R/MFBoot.r

In ABS-dev/MF: Mitigated Fraction

#' @description Estimates bootstrap confidence intervals for the mitigated
#'   fraction.
#' @details Resamples the data and produces bootstrap confidence intervals.
#'   Equal tailed intervals are estimated by the percentile method. Highest
#'   density intervals are estimated by selecting the shortest of all possible
#'   intervals. For BCa intervals, see Efron and Tibshirani section 14.3.
#' @title Bootstrap MF CI
#' @param formula Formula of the form \code{y ~ x}, where y is a continuous
#'   response and x is a factor with two levels.
#' @param data Data frame
#' @param compare Text vector stating the factor levels - \code{compare[1]} is
#'   the control or reference group to which \code{compare[2]} is compared
#' @param b Number of bootstrap samples to take with each cycle
#' @param B Number of cycles, giving the total number of samples = B * b
#' @param alpha Complement of the confidence level
#' @param hpd Estimate highest density intervals?
#' @param bca Estimate BCa intervals?
#' @param return.boot Save the bootstrap sample of the MF statistic?
#' @param trace.it Verbose tracking of the cycles?
#' @param seed to initialize random number generator for reproducibility. Passed
#'   to \code{set.seed}.
#' @return a \code{\link{mfboot-class}} data object
#' @seealso \code{\link{mfboot-class}}
#' @references Siev D. (2005). An estimator of intervention effect on disease
#'   severity. \emph{Journal of Modern Applied Statistical Methods.}
#'   \bold{4:500--508} \cr \cr Efron B, Tibshirani RJ. \emph{An Introduction to
#'   the Bootstrap.} Chapman and Hall, New York, 1993.
#' @author \link{MF-package}
#' @examples
#'
#' MFBoot(lesion~group, calflung, seed = 12345)
#'
#' # 10000 bootstrap samples
#' # 95% confidence interval
#' # Seed = 12345
#' #
#' # Comparing vac to con
#' # observed median lower  upper
#' # Equal Tailed        0.44 0.4496 0.152 0.7088
#' # Highest Density     0.44 0.4496 0.152 0.7088
#' @importFrom stats quantile median model.frame pnorm qnorm
#' @export
MFBoot <- function(formula, data, compare = c("con", "vac"), b = 100, B = 100,
                   alpha = 0.05, hpd = TRUE, bca = FALSE, return.boot = FALSE,
                   trace.it = FALSE, seed = sample(1:100000, 1)) {
  # bootstrap confidence intervals for MF
  # 11/17/99 initial coding
  # 2/24/04 added BC.a interval
  # 5/25/10 added empirical HPD interval
  # takes b bootstrap samples B times, so nboot = B * b
  # 10/1/2018 add seed utility

  # set seed
  set.seed(seed)

  A <- data.frame(model.frame(formula = formula, data = data))
  resp <- A[, 1]
  tx <- A[, 2]
  x <- resp[tx == compare[1]]
  y <- resp[tx == compare[2]]

  # shortcircuit if complete separation
  if (range(x)[1] < range(y)[1]) {
    lowtx <- x
    hitx <- y
  } else {
    lowtx <- y
    hitx <- x
  }

  if (max(lowtx) < min(hitx)) {
    message("Complete separation observed. MF is 1.0 with no c.i.")
    return()
  }

  rng <- "Mersenne-Twister"
  RNGkind(rng)
  nboot <- b * B
  n.x <- length(x)
  n.y <- length(y)
  w <- function(xy, n.x) {
    sum(rank(xy)[1:n.x])
  }
  W <- rep(NA, b * B)
  for (i in 1:B) {
    x.b <- matrix(sample(x, size = b * n.x, replace = TRUE), b, n.x)
    y.b <- matrix(sample(y, size = b * n.y, replace = TRUE), b, n.y)
    W[(i - 1) * b + (1:b)] <- apply(cbind(x.b, y.b), 1, w, n.x)
    if (trace.it) {
      cat("bootstrap samples", (i - 1) * b + 1, "to",
          (i - 1) * b + b, "\n")
    }
  }
  MF <- (2 * W - n.x * (1 + n.x + n.y)) / (n.x * n.y)
  mf <- (2 * w(c(x, y), n.x) - n.x * (1 + n.x + n.y)) / (n.x * n.y)
  qprob <- c(0.5, alpha / 2, 1 - alpha / 2)
  qmf <- quantile(MF, prob = qprob)
  stat <- matrix(c(mf, qmf), 1, 4,
                 dimnames = list(c("Equal Tailed"),
                                 c("observed", "median", "lower", "upper")))
  if (hpd) {
    hpdmf <- emp_hpd(MF, alpha = alpha)
    stat <- rbind(stat, "Highest Density" = c(mf, median(MF), hpdmf))
  }
  if (bca) {
    z0 <- qnorm(sum(MF < mf) / (b * B))
    xy <- c(x, y)
    nx.i <- rep(n.x - (1:0), c(n.x, n.y))
    ny.i <- rep(n.y - (0:1), c(n.x, n.y))
    theta <- rep(NA, n.x + n.y)
    for (i in 1:(n.x + n.y)) {
      theta[i] <- (2 * w(xy[-i], nx.i[i]) - nx.i[i] *
                     (1 + nx.i[i] + ny.i[i])) / (nx.i[i] * ny.i[i])
    }
    theta.hat <- mean(theta)
    acc <- sum((theta.hat - theta)^3) / (6 * sum((theta.hat - theta)^2)^(3 / 2))
    z1 <- qnorm(alpha / 2)
    z2 <- qnorm(1 - alpha / 2)
    a1 <- pnorm(z0 + (z0 + z1) / (1 - acc * (z0 + z1)))
    a2 <- pnorm(z0 + (z0 + z2) / (1 - acc * (z0 + z2)))
    a5 <- pnorm(z0 + (z0 + 0) / (1 - acc * (z0 + 0)))
    qprob <- c(a5, a1, a2)
    stuff <- c(acc, z0, a1, a2)
    names(stuff) <- c("acc", "z0", "a1", "a2")
    if (trace.it) {
      print(round(stuff, 4))
    }
    qmf <- quantile(MF, prob = qprob)
    stat <- rbind(stat, "BC.a" = c(mf, qmf))
  }
  out <- mfboot$new(stat = stat, nboot = nboot, alpha = alpha, seed = seed,
                    rng = rng, compare = compare, sample = MF)

  return(out)
}