R/scprt.R

In gsMAMS: Group Sequential Designs of Multi-Arm Multi-Stage Trials

#' @title  Efficacy and Futility boundary values
#' @description This function calculates the upper and lower bound values for MAMS trial.
#' @param alpha numeric Type I error.
#' @param k numeric Number of treatment arms.
#' @param frac numeric Vector of information time at each look.
#' @return A list of three elements: critical.value, lshape(Futility), and ushape(Efficacy).
#' @examples
#' scprt(alpha = 0.05, k = 3, frac = c(1 / 3, 2 / 3, 1))
#' @keywords internal
#' @noRd


scprt <- function(alpha, k, frac) {
  r <- 1
  J <- length(frac)
  Sigma <- matrix((1 / (1 + r)), k, k)
  diag(Sigma) <- 1
  if (J >= 10) stop("Limit the maximum number of stages to ten")
  root <- function(c) {
    int <- mvtnorm::pmvnorm(lower = rep(-Inf, k), upper = rep(c, k), mean = rep(0, k), sigma = Sigma)[1]
    alpha - (1 - int)
  }
  c <- round(stats::uniroot(root, lower = 0, upper = 999)$root, 3)
  a <- c(1.645, 2.109, 2.645, 2.953, 3.166, 3.327, 3.456, 3.562, 3.652, 3.729)
  a <- a[J]
  l <- round((c * frac - sqrt(2 * a * frac * (1 - frac))) / sqrt(frac), 3)
  u <- round((c * frac + sqrt(2 * a * frac * (1 - frac))) / sqrt(frac), 3)
  l[length(frac)] <- u[length(frac)]
  ans <- list(critical.value = c, lshape = l, ushape = u)
  return(ans)
}