R/ts_fwd_norm_mean.R

In yelleKneK/SMSD: Sequential Methods for Study Design

#' ts_fwd_norm_mean
#'
#' @description Modified Two stage approach to Get Fixed Width
#' Confidence Interval for the mean of normal random variables
#'
#' @param data The data for which to calculate the confidence interval.
#' A numeric vector.
#' @param d Half of the confidence interval width, must be a non-zero positive
#' value.
#' @param alpha The significance level. A value between 0 and 1.
#' @param gamma gamma
#' @param pilot Should a pilot sample be generated. True/False value.
#' default value is \code{FALSE}.
#' @param verbose Should the criterion be printed. Default is \code{FALSE}.
#' @param na.rm This parameter controls whether NA values are removed from
#' the data prior to calculation. Default is \code{TRUE}.
#'
#' @return The calculated confidence interval, the sample size, data mean,
#' and an indicator of if the criterion was satisfied.
#'
#' @author Bhargab Chattopadhyay \email{Bhargab@iiitvadodara.ac.in},
#' Neetu Shah \email{201451015@iiitvadodara.ac.in}, Ken Kelley \email{kkelley@nd.edu}
#'
#' @references
#' Mukhopadhyay, N., \& de Silva, Basil M. (2009). \emph{Sequential Methods and Their Applications}. New York: CRC Press.
#'
#' @export ts_fwd_norm_mean
#'
#' @examples
#' pilot_ss <- ts_fwd_norm_mean(alpha=0.01, d=0.5, gamma=0.6, pilot=TRUE)
#' \dontrun{
#' SLS <- rnorm(pilot_ss)
#' }
#' SLS <- rnorm(100)
#' ts_fwd_norm_mean(data=SLS, d=0.5, alpha=0.01, pilot=FALSE)
ts_fwd_norm_mean <- function(data, d, alpha, gamma, pilot=FALSE,
                             verbose=FALSE, na.rm=TRUE)
{
  if(missing(alpha)){
    stop("You must specify \'alpha\'")
  }

  if(!missing(alpha)){
    if(alpha>1 & alpha<0) stop("alpha should be between 0 and 1")
  }

  if(missing(d)) {
    stop("You must specify \'d\'")
  }

  if(!missing(d)){
    if(d<0){
      stop("d should be a non-zero positive value")
    }
  }

  if(missing(gamma)){
    gamma <- 1
  }

  if(pilot==FALSE)
  {
    if (!is.data.frame(data) && !is.matrix(data) && !is.vector(data)){
      stop("The argument 'data' must be a data.frame
           or matrix with one column")
    }

    if (dim(data)[2] != 1 && !is.null(data) && !is.vector(data)){
      stop("The argument 'data' must have only one column,
           or be 'NULL' for pilot = TRUE")
    }


    if(is.data.frame(data)) {
      data <- as.vector(data)
    }
    if(na.rm){
      data <-  data[!is.na( data)]
    }
    n <- length(data)

    m <- max(2,ceiling((qnorm(1-alpha)/d)^(2/(1+gamma))))

    optimal_N <- max(m,
                     ceiling((stats::qt(1-alpha,
                                        m-1)^2*stats::var(data))/d^2))

    ci <- mean(data)+c(-1,1)*d    # This is the fixed width confidence interval.

    if(verbose==FALSE){
      Outcome <- rbind(list("Confidence Interval"=ci[1],
                            ci[2], N=n, mean=mean(data),
                            "Is.Satisfied?"=(n >= optimal_N),
                            Stage=1))
    }
    if(verbose==TRUE){
      Outcome <- rbind(list("Confidence Interval"=ci[1],
                            ci[2], N=n, mean=mean(data),
                            Criterion=optimal_N,
                            Is.Satisfied=n >= optimal_N,
                            Stage=1))
    }
    if((n >= optimal_N)==FALSE) print(Outcome)
    while((length(data) >= optimal_N)==FALSE){
      cat(optimal_N-length(data)," more are needed ")
      obs <- as.integer(strsplit(readline(), " ")[[1]])
      data <- c(data,obs)
      if(length(data)==optimal_N){
        ci <- mean(data)+c(-1,1)*d    # This is the fixed width confidence interval.
        Outcome <- rbind(list("Confidence Interval"=ci[1],
                              ci[2], N=length(data),
                              mean=mean(data), Stage=2))
      }else if(length(data)> optimal_N){
        ci <- mean(data)+c(-1,1)*stats::qt(1-alpha/2,
                                           length(data)-1)*
          sqrt(stats::var(data)/length(data))
        Outcome <- rbind(list("Confidence Interval"=ci[1],
                              ci[2], N=length(data),
                              mean=mean(data), Stage=2))
      }
    }
  }



  if(pilot==TRUE)
  {
    Outcome <- c(pilot_ss=max(2,ceiling((stats::qnorm(1-alpha)/d)^(2/(1+gamma)))+1))
  }

  return(Outcome)
}