R/Mee_asymptotic_score_CI_2x2.R

In ocbe-uio/contingencytables: Statistical Analysis of Contingency Tables

#' @title The Mee asymptotic score confidence interval for the difference between probabilities
#' @description The Mee asymptotic score confidence interval for the difference between probabilities
#' @description Described in Chapter 4 "The 2x2 Table"
#' @param n the observed counts (a 2x2 matrix)
#' @param alpha the nominal level, e.g. 0.05 for 95% CIs
#' @examples
#' # An RCT of high vs standard dose of epinephrine (Perondi et al., 2004):
#' Mee_asymptotic_score_CI_2x2(perondi_2004)
#'
#' # The association between CHRNA4 genotype and XFS (Ritland et al., 2007):
#' Mee_asymptotic_score_CI_2x2(ritland_2007)
#' @export
#' @return An object of the [contingencytables_result] class,
#' basically a subclass of [base::list()]. Use the [utils::str()] function
#' to see the specific elements returned.
Mee_asymptotic_score_CI_2x2 <- function(n, alpha = 0.05) {
  validateArguments(mget(ls()))

  n11 <- n[1, 1]
  n21 <- n[2, 1]
  n1p <- n[1, 1] + n[1, 2]
  n2p <- n[2, 1] + n[2, 2]

  # Estimates of the two probabilities of success
  pi1hat <- n[1, 1] / n1p
  pi2hat <- n[2, 1] / n2p

  # Estimate of the difference between probabilities (deltahat)
  estimate <- pi1hat - pi2hat

  # Options for Matlab's fzero command
  tol <- 0.0000001
  delta0 <- -0.99999
  delta1 <- 0.99999

  # Lower CI limit
  L <- tryCatch(
    uniroot(
      calculate_limit_lower, c(delta0, estimate),
      n11 = n11, n21 = n21, n1p = n1p, n2p = n2p,
      pi1hat = pi1hat, pi2hat = pi2hat, alpha = alpha, tol = tol
    )$root,
    error = function(e) -1
  )

  # Upper CI limit
  U <- tryCatch(
    uniroot(
      calculate_limit_upper, c(estimate, delta1),
      n11 = n11, n21 = n21, n1p = n1p, n2p = n2p,
      pi1hat = pi1hat, pi2hat = pi2hat, alpha = alpha, tol = tol
    )$root,
    error = function(e) 1
  )

  return(
    contingencytables_result(
      list("lower" = L, "upper" = U, "estimate" = estimate),
      sprintf(
        "Mee asymptotic score CI: estimate = %6.4f (%g%% CI %6.4f to %6.4f)",
        estimate, 100 * (1 - alpha), L, U
      )
    )
  )
}