for the data and choosen criterior
#' @return \code{p} A vector of calculated p-value for the original and permuted data set under the choosen criterior
#'
#'
#' @examples
#' #constructing the covariance matrix
#' co <- matrix(0.2, 10, 10)
#' diag(co) <- 1
#' #simulate a data set
#' dataEx <- data_generator1(d = 0.3, R2 = 0.5, v2 = 1, n = 300,
#' co = co, beta1 = rep(1,10),inter = c(0,0))
#' #calculate the permuted p value
#' dat <- dataEx[[1]]
#' permute_pvalue(dat, permuteN = 200, method = "nu")
#' @export
permute_pvalue <- function(dat, permuteN, method = "F")
{
colnames(dat)[1] <- "trt"
K <- length(unique(dat$trt))
dat[,1] <- factor(dat[,1],labels=c(1:K))
N <- ddply(dat, .(dat$trt), nrow)[,2]
mm <- gem_fit(dat,method)
p <- mm[[3]]
for(i in 1:permuteN)
{
datt <- dat
datt[,1] <- sample(dat$trt)
mmm <- gem_fit(datt,method)
p <- c(p, mmm[[3]])
}
p_value <- sum(p[2:(1+permuteN)] <= p[1])/permuteN
return(list("perm_p"=p_value,
"p"=p))
}
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