R/TypeTwo.R

In MatheMax/OptReSample: Computing Optimal Adaptive Designs

#' Compute the type II error
#'
#' \code{type_two} computes the type II error approximately if the \code{c_2}-function and the \code{n_2}-function
#' are approximated via a set of splines.
#'
#' Note that nodes, c2 and n2 have to be of the same length.
#'
#' @param parameters Parameters (alpha, power, standardized effect) whith which you want to build your design
#' @param cf Boundary for stopping for futility after the first stage
#' @param ce Boundary for stopping for efficacy after the first stage
#' @param nodes Nodes for the stage two functions
#' @param c2 c_2-values that correspond to \code{nodes}
#' @param n1 First stage sample size
#' @param n2 n_2-values that correspond to \code{nodes}
#'
#' @export



type_two <- function(parameters, cf, ce, nodes, c2, n1, n2){
  f <- splinefun(nodes, c2)
  g <- splinefun(nodes, n2)
  N=12
  h = (ce - cf) / N
  x = seq(cf,ce,h)
  alpha=c(1,rep(2,(N-1)),1)

  # w = ( x | alpha )
  tt <- function(w){
    w[2] * pnorm( f(w[1]) - sqrt(abs(g(w[1])))  * parameters$mu ) * dnorm( w[1] - sqrt(abs(n1))  * parameters$mu )
  }

  y <- apply(cbind(x,alpha), 1, tt)
  p <- (h/2) * sum(y)
  p <- p + pnorm( cf - sqrt(abs(n1)) * parameters$mu )
  return(p)
}